Holography and Entropy Bounds in Gauss-Bonnet Gravity

TL;DR

This paper investigates how holographic principles and entropy bounds behave in Gauss-Bonnet gravity, showing some bounds remain unchanged while others differ from Einstein gravity, with implications for cosmological entropy limits.

Contribution

It demonstrates that the Bekenstein entropy bound remains unchanged in Gauss-Bonnet gravity, while deriving modified cosmological entropy bounds and analyzing their relations.

Findings

Bekenstein entropy bound remains form-invariant in Gauss-Bonnet gravity.

The Bekenstein-Hawking and Hubble bounds differ from Einstein gravity.

At $HR=1$, all three entropy bounds coincide.

Abstract

We discuss the holography and entropy bounds in Gauss-Bonnet gravity theory. By applying a Geroch process to an arbitrary spherically symmetric black hole, we show that the Bekenstein entropy bound always keeps its form as $S_{\rm B}=2\pi E R$, independent of gravity theories. As a result, the Bekenstein-Verlinde bound also remains unchanged. Along the Verlinde's approach, we obtain the Bekenstein-Hawking bound and Hubble bound, which are different from those in Einstein gravity. Furthermore, we note that when $HR=1$, the three cosmological entropy bounds become identical as in the case of Einstein gravity. But, the Friedmann equation in Gauss-Bonnet gravity can no longer be cast to the form of cosmological Cardy formula.