Ponente
Descripción
This undergraduate thesis work consists in a deepth study of the Einstein's field equation in general relativity over a thermodynamic perspective. We study the local Minkwoski space-time $(\mathbb{R}⁴,\eta_{\mu\nu})$ evoking the usual causal horizon $t² = |\vec{x}|²$ as a thermal wall and space-like events as a thermodynamic system. In that sense, heat $Q$ is naturally the flux of energy across the horizon, temperature $T$ is associated with the thermal distribution of the Unruh effect, and entropy $S$ emerges naturally as the area of the horizon. Then, following the arguments of Jacobson in Thermodynamics of Spacetime: The Einstein's Equation fo State (1995) it can be shown that the relation $\delta Q = TdS$ implies $T_{\mu\nu}\propto R_{\mu\nu} + fg_{\mu\nu}$, from where the Einstein's field equation is straighforward. In this thesis we explore quantum field theory in curved space-times, Raychaudhuri's equation, Shannon entropy and laws of black hole mechanics given by Hawking, Carter and Bardeen in order to achieve the deduction above.
