7 ms·

Singularities in Space-Time Prove Hard to Kill

38 points by nsoonhui 1y ago

scotty79 1y ago
My non-canonical and possibly wrong view of black hole singularities is that they can form in finite time (sort of) only in their own frame of reference but in any other frame they require infinite time so from our point of view no singularity ever formed and ever will from. And in practice, in this infinite time something might disrupt their collapse, like getting hit with similarly massive amount of anti-matter an turning into photons which might destabilize the whole process and let them get out in massively energetic event similar to Big Bang. Which I believe was the case with ours, so no white-hole singularity either. This view is dismissed by physicist because in GR there's no way to unambiguously define simultaneity so they don't event attempt to consider what's "before" and what's "after" regarding remote events in strong gravitational fields so saying that singularity forming is "after" everything else that ever happens in the universe is a hard sell.
- wizzwizz4 1y ago
  A "matter black hole" and an "antimatter black hole" will combine to form a larger black hole. GR doesn't have a well-defined notion of simultaneity, but it does have a notion of before and after.
  - scotty79 1y ago
    > A "matter black hole" and an "antimatter black hole" will combine to form a larger black hole. I think they'll annihilate forming photon black hole, which might be unstable. > but it does have a notion of before and after. Was forming of any singularity before present day on Earth?
  - fguerraz 1y ago
    With the current theories, I don't think it matters (pun intended) if a matter and anti-matter black holes merge. E=mc2 (+change) In normal space that would have liberated a huge amount of energy, but in sufficiently curved space, the energy stays inside the back hole, mass is conserved, nothing to see (literally).
    - scotty79 1y ago
      I think the question is, will the spacetime stay sufficiently curved if it's now curved by pure energy whizzing around at light-speed or will it now, without the inertia of the matter, fall into some weird growing resonance and ultimately shatter and relax.
      - Valectar 1y ago
        It's not exactly whizzing around at light speed in the way that you imagine if it's beneath an event horizon. The entire point of an event horizon is that everything beyond it physically cannot move outward. The horizon isn't some kind of physical barrier, it is just the farthest distance at which the black hole's gravity becomes inescapable, that doesn't stop applying just because you've moved past the horizon, and in fact it only becomes more true. If you imagine any sphere beneath the event horizon which is centered on the singularity, that sphere is just as inescapable as the farthest such sphere which we call the event horizon. Additionally, the event horizon is inescapable to everything. Even gravitation is transmitted at the speed of light, and cannot outrun the cascade of inwardly falling spacetime beneath the event horizon. So no possible change in the distribution of mass within a black hole could have any effect on the configuration of spacetime at the event horizon, or even on any spacetime further from the singularity than itself.
        scotty79 1y ago
        The point of event horizon is that everything at it expeiriences infinite gravitational time dilation in relation to everything even barely outside it. So talking about things inside event horizon is about as physical as talking about things traveling at superluminal speeds. You can consider such object, it just takes more than infinite acceleration time to get there. I don't really understand why people think they can get rid of the discontinuity at event horizon by changing coordinate system. It's as if we were considering function 1/x in new coordinate system xi where xi is defined as 1/x and suddenly we have a nice continuus function without anything special happening around 0. It's a mathematical sleigh of hand. Sure, from the point of view of infalling matter nothing special happens at event horizon but why would we, outside people, should care about this perspective since the universe will evaporate before this infalling matter crosses event horizon? So when black hole becomes made of mostly photons, they are all still outside of the event horizon, because infinite time has not yet passed outside.
- bufferoverflow 1y ago
  We don't know if singularities are even possible. Maybe the universe has some crazy repulsive force when atoms or subatomic particles get really really close (closer than in neutron stars, where atoms are femtometers apart).
  - CarRamrod 1y ago
    >Maybe the universe has some crazy repulsive force when atoms or subatomic particles get really really close (closer than in neutron stars, where atoms are femtometers apart). The Celestial Ick
  - mytailorisrich 1y ago
    There are no "atoms" in neutron stars. The density and temperature are so high that they are "crushed" and that the electrons and protons form neutrons. The result is tightly packed neutrons, hence the name. I believe it is theorised that it might be possible to go even one step further to a "quark star" since neutrons are not elementary but made of quarks. No idea what a black hole might look like with no singularity...
