Dynamical evolution of the electromagnetic perturbation with Weyl corrections

TL;DR

This paper derives the master equation for electromagnetic perturbations with Weyl corrections in four-dimensional black hole spacetime and investigates their dynamical evolution, revealing parity-dependent effects and critical behavior influenced by the Weyl correction parameter.

Contribution

It introduces the first master equation for electromagnetic perturbations with Weyl corrections in four-dimensional black holes and analyzes their evolution numerically.

Findings

Odd parity perturbations grow exponentially below a critical Weyl parameter.

Even parity perturbations always decay regardless of the Weyl parameter.

Weyl corrections significantly influence electromagnetic wave dynamics in black hole backgrounds.

Abstract

We present firstly the master equation of an electromagnetic perturbation with Weyl correction in the four-dimensional black hole spacetime, which depends not only on the Weyl correction parameter, but also on the parity of the electromagnetic field. It is quite different from that of the usual electromagnetic perturbation without Weyl correction in the four-dimensional spacetime. And then we have investigated numerically the dynamical evolution of the electromagnetic perturbation with Weyl correction in the background of a four-dimensional Schwarzschild black hole spacetime. Our results show that the Weyl correction parameter $\alpha$ and the parities imprint in the wave dynamics of the electromagnetic perturbation. For the odd parity electromagnetic perturbation, we find it grows with exponential rate if the value of $\alpha$ is below the negative critical value $\alpha_c$. However, for the electromagnetic perturbation with even parity, we find that there does not exist such a critical threshold value and the electromagnetic field always decays in the allowed range of $\alpha$.