Deriving the Regge-Wheeler and Zerilli equations in the general static spherically-symmetric case with Mathematica and MathTensor

TL;DR

This paper presents a computational approach using Mathematica and MathTensor to derive the Regge-Wheeler and Zerilli equations, enabling detailed stability analysis of Schwarzschild and Reissner-Nordström metrics.

Contribution

It introduces an efficient computer algebra method for tensor perturbation calculations applicable to static spherically symmetric spacetimes.

Findings

Derived the Regge-Wheeler and Zerilli equations using computer algebra.

Provided a systematic approach for stability analysis of specific metrics.

Enhanced computational tools for tensor perturbation analysis.

Abstract

An efficient approach to tensor perturbation calculations by proper use of computer algebra methods is described, reaching the sufficient generality required for a comprehensive analysis of the Schwarzschild and Reissner-Nordstroem metric stability.