    - chasil 1y ago
      As I referenced in the wiki above, the surface of a neutron star is ordinary atomic matter (fully ionized), perhaps iron.
    - nikbackm 1y ago
      https://en.wikipedia.org/wiki/Planck_star https://en.wikipedia.org/wiki/Planck_star
  - pif 1y ago
    > closer than in neutron stars, where atoms are femtometers apart I suppose you meant neutrons instead of atoms. Atoms do not exist in a neutron star. At least, non in any significant quantity.
    - deleted 1y ago
      [deleted]
- lordfrito 1y ago
  > saying that singularity forming is "after" everything else that ever happens in the universe is a hard sell. This is the only thing that makes sense to me (I'm a total layman here). What's always bothered me is that, if singularities never form in our time reference (they look to us like frozen stars), and black holes can evaporate due to Hawking radiation in our time reference -- then not only does the singularity not exist, but it never will exist all all from the frame of reference of our universe. So what's the sense about talking about events that happen outside of our universe? Can they happen at all? That doesn't seem like physics to me. The frozen star model makes the most sense to me. And it has something to do with entanglement and entropy. From a computational view of a space-time, more and more mass/gravity/entanglement makes computing "space-time events" (causality) increasingly complicated -- and since local causality clock can't "tick" until the computation is complete... time slows down relative to the rest of the universe, much like a CPU under heavy load. The event horizon seems like the place the space-time CPU "crashes" or slows down under heavy load. Like I said, I'm a layman.
  - dustingetz 1y ago
    it exists under superdeterminism, which is the most sane interpretation of wavefunction collapse
    - ubersketch 1y ago
      the most sane interpretation is just evolving wavefunctions according to schrödinger's equation with no extra bells or whistles. collapse is just decoherence.
  - raattgift 1y ago
    First off, let's assume General Relativity (4d time-orientable manifold) is true. That means among other things that when I write "black hole" I mean an approximate solution which is a small perturbation of an exact solution like the McVittie metric, or even Kerr-Newman or Schwarzschild (which lack a cosmology part, but can be stitched into an expanding cosmology à la Darmois-Israel junction). Black hole solutions have inextensible curves or at least the distinction between curves vanishes at a "singularity". Curves are trajectories through spacetime that may in some places be accelerated and in some places may be geodesic. Physical objects bind to everywhere-non-spacelike curves and we further say these curves are everywhere future-pointing (no backwards time travel allowed). The "small" perturbations (e.g. adding outside matter) does not change any of these key features. In that setting we could specify all the matter everywhere and solve the various partial differential equations and have an exact calculation for a particular spacetime. However anyone who has ever tried to do this by hand -- that includes many many grad students over the decades -- knows this is infeasible for complicated spacetimes. One can use automation with perturbation theory (e.g. https://bhptoolkit.org/ https://bhptoolkit.org/ ) but then one discovers that perturbation theory breaks down deep inside black holes. So the practical problem is that we want to do numerical relativity (NR) within black holes, and unfortunately singularities turn out to be numerically intractable with current methods. How NR works, very roughly (and quite differently from your second-last paragraph) is that we slice up a model spacetime (with boundary and initial conditions) into 3 spatial + 1 time dimension, "foliating" on a time axis chosen (from the infinite possibilities) for pragmatic reasons. The axis is global for the whole spacetime. We have to note here that the relativity principle is that nobody's time axis is special, which means there is no right choice and no wrong choice here. However different choices come with different trade-offs, including in how straightforward it is to interconvert a system of coordinates adapted to our chosen time axis and those adapted to any other useful time axis. We then canonicalize curves through this foliation into per-spatial-slice quantities reflecting position and momentum; we also make arbitrary choices about what represents "empty" spacetime so we can choose a shift vector (capturing how spatial coordinates differ from one slice to its neighbours) and a lapse function (capturing how coordinate time (e.g. proper-time of a massive particle) evolves from one slice to another). This gives us constraints (how quantities on a particular spatial slice relate to one another) and evolutions (how these quantities change from one slice to its infinitesimally future successor, and what was in its infinitesimally past predecessor). There is no local "causality" clock ticking, there are only quantities on each whole-universe-spatial-slice and an ordering of slices. Suitable