Agujeros negros tridimensionales acoplados a campos conformes

Abstract

A three dimensional black hole solution of Einstein equations with negative cosmological constant coupled to a conformal scalar field is given. The solution is static, circularly symmetric, asymptotically anti-de sitter and nonperturbative in the conformal field. The curvature tensor is singular at the origin while the scalar field is regular everywhere. The condition that the Euclidean geometry be regular at the horizon fixes the temperature to be 7 - ffi. u"inc the Hamiltonian formulation including boundary terms of the Euclidean action, the entropy is found to be J of the standa¡d value (|,4), and in agreement with the first law of thermodynamics. Morever, it is shown that ihe system is unstable against linear circularly symmetric perturbations. In the last chapter, the first order correction in ñ to the entropy and temperature of three dimensional BTZ black hole due to back-reaction of a massless conformal scalar fie1d is computed. we consider the re,ormalized stress energy tensor associated with the scalar field as source of Einstein equations. These semiclassica,l equations are solved by a static, circularly symmetric and asymptotically anti-de sitter black hole solution. The temperature and entropy of this perturbed black hole are determinecl using the standa¡d Euclidean rnethocl. The cleviations of these thermodynamical quantities respect to BTZ ones give the back-reaction corrections.