Two-Dimensional Black Holes and Planar General Relativity

TL;DR

This paper derives a new two-dimensional gravitational theory from the Einstein-Hilbert action, showing it admits black holes and dilatons, and relates to four-dimensional General Relativity, offering insights into lower-dimensional models.

Contribution

It introduces a novel 1+1 dimensional action equivalent to planar symmetry in General Relativity, connecting two-dimensional models with four-dimensional black hole solutions.

Findings

Two-dimensional theory admits black holes and dilatons.

Solutions also solve Einstein's equations in four dimensions.

The theory links 2D string theories with four-dimensional gravity.

Abstract

The Einstein-Hilbert action with a cosmological term is used to derive a new action in 1+1 spacetime dimensions. It is shown that the two-dimensional theory is equivalent to planar symmetry in General Relativity. The two-dimensional theory admits black holes and free dilatons, and has a structure similar to two-dimensional string theories. Since by construction these solutions also solve Einstein's equations, such a theory can bring two-dimensional results into the four-dimensional real world. In particular the two-dimensional black hole is also a black hole in General Relativity.