causal conditions -- notably globally hyperbolic solutions to a number of partial differential equations -- let us fill in the whole spacetime from infinite past to infinite future, and should be a formalism (the Initial-Value Formulation) of the full solution in general relativity up to numerical errors. This is the most common approach to doing General Relativity on computers when perturbation theory breaks down (as it does deep inside black holes and in some cases where there are unusual gravitational-wave/gravitational-wave interactions and where matter waves strongly interact near one of these extreme events (this includes lensing close to a black hole)). A concrete example of this is in SXS (Simulating eXtreme Spacetimes) numerical relativity kit, which you can begin reading about at https://www.black-holes.org/the-science/numerical-relativity/ https://www.black-holes.org/the-science/numerical-relativity... It's not practical (and is likely highly error-prone) to use computers this way to calculate very close to a singularity, so various methods are used to "ignore" it, containing the inextensible curves inside a tiny region which we hope can be computationally smooth on the region's surface. This isn't totally new -- Gauss's gravity works that way too. But this raises the question: do we lose effects at the apparent black hole horizon (a "surface" we can obtain by doing local measurements, unlike the event horizon) when we blur the singularity inside the BH? And how do we calculate complete evaporation when relying on techniques like this? These and many related questions are active fields of study in NR. A reminder: this is General Relativity, therefore the singularity is taken to be physically present. There is nothing that blocks the singularity from happening without adjusting the behaviour of stress-energy to introduce or substitute negative energy deep inside the black hole as matter moves inwards from one slice to the next (and there's no evidence that real matter does this), or substituting a global solution to the Einstein Field Equations which manifestly is not a black hole spacetime (even on the "initial" slice). Physically, then, there is the question of whether matter somehow blocks the formation of singularities. Your "frozen star" idea is a very very very rough way of thinking about that question. There are many ideas in that space, and it's safe enough to generate those (although it's hard to keep them self-consistent) because there is no real hope for experimental verification of any of them in a human lifetime. However, there was in recent decades hope for exactly this sort of resolution when ideas in the particle physics space like (relatively) low-energy supersymmetry had not largely been killed off in contact with evidence from particle colliders like the LHC. One can also find in the literature examples of "frozen star" ideas meaning that one doesn't use a black hole spacetime at all, for whatever reason. That raises lots of questions about why there are objects in our sky that radiate really really similarly to black hole spacetimes. "Frozen star" (of this kind) simulations tend to produce clearly wrong results far from the surface of the black hole. > So what's the sense about talking about events that happen outside our universe? Sure, this is the intuition between the puncture and excision approaches to the deep regions of black holes in numerical relativity. As long as whatever falls in also stays in, the approach is good. But what stops black holes from completely evaporating? In that case, what the hell is supposed to come out of the singularity / deep region / puncture region / excised region? Sadly the lifetimes -- from our point of view -- of even low-mass primordial black holes or young stellar black holes is more than enough for anything crossing the apparent horizon (like primordial radiation, cosmic microwaves, distant starlight, and so on) to hit the singularity. This problem is even worse as we increase the black hole mass. There is no support in General Relativity for matter as we know it to "freeze" long enough in a black hole spacetime. The infalling matter doesn't care what we see happen from our perspective. We are allowed to experience optical illusions, or be misled by poor choices of systems of coordinates. > our time reference turns out to be a poor choice of time axis for many astrophysical events. One can choose more suitable systems of coordinates for events "over there" (or for a global foliation) and then do careful coordinate transforms from those coordinates to coordinates more in line with our day-to-day experiences. For example one might attach Fermi normal coordinates to an infalling particle approaching an astrophysical black hole, and do a series of coordinate transformations to "cosmic time", from which we can do further transformations to TDB/TCB/TAI or whatever we want. The particle's collision with the singularity will be in our past. The flashes we detect from dust clouds and in our galaxy's central parsec or flashes from tidal disruption events in other galaxies are messages from matter which is already "in" their respective singularities.
