A Simple Line Element to the Dilaton Gravity

TL;DR

This paper introduces a simplified line element for two-dimensional dilaton gravity, enabling easier analysis of black hole properties and addressing horizon singularities, with applications to Hawking temperature calculations.

Contribution

It presents an alternative, simplified metric form for 2D dilaton gravity that clarifies physical quantities and provides a method to remove horizon singularities.

Findings

The new metric form resembles the Schwarzschild metric.

A procedure to eliminate horizon singularity is proposed.

The Hawking temperature is derived using the new metric.

Abstract

The metric to the two-dimensional dilaton gravity can be writen in an alternative form, similar to the two-dimensional Schwarzschild metric, and allow us the identification of some quantitiies with those equivalent in the Schwarzschild solution. This new form, howewer, presents a non-physical singularity at the horizon in the same way that in the realistic four dimensional case. We show a procedure to eliminate this horizon singularity and, as an application, the resulting metric is used to obtain the associated Hawking temperature. We discuss also some differents between this metric and the Schwarzcchild one.