Analysis of scalar fields with series convolution

TL;DR

This paper explores methods for solving wave equations in curved spacetimes when closed-form solutions are unavailable, focusing on series convolution techniques with special functions to obtain analytical solutions.

Contribution

It introduces a novel approach of using series convolution with special functions to analyze scalar fields in complex wave equations.

Findings

Series convolution can effectively handle functions preventing closed-form solutions.

Analytical solutions can be derived using series expansions and transformations.

The method applies to wave equations involving special functions in curved spacetimes.

Abstract

Wave equations for some curved spacetimes may involve functions that prevent a solution in a closed form. In some cases, these functions can be eliminated by transformations and the solutions can be found analytically. In the cases where such transformations are not available, the infinite series expansions of these functions can be convoluted with the power series solution ansatz. We study such an example where the solution is based on a special function.