- amluto 1y ago
  I think this is wrong, or at least inapplicable to our universe, for a reason that is interesting. The simplest model of a black hole is the Schwartzchild metric, which describes a non-rotating, uncharged black hole that is alone in the universe and has existed forever. One can imagine a scientist very far away throwing a zero mass rock at the black hole and watching it fall in, and it will never actually fall in from the scientist’s perspective. I think that popular scientists like to talk about Schwarzchild black holes because they seem simple. The black holes in our universe are not like this. They formed from stars and such, and they have not been there forever. One model of these is the Oppenheimer-Snyder metric, and I believe that objects do cross the event horizon in finite time as measured by faraway observers. (I’ve never personally done the math for this metric.) And there is a singularity at the center that forms at a finite time. Heuristically, if you throw a large rock at a black hole, the rock will approach the event horizon and, at some point, the event horizon moves outward to meet it, because the addition of the rock makes the black hole bigger. I’m not sure how good this heuristic is :)
  - raattgift 1y ago
    I agree with you so much that I can't resist a nitpick. I'll also amplify your points in the last two paragraphs and justify "the popular scientists". > the event horizon moves outwards to meet it The event horizon is a global surface that might even be measurable locally in principle, and certainly might not be where one thinks. The event horizon is determined by what's inside and outside it, and arguably it's only "dynamical" if one takes a 3+1 view of the spacetime containing it. Local measurements can determine which side of an apparent horizon the measurer is on. That's arguably more useful than the event horizon, since for all practical purposes it's the apparent horizon that is the point of no return. Anything inside that will quickly end up in a region where local measurements lose predictive power (roughly, "the singularity"). Visser 2014 <https://arxiv.org/abs/1407.7295 https://arxiv.org/abs/1407.7295> has more detail The apparent horizon is dynamical in the sense that it will deform -- a small black hole orbiting a supermassive black hole raises a bump on the supermassive black hole's apparent horizon. (The event horizon has the same gross property, but you can't know the bump's details until you know the whole spacetime! Observed disturbances in the material surrounding such a binary represent the apparent horizon.) Schwarzschild is a special case: an exact solution of a family of approximate solutions to astrophysical black holes which aren't isolated and which are immersed in a cosmology, and which are also probably rotating and may have some residual charge (not necessarily electromagnetic charge à la Kerr-Newman) from time to time. They may also radiate (but probably not isotropically like Vaiyda) and certainly intercept radiation (cosmic, from their local environment in their host galaxy, and otherwise) non-isotropically and with different inbound/outbound fluxes over time. And so on. There is lots of literature about the stability of e.g. K-N to small perturbations (e.g. if you shine a very bright light on half of a K-N black hole, is K-N (with new parameter-values) still a good representation of the black hole once the light is off?), and it is pretty reasonable to think that an OS black hole even with lots of extra charges decorating the scene (and with other masses making a mess of the asymptotically flat region) settles down to a state very well modelled by K-N or even Schwarzschild. i.e. Black holes go bald. (but then lurking around the barber shop are the gravitational memory effect, BMS supertranslations, and so on ...).
randomtoast 1y ago
One solution to the black hole singularity problem is Fuzzballs, a string-theoretic proposal suggesting that what we thought was a singularity is actually a tangled mess of strings and branes, replacing the notion of a smooth event horizon with a quantum "fuzz" that preserves information. If true, this would resolve the information paradox without requiring firewalls or breaking semi-classical gravity near the horizon. Still controversial, but it’s one of the few proposals with a concrete realization in a quantum gravity framework.
- vlovich123 1y ago
  Cool. How do we test string theory in a way that shows it’s correct and the experiment can’t be explained by simpler theories? As I understand it, string theory itself has so many tunable parameters that in a sense it can be made to fit any set of observations.
  - Pet_Ant 1y ago
    The optimist in me believes that String Theory is the physics of universes, not just our own which is why it has so much fine-tuning needed.
  - drdeca 1y ago
    My understanding is that part of the issue with string theory is that the computations are extremely difficult. Like, yes, the landscape is very large, but it’s also very difficult to, even picking one particular option, it is very hard to get a prediction out of it. However, I think some correct but very loose postdictions have been made about some mass ratios?
  - randomtoast 1y ago
    There are many critics of string theory, and their voices deserve to be heard. However, I would also like to ask these critics: Can you come up with something better? String theory explains many phenomena with mathematical elegance, but at the moment, there is no way to test it.
