Narrow Results

The Second Law of black hole thermodynamics is shown to hold for arbitrarily complicated theories of higher curvature gravity, so long as we allow only linearized perturbations to stationary black holes. Some ambiguities in Wald’s Noether charge method are resolved. The increasing quantity turns out to be the same as the holographic entanglement entropy calculated by Dong. It is suggested that only the linearization of the higher curvature Second Law is important, when consistently truncating a UV-complete quantum gravity theory.

The purpose of this paper is to give some relevant clarification on the validity of the laws of thermodynamics and the stability of the horizon by scalar field scattering formalism. On the one side, the connection between the energy of the absorbed particle and the change of the enthalpy of the black hole appears to resolve the violation of the second law. On the other side, such connection stipulates a fixed rank of the gauge group $N$ in the boundary conformal field theory which is against the extended phase-space spirit, where the cosmological constant is allowed to vary inducing a holographical dually changing of $N$. By recalling the Grand potential, we suggest more stringent conditions under which the second law holds taking into account the missing information about the variation of the cosmological constant, i.e. the pressure. Our result offers direct evidence of no violation of the second law in the extended phase-space.

A new perspective toward Einstein’s theory of general relativity, called mimetic gravity, was suggested in [A. H. Chamseddine and V. Mukhanov, J. High Energy Phys.1311 (2013) 135] by isolating the conformal degree of freedom in a covariant fashion through a re-parametrization of the physical metric in terms of an auxiliary metric and a mimetic field. In this paper, we first derive the Friedmann equations of the Friedmann–Robertson–Walker (FRW) universe with any spatial curvature in mimetic gravity. Then, we disclose that one can always rewrite the Friedmann equations of mimetic cosmology in the form of the first law of thermodynamics, $d{E}_{\mathrm{\text{eff}}}=T_{h}d{S}_h+WdV$, on the apparent horizon. We confirm that the entropy associated with the apparent horizon in mimetic cosmology still obeys the area law of entropy which is useful in studying the thermodynamical properties of the black holes in mimetic gravity. We also examine the time evolution of the total entropy in mimetic cosmology and show that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon. Our study further supports the viability of the mimetic gravity from a thermodynamic viewpoint and provides a strong consistency check of this model.