Thermodynamics of the FLRW apparent horizon in Einstein-Gauss-Bonnet gravity

Abstract

We analyze the thermodynamic properties of the apparent horizon of Friedmann-Lemaître-Roberson-Walker (FLRW) spacetimes in Einstein-Gauss-Bonnet gravity. We use the generalized definition of entropy for gravity theories in higher dimensions to determine the main thermodynamic variables and to compare their behavior with the corresponding quantities in Einstein's theory, emphasizing the role of the Gauss-Bonnet coupling constant and the dimension number. By imposing the validity of the laws of thermodynamics, we show that the apparent horizon can be interpreted thermodynamically as a dark energy fluid, independently of the coupling constant and the dimension number. Using the response functions, we determine the adiabatic index and the number of thermally accesible degrees of freedom of the apparent horizon and argue that this leads to a discretization of the Gauss-Bonnet coupling constant.

Figures (7)

• Figure 1: Horizon radius versus energy for $n=4$, $V=100$ and different values of the coupling constant $\alpha_0$. The black solid curve represents the case of Einstein's theory.
• Figure 2: Horizon radius versus energy for $\alpha_0 = 1$, $V=1$, and different values of the dimension $n$. The black solid line represents the case of Einstein's gravity.
• Figure 3: Entropy of the apparent horizon as a function of the energy $E$ for $V=100$, $n=4$, and different values of the coupling constant $\alpha_0$. The black solid line represents the entropy in Einstein's gravity.
• Figure 4: Entropy of the apparent horizon as a function of the energy for $V=1$, $\alpha_0=1$, and different values of the dimension parameter $n$.
• Figure 5: Temperatue of the apparent horizon as a function of the energy for $n=4$, $V=1$, and different values of the coupling constant $\alpha_0=1$. The black solid line represents the temperature in Einstein's gravity.