Gravitational duals from equations of state

Abstract

Holography relates gravitational theories in five dimensions to four-dimensionalquantum field theories in flat space. Under this map, the equation of state of the field theoryis encoded in the black hole solutions of the gravitational theory. Solving the five-dimensionalEinstein’s equations to determine the equation of state is an algorithmic, direct problem.Determining the gravitational theory that gives rise to a prescribed equation of state is amuch more challenging, inverse problem. We present a novel approach to solve this problembased on physics-informed neural networks. The resulting algorithm is not only data-drivenbut also informed by the physics of the Einstein’s equations. We successfully apply it totheories with crossovers, first- and second-order phase transitions