Statistical approaches and the Bekenstein bound conjecture in Schwarzschild black holes

One of the challenges of today's theoretical physics is to fully understand the connection between a geometrical object like area and a thermostatistical one like entropy, since we have theoretical proofs that the area behaves analogously like entropy does. The Bekenstein bound suggests a universal constraint for the entropy in a flat space region. The Bekenstein-Hawking entropy of black holes satisfies the Bekenstein bound conjecture. In this paper we have shown that when we use important non-Gaussian entropies, like the ones of Barrow, Tsallis and Kaniadakis to describe the Schwarzschild black hole, then the Bekenstein bound conjecture seems to fail.

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