Bekenstein Bound for the BH entropy?

[RedShiftam]

Hi I'm writing in the hope that someone can help me to understand my confusion on a question. It's about the upper limit of entropy S or information I, which can be contained in a limited region of space that has a finite amount of energy. I looked at the formula and thought that if my energy is constant (say it is a one solar mass) and the radius, for example, starts approaching the zero, entropy it will be quite small. At some point, when the radius becomes equal to the Schwarzschild Radius, the object will become a black hole which it has a certain entropy. But In General Theory of Relativity mass will continue to shrink into a smaller and smaller region, which means smaller and smaller entropy. But it is known that the black hole has defined entropy, as long as something does not come into it. In this line of thought, does this mean that after we passes the Schwarzschild Radius, the Bekenstein bound is not a solution for the BH interior? Or everything is fine the value for the entropy is preserved and all we need is а better understanding for what is happening with the mass after the Schwarzschild Radius?

Thank you for your attention!

Greetings!
 

Edited December 20, 2018 by RedShiftam

[MigL]

Once a BH is formed ( mass-enrgy collapses through the Schwarzshild radius ), the entropy is encoded on the surface area of the event horizon  ( which is at the Schwarzschild radius ).
it does not follow the further collapse to a possible point.

[RedShiftam]

Yeah i know that! But the Bekenstein Bound doesn't tell you this. I mean the Schwarzschild radius is a special case. The mass still collapses. I thing that the formula must be writen in some other way in wich it keeps the entropy a constant even after the Schwarzschild radius and preserv all other cases.

[MigL]

Not sure I understand the problem.

The Bekenstein Bound is the maximum entropy ( or information ) that can be stored within a given volume of space.
Upon exceeding this limit, that volume must necessarily collapse into a Black Hole.

It was Bekenstein and Hawking who introduced the idea that A BH's entropy, or the information it contains, is stored on the surface of the event horizon. I.E. as the Bound is exceeded more and more, the area of the event horizon keeps getting larger and larger.
The conditions inside the event horizon, and the original mass-energy that underwent collapse, are no longer relevant to discussions of entropy and information.

[RedShiftam]

On 25.12.2018 г. at 5:59 AM, MigL said:

The conditions inside the event horizon, and the original mass-energy that underwent collapse, are no longer relevant to discussions of entropy and information.

Ok and why is that? Clearly the formula doesn't say that. You can put any value for a radius.I mean that there are so many possible configurations of Energy and radius in the formula. My point is that the Bekenstein Bound formula must be written in some other way in which you can see the conservation of the entropy of a black hole.

Edited December 27, 2018 by RedShiftam

[MigL]

Once the Bekenstein Bound is exceeded, the original information ( mass-energy ) collapses into a BH and throws up a 'curtain' which limits access to the interior of the Event Horizon.
This 'curtain' is one way only; Mass-energy can enter, but cannot leave.
So that while mass-energy ( information ) can still travel to the interior of the EH, The only change it can make is to the area of the EH by increasing it.

The Bekenstein Bound is only valid up to the point where it is exceeded, and collapse to a BH is mandated.
( I would think that is evident in its name, 'Bound' as in boundary.