The Effect of Gravitational Tidal Forces on Renormalized Quantum Fields

TL;DR

This paper explores how gravitational tidal forces influence renormalized quantum fields in curved spacetime, revealing phenomena like local amplitude increases and potential unitarity violations, and generalizes the optical theorem to curved spacetime.

Contribution

It introduces a generalized optical theorem applicable in curved spacetime and demonstrates how gravitational tidal forces affect quantum field dressing and undressing, with implications for phenomena near black holes.

Findings

Photon amplitude can locally increase due to tidal forces.

A generalized optical theorem maintains unitarity in curved spacetime.

Photon undressing occurs near black hole singularities.

Abstract

The effect of gravitational tidal forces on renormalized quantum fields propagating in curved spacetime is investigated and a generalisation of the optical theorem to curved spacetime is proved. In the case of QED, the interaction of tidal forces with the vacuum polarization cloud of virtual e^+ e^- pairs dressing the renormalized photon has been shown to produce several novel phenomena. In particular, the photon field amplitude can locally increase as well as decrease, corresponding to a negative imaginary part of the refractive index, in apparent violation of unitarity and the optical theorem. Below threshold decays into e^+ e^- pairs may also occur. In this paper, these issues are studied from the point of view of a non-equilibrium initial-value problem, with the field evolution from an initial null surface being calculated for physically distinct initial conditions and for both scalar field theories and QED. It is shown how a generalised version of the optical theorem, valid in curved spacetime, allows a local increase in amplitude while maintaining consistency with unitarity. The picture emerges of the field being dressed and undressed as it propagates through curved spacetime, with the local gravitational tidal forces determining the degree of dressing and hence the amplitude of the renormalized quantum field. These effects are illustrated with many examples, including a description of the undressing of a photon in the vicinity of a black hole singularity.