# Entropy corresponding to the interior of a Schwarzschild black hole

## TL;DR

This paper demonstrates that the entropy within the maximum interior volume of a Schwarzschild black hole, for massless modes, is proportional to the Bekenstein-Hawking entropy, with the horizon having greater entropy than the interior.

## Contribution

It provides a systematic derivation showing the interior entropy's proportionality to the horizon entropy, clarifying the entropy distribution between the interior and the horizon.

## Key findings

- Interior entropy is proportional to Bekenstein-Hawking entropy.
- Horizon entropy exceeds interior entropy.
- Derived precise energy of interior modes via constraint analysis.

## Abstract

Interior volume within the horizon of a black hole is a non-trivial concept which turns out to be very important to explain several issues in the context of quantum nature of black hole. Here we show that the entropy, contained by the {\it maximum} interior volume for massless modes, is proportional to the Bekenstein-Hawking expression. The proportionality constant is less than unity implying the horizon bears maximum entropy than that by the interior. The derivation is very systematic and free of any ambiguity. To do so the precise value of the energy of the modes, living in the interior, is derived by constraint analysis. Finally, the implications of the result are discussed.