    - 1y ago

38 points by nsoonhui 1y ago

My non-canonical and possibly wrong view of black hole singularities is that they can form in finite time (sort of) only in their own frame of reference but in any other frame they require infinite time so from our point of view no singularity ever formed and ever will from. And in practice, in this infinite time something might disrupt their collapse, like getting hit with similarly massive amount of anti-matter an turning into photons which might destabilize the whole process and let them get out in massively energetic event similar to Big Bang. Which I believe was the case with ours, so no white-hole singularity either. This view is dismissed by physicist because in GR there's no way to unambiguously define simultaneity so they don't event attempt to consider what's "before" and what's "after" regarding remote events in strong gravitational fields so saying that singularity forming is "after" everything else that ever happens in the universe is a hard sell.

wizzwizz4 1y ago
A "matter black hole" and an "antimatter black hole" will combine to form a larger black hole. GR doesn't have a well-defined notion of simultaneity, but it does have a notion of before and after.
- scotty79 1y ago
  > A "matter black hole" and an "antimatter black hole" will combine to form a larger black hole. I think they'll annihilate forming photon black hole, which might be unstable. > but it does have a notion of before and after. Was forming of any singularity before present day on Earth?
- fguerraz 1y ago
  With the current theories, I don't think it matters (pun intended) if a matter and anti-matter black holes merge. E=mc2 (+change) In normal space that would have liberated a huge amount of energy, but in sufficiently curved space, the energy stays inside the back hole, mass is conserved, nothing to see (literally).
  - scotty79 1y ago
    I think the question is, will the spacetime stay sufficiently curved if it's now curved by pure energy whizzing around at light-speed or will it now, without the inertia of the matter, fall into some weird growing resonance and ultimately shatter and relax.
    - Valectar 1y ago
      It's not exactly whizzing around at light speed in the way that you imagine if it's beneath an event horizon. The entire point of an event horizon is that everything beyond it physically cannot move outward. The horizon isn't some kind of physical barrier, it is just the farthest distance at which the black hole's gravity becomes inescapable, that doesn't stop applying just because you've moved past the horizon, and in fact it only becomes more true. If you imagine any sphere beneath the event horizon which is centered on the singularity, that sphere is just as inescapable as the farthest such sphere which we call the event horizon. Additionally, the event horizon is inescapable to everything. Even gravitation is transmitted at the speed of light, and cannot outrun the cascade of inwardly falling spacetime beneath the event horizon. So no possible change in the distribution of mass within a black hole could have any effect on the configuration of spacetime at the event horizon, or even on any spacetime further from the singularity than itself.
      - scotty79 1y ago
        The point of event horizon is that everything at it expeiriences infinite gravitational time dilation in relation to everything even barely outside it. So talking about things inside event horizon is about as physical as talking about things traveling at superluminal speeds. You can consider such object, it just takes more than infinite acceleration time to get there. I don't really understand why people think they can get rid of the discontinuity at event horizon by changing coordinate system. It's as if we were considering function 1/x in new coordinate system xi where xi is defined as 1/x and suddenly we have a nice continuus function without anything special happening around 0. It's a mathematical sleigh of hand. Sure, from the point of view of infalling matter nothing special happens at event horizon but why would we, outside people, should care about this perspective since the universe will evaporate before this infalling matter crosses event horizon? So when black hole becomes made of mostly photons, they are all still outside of the event horizon, because infinite time has not yet passed outside.
bufferoverflow 1y ago
We don't know if singularities are even possible. Maybe the universe has some crazy repulsive force when atoms or subatomic particles get really really close (closer than in neutron stars, where atoms are femtometers apart).
- CarRamrod 1y ago
  >Maybe the universe has some crazy repulsive force when atoms or subatomic particles get really really close (closer than in neutron stars, where atoms are femtometers apart). The Celestial Ick
- mytailorisrich 1y ago
  There are no "atoms" in neutron stars. The density and temperature are so high that they are "crushed" and that the electrons and protons form neutrons. The result is tightly packed neutrons, hence the name. I believe it is theorised that it might be possible to go even one step further to a "quark star" since neutrons are not elementary but made of quarks. No idea what a black hole might look like with no singularity...
