3 ms·

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 metr

by 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 ...).
gavinray 1y ago
> a zero mass rock A what, now?
- amluto 1y ago
  That's kind of the point. It's true that, in the Schwartzchild metric, an object falling into a black hole would seem to take forever to fall in. And one can start making various extrapolations about what happens if you throw a whole lot of grains of dust in and how those grains of dust would pile up at infinite density near the event horizon. But once you notice that the Schwartzchild metric doesn't actually include these grains of dust and that it only really makes sense if the dust has zero mass, zero energy, etc, then the extrapolations are less interesting (look, infinite density of zero-energy things!). You need at least a perturbed Schwartzchild metric that accounts for the effect of the things falling in, and that might get different answers.

by amluto 1y ago

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 ...).

gavinray 1y ago

> a zero mass rock A what, now?

amluto 1y ago
That's kind of the point. It's true that, in the Schwartzchild metric, an object falling into a black hole would seem to take forever to fall in. And one can start making various extrapolations about what happens if you throw a whole lot of grains of dust in and how those grains of dust would pile up at infinite density near the event horizon. But once you notice that the Schwartzchild metric doesn't actually include these grains of dust and that it only really makes sense if the dust has zero mass, zero energy, etc, then the extrapolations are less interesting (look, infinite density of zero-energy things!). You need at least a perturbed Schwartzchild metric that accounts for the effect of the things falling in, and that might get different answers.