# Could the spacetime manifold itself end at the event horizon? [closed]

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

## closed as unclear what you're asking by Ben Crowell, Emilio Pisanty, akhmeteli, Qmechanic♦Oct 23 '13 at 14:34

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• This isn't really a question, so not really too sure how to deal with this. But as an extra point maybe, I've always found it interesting that black holes can't really be said to have any internal structure. – Justin L. Oct 22 '13 at 3:28
• @JustinL. when you see something that looks like it's not a question, flag it as "unclear what you're asking." Even if it seems very insightful and is otherwise well written, remember that this is a site for questions which can be answered, so if something isn't a question, it doesn't belong here. Usually in such cases, the question is put on hold, edited, and then reopened shortly thereafter. – David Z Oct 22 '13 at 4:30
• By the way, dcgeorge, I think Justin is right: it's not clear what you're asking here. Could you edit the body of your post to clarify that? – David Z Oct 22 '13 at 4:30
• I believe you have answered your own question time and space can not continue as normal past the horizon therefore nothing we understand can exist without time and/or space. -1 – Argus Oct 22 '13 at 5:03

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.

• We discussed this here. It's not wrong, just meaningless. With all due respect, Ben, in that discussion, you tried to disparage the paper by calling the MNRAS a crap journal (guilt by association, I guess). Now you're saying their conclusion isn't wrong, it's just meaningless. Frankly, I don't understand your conclusion that all the mass of a black hole being outside the event horizon is meaningless. The meaning is perfectly clear to me. Not only is it clear, since it is directly counter to the accepted view, if it's correct, it's astoundingly significant. – dcgeorge Oct 23 '13 at 16:22
• The Schwarzschild solution has m∝r. It's proportional to neither its area not its volume. This is wrong, Ben. The Schwarzschild radius is proportional to the mass but the mass of the black hole itself is proportional to either the radius squared or cubed depending on who you ask. Ron Maimon says "... the scaling of the Schwarzschild radius is linear in mass, while the scaling of mass is cubic in the radius, ..." Raphael Bousso (re the holographic principle) says the black hole's mass is proportional to its radius squared, i.e. its surface area. This is the black hole scaling problem. – dcgeorge Oct 24 '13 at 15:28
• The equivalence principle doesn't allow anything special to happen at the event horizon. Only if you assume that the spacetime manifold is unbroken, that it continues past the event horizon. Which means you also have to ignore the whole issue of black hole firewalls and Bousso's idea that "space and time actually end there." – dcgeorge Oct 24 '13 at 15:48
• @dcgeorge: You're confused re $m\propto r$. You can clear this up for yourself by looking it up in a reliable source. – Ben Crowell Oct 24 '13 at 15:52
• Thanks Ben, I had that totally screwed up (we're dealing with a 75 year-old brain here). I edited it accordingly. This mass scaling issue is also mixed up somehow with entropy and surface area and Bousso's take on the holographic principle. I'm trying to sort it out. – dcgeorge Nov 5 '13 at 15:45