Wednesday, January 3, 2018

event horizon - Black hole as a gravitational spherical shell. Why not?


I think that Leonard Susskind's holography, George Chapline's "dark energy star," the Emil Mottola and Pawel Mazur's "Gravastar," the Polchinski's "firewall," and the recent ideas of nonsingular black holes clearly suggest possibility of understanding this phenomenon as a massive spherical shell with an asymptotically thin wall.


I think that whole mass of the black hole can be located on the same place of the surface that today we call events horizon.


What could prevent the collapse of this shell, is the hypothesis that gravity has a limit of intensity. This limit only happens in the event horizon.


I imagine that the intensity of gravity should not be infinite. If this is possible, then black holes have no content, because inside them there would be no gravitational field, no space, no time. A place that does not really exist. A contour region of our universe.


Can a black hole be a spherical shell?



Answer




The problem with this model of the gravitational field (a problem that was first noticed by Einstein) is that something needs to keep the mass shell from collapsing in upon itself. The simplest way to try to do this is to suppose that the mass shell is really made up of many bodies in circular orbits around the center of mass. This works fine, so long as the radius of the shell is larger than the Schwarzschild radius $R_{S}=\frac{2GM}{c^{2}}$ (the radius of the event horizon); however, as the radius approaches $R_{S}$, the orbital speed of particles approaches $c$, which is impossible. (If you try to make the shell a solid, you run into a similar problem with the speed of acoustic waves that can propagate along the solid shell.)


Einstein concluded, on the basis of this kind of calculation, that black holes were not possible. However, that is not quite correct. What is not possible is for there to be a static black hole (like the mass shell model). There is no timelike Killing vector in Schwarzschild spacetime, because at the event horizon, the variable $t$ changes from timelike to spacelike. (And $r$ becomes timelike; this represents the fact that if you are falling into the black hole, a location at smaller $r$ must lie in in your future.)


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