Generalization of Equatorial Impact-Parameter Formulas for Rotating Bodies

TL;DR

This paper generalizes impact-parameter formulas for rotating bodies in all metric theories of gravity, aiding the study of black holes and neutron stars by extending previous Kerr and spherical formulas.

Contribution

It provides a unified derivation of impact-parameter formulas for any rotating body in all metric theories, extending prior Kerr and spherical results.

Findings

Derived impact-parameter formulas for co-rotating and contra-rotating cases.

Applicable to all metric theories of gravity, including general relativity.

Generalizes previous formulas for Kerr and spherical bodies.

Abstract

This paper computes co-rotating and contra-rotating impact-parameter formulas in the plane of symmetry for any plane symmetric and axisymmetric rotating body in all metric theories of gravity, including general relativity. Impact-parameter formulas are useful to compute the appearance of accreting black holes, neutron stars, and other emitting or reflecting matter near a gravitationally compact rotating body. These rotating-body impact-parameter formulas generalize similar impact-parameter formulas for the Kerr case derived by Bardeen and coworkers in 1972, and another general-metric formula for the spherical case published by Bodenner and Will in 2003.