Thermodynamical aspects of gravity: from event horizon to emergent gravity

In this thesis we explore various aspects of horizon thermodynamics and its relation with gravitational dynamics. We start with addressing the issue about the region of origin of the Hawking quanta, using both a heuristic argument and a detailed study of the renormalized stress energy tensor (RSET). We present compelling evidence that the Hawking quanta originate from what might be called a quantum atmosphere around the black hole with energy density and fluxes of particles peaked at about 4M, running contrary to the popular belief that these originate from the ultra high energy excitations very close to the horizon. We then study the behavior of the effective Hawking temperature as perceived by a free falling observer. We compute the energy density using this temperature and compare it with the energy density obtained from RSET measured by the same observer and notice a discrepancy. We further compute the adiabaticity of this temperature and try to explain the reason for this discrepancy. Next we move on to thermodynamics of local causal horizon (LCH) and in particular focus on derivation of equations of motion for theories beyond general relativity as an equation of state. Jacobson showed that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. The extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher-curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy. Here we derive a new entropy density, closely related to the Noetheresque form, such that the field equation of any diffeomorphism-invariant metric theory of gravity can be obtained by imposing the Clausius relation on a small patch of a local causal horizon. Finally, we shall demonstrate how the equation of state derivation can be carried on to theories having torsion as an independent degree of freedom, such as Einstein–Cartan gravity, by using the irreversible Clausius equation.