  - chasil 1y ago
    As I referenced in the wiki above, the surface of a neutron star is ordinary atomic matter (fully ionized), perhaps iron.
  - nikbackm 1y ago
    https://en.wikipedia.org/wiki/Planck_star https://en.wikipedia.org/wiki/Planck_star
- pif 1y ago
  > closer than in neutron stars, where atoms are femtometers apart I suppose you meant neutrons instead of atoms. Atoms do not exist in a neutron star. At least, non in any significant quantity.
  - deleted 1y ago
    [deleted]
lordfrito 1y ago
> saying that singularity forming is "after" everything else that ever happens in the universe is a hard sell. This is the only thing that makes sense to me (I'm a total layman here). What's always bothered me is that, if singularities never form in our time reference (they look to us like frozen stars), and black holes can evaporate due to Hawking radiation in our time reference -- then not only does the singularity not exist, but it never will exist all all from the frame of reference of our universe. So what's the sense about talking about events that happen outside of our universe? Can they happen at all? That doesn't seem like physics to me. The frozen star model makes the most sense to me. And it has something to do with entanglement and entropy. From a computational view of a space-time, more and more mass/gravity/entanglement makes computing "space-time events" (causality) increasingly complicated -- and since local causality clock can't "tick" until the computation is complete... time slows down relative to the rest of the universe, much like a CPU under heavy load. The event horizon seems like the place the space-time CPU "crashes" or slows down under heavy load. Like I said, I'm a layman.
- dustingetz 1y ago
  it exists under superdeterminism, which is the most sane interpretation of wavefunction collapse
  - ubersketch 1y ago
    the most sane interpretation is just evolving wavefunctions according to schrödinger's equation with no extra bells or whistles. collapse is just decoherence.
- raattgift 1y ago
  First off, let's assume General Relativity (4d time-orientable manifold) is true. That means among other things that when I write "black hole" I mean an approximate solution which is a small perturbation of an exact solution like the McVittie metric, or even Kerr-Newman or Schwarzschild (which lack a cosmology part, but can be stitched into an expanding cosmology à la Darmois-Israel junction). Black hole solutions have inextensible curves or at least the distinction between curves vanishes at a "singularity". Curves are trajectories through spacetime that may in some places be accelerated and in some places may be geodesic. Physical objects bind to everywhere-non-spacelike curves and we further say these curves are everywhere future-pointing (no backwards time travel allowed). The "small" perturbations (e.g. adding outside matter) does not change any of these key features. In that setting we could specify all the matter everywhere and solve the various partial differential equations and have an exact calculation for a particular spacetime. However anyone who has ever tried to do this by hand -- that includes many many grad students over the decades -- knows this is infeasible for complicated spacetimes. One can use automation with perturbation theory (e.g. https://bhptoolkit.org/ https://bhptoolkit.org/ ) but then one discovers that perturbation theory breaks down deep inside black holes. So the practical problem is that we want to do numerical relativity (NR) within black holes, and unfortunately singularities turn out to be numerically intractable with current methods. How NR works, very roughly (and quite differently from your second-last paragraph) is that we slice up a model spacetime (with boundary and initial conditions) into 3 spatial + 1 time dimension, "foliating" on a time axis chosen (from the infinite possibilities) for pragmatic reasons. The axis is global for the whole spacetime. We have to note here that the relativity principle is that nobody's time axis is special, which means there is no right choice and no wrong choice here. However different choices come with different trade-offs, including in how straightforward it is to interconvert a system of coordinates adapted to our chosen time axis and those adapted to any other useful time axis. We then canonicalize curves through this foliation into per-spatial-slice quantities reflecting position and momentum; we also make arbitrary choices about what represents "empty" spacetime so we can choose a shift vector (capturing how spatial coordinates differ from one slice to its neighbours) and a lapse function (capturing how coordinate time (e.g. proper-time of a massive particle) evolves from one slice to another). This gives us constraints (how quantities on a particular spatial slice relate to one another) and evolutions (how these quantities change from one slice to its infinitesimally future successor, and what was in its infinitesimally past predecessor). There is no local "causality" clock ticking, there are only quantities on each whole-universe-spatial-slice and an ordering of slices. Suitable causal conditions -- notably globally hyperbolic solutions to a number of partial differential equations -- let us fill in the whole spacetime from infinite past to infinite future, and should be a formalism (the Initial-Value Formulation) of the full solution in general relativity up to numerical errors. This is the most common approach to doing General Relativity on computers when perturbation theory breaks down (as it does deep inside black holes and in some cases where there are unusual gravitational-wave/gravitational-wave interactions and where matter waves strongly interact near one of these extreme events (this includes lensing close to a black hole)). A concrete example of this is in SXS (Simulating eXtreme Spacetimes) numerical relativity kit, which you can begin reading about at https://www.black-holes.org/the-science/numerical-relativity/ https://www.black-holes.org/the-science/numerical-relativity... It's not practical (and is likely highly error-prone) to use computers this way to calculate very close to a singularity, so various methods are used to "ignore" it, containing the inextensible curves inside a tiny region which we hope can be computationally smooth on the region's surface. This isn't totally new -- Gauss's gravity works that way too. But this raises the question: do we lose effects at the apparent black hole horizon (a "surface" we can obtain by doing local measurements, unlike the event horizon) when we blur the singularity inside the BH? And how do we calculate complete evaporation when relying on techniques like this? These and many related questions are active fields of study in NR. A reminder: this is General Relativity, therefore the singularity is taken to be physically present. There is nothing that blocks the singularity from happening without adjusting the behaviour of stress-energy to introduce or substitute negative energy deep inside the black hole as matter moves inwards from one slice to the next (and there's no evidence that real matter does this), or substituting a global solution to the Einstein Field Equations which manifestly is not a black hole spacetime (even on the "initial" slice). Physically, then, there is the question of whether matter somehow blocks the formation of singularities. Your "frozen star" idea is a very very very rough way of thinking about that question. There are many ideas in that space, and it's safe enough to generate those (although it's hard to keep them self-consistent) because there is no real hope for experimental verification of any of them in a human lifetime. However, there was in recent decades hope for exactly this sort of resolution when ideas in the particle physics space like (relatively) low-energy supersymmetry had not largely been killed off in contact with evidence from particle colliders like the LHC. One can also find in the literature examples of "frozen star" ideas meaning that one doesn't use a black hole spacetime at all, for whatever reason. That raises lots of questions about why there are objects in our sky that radiate really really similarly to black hole spacetimes. "Frozen star" (of this kind) simulations tend to produce clearly wrong results far from the surface of the black hole. > So what's the sense about talking about events that happen outside our universe? Sure, this is the intuition between the puncture and excision approaches to the deep regions of black holes in numerical relativity. As long as whatever falls in also stays in, the approach is good. But what stops black holes from completely evaporating? In that case, what the hell is supposed to come out of the singularity / deep region / puncture region / excised region? Sadly the lifetimes -- from our point of view -- of even low-mass primordial black holes or young stellar black holes is more than enough for anything crossing the apparent horizon (like primordial radiation, cosmic microwaves, distant starlight, and so on) to hit the singularity. This problem is even worse as we increase the black hole mass. There is no support in General Relativity for matter as we know it to "freeze" long enough in a black hole spacetime. The infalling matter doesn't care what we see happen from our perspective. We are allowed to experience optical illusions, or be misled by poor choices of systems of coordinates. > our time reference turns out to be a poor choice of time axis for many astrophysical events. One can choose more suitable systems of coordinates for events "over there" (or for a global foliation) and then do careful coordinate transforms from those coordinates to coordinates more in line with our day-to-day experiences. For example one might attach Fermi normal coordinates to an infalling particle approaching an astrophysical black hole, and do a series of coordinate transformations to "cosmic time", from which we can do further transformations to TDB/TCB/TAI or whatever we want. The particle's collision with the singularity will be in our past. The flashes we detect from dust clouds and in our galaxy's central parsec or flashes from tidal disruption events in other galaxies are messages from matter which is already "in" their respective singularities.
