Schwarzschild Quantum Fluctuations from Regge-Wheeler Scattering

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.

12 pages, 4 .eps figures; v2: fixed typos, added example calculation; v3: fixed typo (correct sign in Eq. A7); v4: fixed typo (missing factor in Eq. 28), added clarification of techniques for numerical calculation

References in corpus (12)

• Sinc approximation of algebraically decaying functions
• Bounding the greybody factors for Schwarzschild black holes
• Achronal averaged null energy condition
• Fermion scattering by a Schwarzschild black hole
• Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes
• WKB analysis of the Regge-Wheeler equation down in the frequency plane
• A holographic proof of the averaged null energy condition
• Averaged null energy condition in spacetimes with boundaries
• Averaged null energy condition in a classical curved background
• A scattering approach to some aspects of the Schwarzschild Black Hole
• Variable Phase S-Matrix Calculations for Asymmetric Potentials and Dielectrics
• Casimir Energies of Periodic Dielectric Gratings