Generalization of Equatorial Impact-Parameter Formulas for Rotating 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.