Optical geometry across the horizon

TL;DR

This paper extends optical geometry formalism to finite regions of spherically symmetric spacetimes, including across black hole horizons, enabling analysis of photon motion, inertial forces, and gyroscope precession with a consistent embedding.

Contribution

It applies a generalized optical geometry formalism to finite regions of spherically symmetric spacetimes, including across horizons, with a non-static reference congruence for consistent embeddings.

Findings

Optical geometry formalism can be applied across black hole horizons.

A specific choice of reference congruence yields a time-independent embedded geometry.

Analysis of photon trajectories and inertial effects in this framework.

Abstract

In a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to a finite four-volume of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework.