Numerical Solutions of Dilaton Gravity and the Semi-Classical Singularity

TL;DR

This paper numerically solves a two-dimensional dilaton gravity model with quantum corrections, revealing how semi-classical effects induce singularities and affect spacetime structure.

Contribution

It provides the first numerical solutions of semi-classical dilaton gravity with quantum matter corrections, analyzing singularity formation and spacetime matching.

Findings

Semi-classical theory limits the dilaton field below a critical value.

Solutions exist for both sub- and super-critical dilaton fields.

Discussion on matching spacetime across singularities in semi-classical gravity.

Abstract

A general homogeneous two dimensional dilaton gravity model considered recently by Lemos and S\` a, is given quantum matter Polyakov corrections and is solved numerically for several static, equilibrium scenarii. Classically the dilaton field ranges the whole real line, whereas in the semi-classical theory, with the usual definition, it is always below a certain critical value at which a singularity appears. We give solutions for both sub- and super-critical dilaton field. The pasting together of the spacetime on both sides of a singularity in semi-classical planar general relativity is discussed.