On the Classical Solutions of the Perturbed, Massless Wave Equation with Singular Potential

TL;DR

This paper analyzes classical solutions to the perturbed massless wave equation with singular potentials across various dimensions, employing separation of variables and exploring special cases like even dimensions and the 2D Cauchy problem.

Contribution

It provides explicit classical solutions for the perturbed wave equation with singular potentials in arbitrary dimensions, including special solutions for even dimensions and the 2D case.

Findings

Classical solutions derived for any dimension n.

Special solutions identified for even n.

Analysis of the 2D Cauchy problem included.

Abstract

This paper discusses the solutions to the perturbed wave equation containing a singular potential term in the Lorentzian metric. We present the classical solution to the problem using the separation of variables method for any dimension, n. Special solutions are obtained for even n's and properties of these solutions are discussed. Finally, we also consider the solution to the Cauchy problem for the case n=2.