Higher Spin Field Equation in a Virtual Black Hole Metric

TL;DR

This paper extends the analysis of quantum coherence loss due to virtual black holes by solving higher spin field equations in a C metric background, providing new insights into scattering processes beyond scalar fields.

Contribution

It derives and solves the Teukolsky equations for higher spin fields in a virtual black hole metric, generalizing previous scalar field results to include fields of arbitrary spin.

Findings

Angular solutions reduce to spin-weighted spherical harmonics

Radial solutions approach hypergeometric functions near horizons

Transmission coefficients estimated for higher spin fields

Abstract

In a quantum theory of gravity, fluctuations about the vacuum may be considered as Planck scale virtual black holes appearing and annihilating in pairs. Incident fields scattering from such fluctuations would lose quantum coherence. In a recent paper (hep-th/9705147), Hawking and Ross obtained an estimate for the magnitude of this loss in the case of a scalar field. Their calculation exploited the separability of the conformally invariant scalar wave equation in the electrovac C metric background, which is justified as a sufficiently good description of a virtual black hole pair in the limit considered. In anticipation of extending this result, the Teukolsky equations for incident fields of higher spin are separated on the vacuum C metric background and solved in the same limit. With the exception of spin 2 fields, these equations are shown in addition to be valid on the electrovac C metric background. The angular solutions are found to reduce to the spin- weighted spherical harmonics, and the radial solutions are found to approach hypergeometrics close to the horizons. By defining appropriate scattering boundary conditions, these solutions are then used to estimate the transmission and reflection coefficients for an incident field of spin s. The transmission coefficient is required in order to estimate the loss of quantum coherence of an incident field through scattering off virtual black holes.