On the normalization of Killing vectors and energy conservation in two-dimensional gravity

TL;DR

This paper demonstrates that in a specific 2D dilaton gravity model, energy conservation imposes an unconventional normalization on the Killing vector, affecting the calculation of Hawking temperature.

Contribution

It reveals the necessity of an unusual Killing vector normalization for energy conservation in 2D dilaton gravity and computes the resulting Hawking temperature.

Findings

Energy conservation dictates a non-standard Killing vector normalization.

The Hawking temperature is derived using this normalization.

The result impacts the understanding of thermodynamics in 2D gravity.

Abstract

We explicitly show that, in the context of a recently proposed 2D dilaton gravity theory, energy conservation requires the ``natural'' Killing vector to have, asymptotically, an unusual normalization. The Hawking temperature $T_H$ is then calculated according to this prescription.