Metric of a tidally distorted, nonrotating black hole

TL;DR

This paper derives an explicit metric for a nonrotating black hole under tidal distortion in a coordinate system that penetrates the horizon, enabling analysis of horizon properties and tidal interactions.

Contribution

It introduces a new light-cone coordinate metric for tidally distorted black holes, valid near the horizon, with explicit expressions for horizon properties and tidal effects.

Findings

Metric expressed as an expansion in (r/R)^n up to order 4

Provides formulas for horizon surface gravity

Calculates mass and angular momentum transfer rates

Abstract

The metric of a tidally distorted, nonrotating black hole is presented in a light-cone coordinate system that penetrates the event horizon and possesses a clear geometrical meaning. The metric is expressed as an expansion in powers of r/R << 1, where r is a measure of distance from the black hole and R is the local radius of curvature of the external spacetime; this is assumed to be much larger than M, the mass of the black hole. The metric is calculated up to a remainder of order (r/R)^4, and it depends on a family of tidal gravitational fields which characterize the hole's local environment. The coordinate system allows an easy identification of the event horizon, and expressions are derived for its surface gravity and the rates at which the tidal interaction transfers mass and angular momentum to the black hole.