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Could there be cut-outs in the manifold? There have been a number of intriguing ideas over the years hinting at the possibility that a black hole might not have an inside, that it might consist of nothing but a surface and an external gravitational field.

Here are some of the ideas that lead me to ask the question, in no particular order:

  • Black hole firewalls---of which Raphael Bousso says: "In some sense, space and time actually end there." http://worldsciencefestival.com/videos/the_black_hole_mystery_that_keeps_physicist_raphael_bousso_up_at_night"

  • According to the Cambridge astrophysicist, Professor Donald Lynden-Bell and Professor Emeritus, Joseph Katz, Racah Institute of Physics, in their paper Gravitational field energy density for spheres and black holes, the total coordinate-independent field energy distributed in the gravitational field of a Schwarzschild black hole is mc^2. They conclude, explicitly, that all the mass of the black hole resides outside the event horizon. http://adsabs.harvard.edu/full/1985MNRAS.213P..21L

  • The radial component of the Schwarzschild metric shows that, due to metric stretching, the energy density of space thins out and disappears at the event horizon.

  • There is no ironclad rule that requires the spacetime manifold to continue past the event horizon.

  • There is no way to verify (or falsify) what we think goes on inside the event horizon.

These ideas, individually and collectively, point to the possibility that its surface and its external field might be all there is to a black hole. What's particularly interesting to me is that this "surface only" picture is entirely consistent with them being cutouts, or holes, in the spacetime manifold.

Any thoughts would, of course, be most welcome.

Update: Here's a quote from a recent, six minute NPR interview with Leonard Susskind and Joesph Polchinski. Polchinski, speaking for his research group, says :"Our hypothesis is that the inside of a black hole — it may not be there. Probably that's the end of space itself. There's no inside at all."

Here's the link to the interview: http://www.npr.org/player/v2/mediaPlayer.html? action=1&t=1&islist=false&id=256897343&m=257674048

And a short article quoting from the interview: http://www.npr.org/2013/12/27/256897343/stretch-or-splat-how-a-black-hole-kills-you-matters-a-lot

Qmechanic
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dcgeorge
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The mass of a black hole scales with its surface area instead of with its volume (The black hole scaling problem).

This is wrong. The Schwarzschild solution has $m\propto r$. It's proportional to neither its area not its volume.

They conclude, explicitly, that all the mass of the black hole resides outside the event horizon.

We discussed this here. It's not wrong, just meaningless.

The radial component of the Schwarzschild metric shows that, due to metric stretching, the energy density of space thins out and disappears at the event horizon.

No, general relativity doesn't have a locally definable energy density due to the gravitational field. This is a straightforward consequence of the equivalence principle.

There is no ironclad rule that requires the spacetime manifold to continue past the event horizon.

The equivalence principle doesn't allow anything special to happen at the event horizon.

What's particularly interesting to me is that this "surface only" picture is entirely consistent with them being cutouts, or holes, in the spacetime manifold.

See Does spacetime in general relativity contain holes?

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