Wahlquist Metric Revisited

TL;DR

This paper revisits the Wahlquist metric, reformulates the wave equation for a scalar particle into Heun function form, and computes the wave reflection coefficient using two independent methods.

Contribution

It provides a new formulation of the wave equation in the Wahlquist metric as a Heun function and calculates the reflection coefficient through two different approaches.

Findings

Wave equation expressed in Heun function form.

Reflection coefficient computed for scalar waves.

Consistent results obtained from two methods.

Abstract

Here we continue studying the Wahlquist metric. We know that the wave equation written for a zero mass scalar particle in the background of this metric gives Heun type solutions. To be able to use the existing literature on Heun functions, we try to put our wave equation to the standard form for these functions. Then we calculate the reflection coefficient of a wave coming from infinity and scattered at the center using this formalism using two independent methods.