Speaker
Description
Horizon thermodynamics constitutes an interesting area of research in the context of gravitation. This rela- tionship has been extensively studied for both black hole event horizon and the cosmological apparent horizon, mainly from two perspectives, on the one hand, by considering different proposals for the horizon entropy and analyzing the additional contributions required to satisfy the first law of thermodynamics, on the other hand, by determining the entropy associated with a specific modified gravity model. In recent years, the rela- tionship between gravitation and thermodynamics has led to new developments, including the work of Shin’ ichi Nojiri et al. (2024), in which the horizon entropy was obtained for a general gravitational theory under the assumption that the first law holds. In this talk, we propose a thermodynamic reconstruction procedure that establishes a correspondence between the dynamics of modified gravity and horizon thermodynamics. The method is based on the derivation of the Misner–Sharp energy by means of the conserved Kodama current and the integration method developed by R. Cai et al. (2009). By imposing the first law of horizon thermodynamics, an equation relating the modified gravitational dynamics to the horizon entropy is obtained. An interesting feature of the proposed procedure is that it can be applied in both directions. Starting from a given modified gravity theory, it provides the horizon entropy compatible with the first law. Conversely, by assuming a physically motivated entropy, it allows the reconstruction of the corresponding gravitational theory. The procedure is particularly well suited to modified gravity theories characterized by an arbitrary function, such as f (T ) and f (Q), where the resulting equation reduces to an integral equation whose solution determines either the gravitational function or the corresponding horizon entropy.