Laws Governing Isolated Horizons: Inclusion of Dilaton Couplings

TL;DR

This paper extends the isolated horizon framework to include dilaton couplings, establishing local definitions of horizon parameters and proving the zeroth and first laws without relying on asymptotic infinity.

Contribution

It introduces a tensorial formulation of isolated horizons with dilaton couplings, enabling local horizon mechanics without reference to infinity.

Findings

Established the zeroth law for dilaton-coupled horizons.

Proved the first law using local horizon parameters.

Formulated the entire framework tensorially, avoiding spinor methods.

Abstract

Mechanics of non-rotating black holes was recently generalized by replacing the static event horizons used in standard treatments with `isolated horizons.' This framework is extended to incorporate dilaton couplings. Since there can be gravitational and matter radiation outside isolated horizons, now the fundamental parameters of the horizon, used in mechanics, must be defined using only the local structure of the horizon, without reference to infinity. This task is accomplished and the zeroth and first laws are established. To complement the previous work, the entire discussion is formulated tensorially, without any reference to spinors.