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It irks me so many physicists/cosmologists jump from the mathematical GR singularity at the center of a BH to "matter there has infinite density." That's highly

It irks me so many physicists/cosmologists jump from the mathematical GR singularity at the center of a BH to "matter there has infinite density." That's highly unlikely, it's probably quark plasma.

jiggawatts 2y ago
My simple model of it is to just think about spatial surfaces and do "accounting" of the total flux through them. If you draw a sphere around a star collapsing into a black hole, you can treat it as a closed system. If the black hole evaporates, then all of the mass-energy of its progenitor original star needs to leave through these concentric surfaces. This is on the same order of magnitude as a supernova, as it is equal to the collapsed core of the star being converted into pure radiated energy! An infalling observer accounting of the mass-energy flows must match this external view point. As they cross smaller and smaller bounding spheres, they must see this energy flowing out through those boundaries, adding up to the same total. (There is nowhere else for the energy to go; it has to be blasting you in the face as you fall in!) Oversimplified models of black holes concentrate the mass-energy to a point, leaving spacetime around it an empty vacuum. So an infalling observer will see zero, zero, zero, zero... infinite energy density for an infinitesimal time. This is non-physical nonsense, and isn't even mathematically sound! From Hawking we know that infalling (and distant) observers see some finite energy flux, and from Einstein's GR we know that infalling observers will see this blue-shifted and time-accelerated on the way in. The logical conclusion is that the flux is observed to increase smoothly by infalling observers until the entire amount is accounted for in a finite time. This is a staggering total amount of radiated energy, equivalent to an matter/anti-matter explosion of matter the density of a neutron star core! There is no way anything could "fall through" this while jotting down their observations. It's not a survivable journey. There are no wormholes, reachable parallel universes, and there are no separate white holes "elsewhere" in the universe. A black hole is the white hole, smeared out trillions of years into the future so that the enormous total energy is radiated out so slowly from an outside perspective that they just look black. Infalling observers see the "true" white nature of these explosions frozen in time.
- codethief 2y ago
  > If you draw a sphere around a star collapsing into a black hole, you can treat it as a closed system. If the black hole evaporates, then all of the mass-energy of its progenitor original star needs to leave through these concentric surfaces. That would be great if energy were a conserved quantity in General Relativity, which it isn't. Heck, we don't even know how to write down the total energy/momentum of a given spacetime volume.
  - jiggawatts 2y ago
    > energy were a conserved quantity in General Relativity, which it isn't It is conserved, except at cosmological scales. Locally GR conserves energy the same as any other self-consistent physical theory.
    - codethief 2y ago
      > It is conserved, except at cosmological scales That's incorrect. Energy conservation can be violated at a much smaller scale, e.g. when gravitational waves are involved, or redshift phenomena (e.g. in Schwarzschild). Yes, we usually talk about the fact that gravitational waves can carry energy but what exactly is their energy content? And what exactly is the conservation equation here? > Locally GR conserves energy the same as any other self-consistent physical theory. Locally, you can write down a divergence equation for the energy momentum tensor, yes. However, locally we're in Minkowski space anyway, so that is not really surprising. The point is that the local divergence equation doesn't take into account the energy carried by the gravitational field itself. To give another example beyond gravitational waves: A Schwarzschild black hole carries mass, even though it is a vacuum solution to the Einstein field equations. See also https://en.m.wikipedia.org/wiki/Mass_in_general_relativity https://en.m.wikipedia.org/wiki/Mass_in_general_relativity and in particular the section on quasi-local mass.
af3d 2y ago
From what I understand of it the singularity is analogous to what happens in the 2D Cartesian plane with functions such as f(x) = 1/x. When x equals 0, the function itself "breaks down" because the y-coordinate extends to infinity (ie f(0) is "undefined"). In the context of a black hole that means that neither time nor space (hence neither does matter) "exist" at this singularity. In other words upon arrival the falling object has essentially "reached the end of time".

It irks me so many physicists/cosmologists jump from the mathematical GR singularity at the center of a BH to "matter there has infinite density." That's highly unlikely, it's probably quark plasma.

jiggawatts 2y ago

My simple model of it is to just think about spatial surfaces and do "accounting" of the total flux through them. If you draw a sphere around a star collapsing into a black hole, you can treat it as a closed system. If the black hole evaporates, then all of the mass-energy of its progenitor original star needs to leave through these concentric surfaces. This is on the same order of magnitude as a supernova, as it is equal to the collapsed core of the star being converted into pure radiated energy! An infalling observer accounting of the mass-energy flows must match this external view point. As they cross smaller and smaller bounding spheres, they must see this energy flowing out through those boundaries, adding up to the same total. (There is nowhere else for the energy to go; it has to be blasting you in the face as you fall in!) Oversimplified models of black holes concentrate the mass-energy to a point, leaving spacetime around it an empty vacuum. So an infalling observer will see zero, zero, zero, zero... infinite energy density for an infinitesimal time. This is non-physical nonsense, and isn't even mathematically sound! From Hawking we know that infalling (and distant) observers see some finite energy flux, and from Einstein's GR we know that infalling observers will see this blue-shifted and time-accelerated on the way in. The logical conclusion is that the flux is observed to increase smoothly by infalling observers until the entire amount is accounted for in a finite time. This is a staggering total amount of radiated energy, equivalent to an matter/anti-matter explosion of matter the density of a neutron star core! There is no way anything could "fall through" this while jotting down their observations. It's not a survivable journey. There are no wormholes, reachable parallel universes, and there are no separate white holes "elsewhere" in the universe. A black hole is the white hole, smeared out trillions of years into the future so that the enormous total energy is radiated out so slowly from an outside perspective that they just look black. Infalling observers see the "true" white nature of these explosions frozen in time.

codethief 2y ago
> If you draw a sphere around a star collapsing into a black hole, you can treat it as a closed system. If the black hole evaporates, then all of the mass-energy of its progenitor original star needs to leave through these concentric surfaces. That would be great if energy were a conserved quantity in General Relativity, which it isn't. Heck, we don't even know how to write down the total energy/momentum of a given spacetime volume.
- jiggawatts 2y ago
  > energy were a conserved quantity in General Relativity, which it isn't It is conserved, except at cosmological scales. Locally GR conserves energy the same as any other self-consistent physical theory.
  - codethief 2y ago
    > It is conserved, except at cosmological scales That's incorrect. Energy conservation can be violated at a much smaller scale, e.g. when gravitational waves are involved, or redshift phenomena (e.g. in Schwarzschild). Yes, we usually talk about the fact that gravitational waves can carry energy but what exactly is their energy content? And what exactly is the conservation equation here? > Locally GR conserves energy the same as any other self-consistent physical theory. Locally, you can write down a divergence equation for the energy momentum tensor, yes. However, locally we're in Minkowski space anyway, so that is not really surprising. The point is that the local divergence equation doesn't take into account the energy carried by the gravitational field itself. To give another example beyond gravitational waves: A Schwarzschild black hole carries mass, even though it is a vacuum solution to the Einstein field equations. See also https://en.m.wikipedia.org/wiki/Mass_in_general_relativity https://en.m.wikipedia.org/wiki/Mass_in_general_relativity and in particular the section on quasi-local mass.

af3d 2y ago

From what I understand of it the singularity is analogous to what happens in the 2D Cartesian plane with functions such as f(x) = 1/x. When x equals 0, the function itself "breaks down" because the y-coordinate extends to infinity (ie f(0) is "undefined"). In the context of a black hole that means that neither time nor space (hence neither does matter) "exist" at this singularity. In other words upon arrival the falling object has essentially "reached the end of time".