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 SB=2πER, independent of gravity theories. As a result, the Bekenstein–Verlinde bound also remains unchanged. Along the Verlindeʹs 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 corresponding Friedmann equation in Gauss–Bonnet gravity can no longer be cast to the form of cosmological Cardy formula.