Schwarzschild Quantum Fluctuations from Regge-Wheeler Scattering

TL;DR

This paper introduces a numerical method for calculating quantum fluctuations in Schwarzschild spacetime by applying scattering theory techniques to Regge-Wheeler potentials, enabling efficient computation of quantum expectation values.

Contribution

It develops a multichannel variable phase approach combined with a modified WKB subtraction for efficient quantum fluctuation calculations in curved spacetime.

Findings

Efficient numerical computation of scattering data for imaginary wave numbers.

Application of scattering techniques to quantum field theory in curved spacetime.

Potential extension of methods to other wave propagation problems in curved backgrounds.

Abstract

We apply a multichannel variable phase method to scattering from Regge-Wheeler potentials. Using a reduced version of the WKB subtraction developed by Candelas and Howard, this approach allows for efficient numerical calculations of scattering data for imaginary wave number, making it possible to compute quantum expectation values in a Schwarzschild curved spacetime background through Wick rotation to the imaginary frequency axis. These scattering theory techniques are also potentially applicable to a variety of other problems involving wave propagation in curved spacetime.