Back-reaction of a conformal field on a three-dimensional black hole

TL;DR

This paper calculates the first-order geometric corrections to a (2+1)-dimensional black hole caused by a conformal scalar field's back-reaction, providing a semiclassical solution and thermodynamic modifications.

Contribution

It presents the first perturbative analysis of back-reaction effects of a conformal scalar field on a 3D black hole, deriving a new semiclassical solution with thermodynamic insights.

Findings

Derived the renormalized stress-energy tensor for the scalar field.

Obtained a static, circularly symmetric black hole solution with back-reaction.

Computed corrections to black hole thermodynamic quantities.

Abstract

The first order corrections to the geometry of the (2+1)-dimensional black hole due to back-reaction of a massless conformal scalar field are computed. The renormalized stress energy tensor used as the source of Einstein equations is computed with the Green function for the black-hole background with transparent boundary conditions. This tensor has the same functional form as the one found in the nonperturbative case which can be exactly solved. Thus, a static, circularly symmetric and asymptotically anti-de Sitter black hole solution of the semiclassical equations is found. The corrections to the thermodynamic quantities are also computed.