# On matrix method for black hole quasinormal modes

## TL;DR

This paper surveys the matrix method's broad applicability for computing black hole quasinormal modes across various metrics, emphasizing its flexibility, efficiency, and adaptability to different equations and boundary conditions.

## Contribution

It introduces a comprehensive survey of the matrix method for black hole quasinormal modes, highlighting its versatility and potential for various metric types and coupled equations.

## Key findings

- Applicable to various background metrics
- Handles both analytic and numerical tortoise coordinates
- Efficiently balances precision and computational cost

## Abstract

In this paper, we provide a comprehensive survey of possible applications of the matrix method for black hole quasinormal modes. The proposed algorithm can generally be applied to various background metrics, and in particular, it accommodates for both analytic and numerical forms of the tortoise coordinates, as well as black hole spacetimes. Our discussions give a detailed account of different types of black hole metrics, master equations, and the corresponding boundary conditions. Besides, we argue that the method can readily be applied to cases where the master equation is a system of coupled equations. By adjusting the number of interpolation points, the present method provides a desirable degree of precision, in reasonable balance with its efficiency. The method is flexible and can easily be adopted by various distinctive physical scenarios.