# Detect black holes using photons for coupling model of electromagnetic and gravitational fields

## TL;DR

This paper proposes an effective spacetime approach to detect black holes using photons affected by electromagnetic-gravitational coupling, revealing modifications in horizon area and entropy while preserving key thermodynamic properties.

## Contribution

It introduces an effective spacetime framework for analyzing black holes with coupled electromagnetic and gravitational fields, addressing photon propagation issues and entropy contributions.

## Key findings

- Event horizon and temperature remain unchanged.
- Horizon area and Bekenstein-Hawking entropy are modified.
- Total entropy includes electromagnetic coupling contributions.

## Abstract

For a model of the electromagnetic field coupled to Weyl tensor, Maxwell equations are modified and photons at low frequencies no longer propagate along light cone. If we detect a black hole using these photons, some difficulties appear because we can not determine the position of event horizon which is defined by null surface. To overcome these difficulties, the simplest way may be an effective description by introducing an effective spacetime in which the photons propagate along the light cone. Then, we find, comparing the results with those of the original spacetime, that the event horizon and temperature do not change, but the area of the event horizon and Bekenstein-Hawking entropy become different. We show that the total entropy for this system, which is still the same as that of original spacetime, consists of two parts, one is the Bekenstein-Hawking entropy and the other is the entropy arising from the coupling of electromagnetic field and Weyl tensor. We also present the effective descriptions for the Smarr relation and first law of thermodynamics.