Holography and Entropy Bounds in Gauss-Bonnet Gravity

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.