amluto 1y ago
I think this is wrong, or at least inapplicable to our universe, for a reason that is interesting. The simplest model of a black hole is the Schwartzchild metric, which describes a non-rotating, uncharged black hole that is alone in the universe and has existed forever. One can imagine a scientist very far away throwing a zero mass rock at the black hole and watching it fall in, and it will never actually fall in from the scientist’s perspective. I think that popular scientists like to talk about Schwarzchild black holes because they seem simple. The black holes in our universe are not like this. They formed from stars and such, and they have not been there forever. One model of these is the Oppenheimer-Snyder metric, and I believe that objects do cross the event horizon in finite time as measured by faraway observers. (I’ve never personally done the math for this metric.) And there is a singularity at the center that forms at a finite time. Heuristically, if you throw a large rock at a black hole, the rock will approach the event horizon and, at some point, the event horizon moves outward to meet it, because the addition of the rock makes the black hole bigger. I’m not sure how good this heuristic is :)
- raattgift 1y ago
  I agree with you so much that I can't resist a nitpick. I'll also amplify your points in the last two paragraphs and justify "the popular scientists". > the event horizon moves outwards to meet it The event horizon is a global surface that might even be measurable locally in principle, and certainly might not be where one thinks. The event horizon is determined by what's inside and outside it, and arguably it's only "dynamical" if one takes a 3+1 view of the spacetime containing it. Local measurements can determine which side of an apparent horizon the measurer is on. That's arguably more useful than the event horizon, since for all practical purposes it's the apparent horizon that is the point of no return. Anything inside that will quickly end up in a region where local measurements lose predictive power (roughly, "the singularity"). Visser 2014 <https://arxiv.org/abs/1407.7295 https://arxiv.org/abs/1407.7295> has more detail The apparent horizon is dynamical in the sense that it will deform -- a small black hole orbiting a supermassive black hole raises a bump on the supermassive black hole's apparent horizon. (The event horizon has the same gross property, but you can't know the bump's details until you know the whole spacetime! Observed disturbances in the material surrounding such a binary represent the apparent horizon.) Schwarzschild is a special case: an exact solution of a family of approximate solutions to astrophysical black holes which aren't isolated and which are immersed in a cosmology, and which are also probably rotating and may have some residual charge (not necessarily electromagnetic charge à la Kerr-Newman) from time to time. They may also radiate (but probably not isotropically like Vaiyda) and certainly intercept radiation (cosmic, from their local environment in their host galaxy, and otherwise) non-isotropically and with different inbound/outbound fluxes over time. And so on. There is lots of literature about the stability of e.g. K-N to small perturbations (e.g. if you shine a very bright light on half of a K-N black hole, is K-N (with new parameter-values) still a good representation of the black hole once the light is off?), and it is pretty reasonable to think that an OS black hole even with lots of extra charges decorating the scene (and with other masses making a mess of the asymptotically flat region) settles down to a state very well modelled by K-N or even Schwarzschild. i.e. Black holes go bald. (but then lurking around the barber shop are the gravitational memory effect, BMS supertranslations, and so on ...).

randomtoast 1y ago

One solution to the black hole singularity problem is Fuzzballs, a string-theoretic proposal suggesting that what we thought was a singularity is actually a tangled mess of strings and branes, replacing the notion of a smooth event horizon with a quantum "fuzz" that preserves information. If true, this would resolve the information paradox without requiring firewalls or breaking semi-classical gravity near the horizon. Still controversial, but it’s one of the few proposals with a concrete realization in a quantum gravity framework.

vlovich123 1y ago
Cool. How do we test string theory in a way that shows it’s correct and the experiment can’t be explained by simpler theories? As I understand it, string theory itself has so many tunable parameters that in a sense it can be made to fit any set of observations.
- Pet_Ant 1y ago
  The optimist in me believes that String Theory is the physics of universes, not just our own which is why it has so much fine-tuning needed.
- drdeca 1y ago
  My understanding is that part of the issue with string theory is that the computations are extremely difficult. Like, yes, the landscape is very large, but it’s also very difficult to, even picking one particular option, it is very hard to get a prediction out of it. However, I think some correct but very loose postdictions have been made about some mass ratios?
- randomtoast 1y ago
  There are many critics of string theory, and their voices deserve to be heard. However, I would also like to ask these critics: Can you come up with something better? String theory explains many phenomena with mathematical elegance, but at the moment, there is no way to test it.
  - 1y ago