Light's Bending Angle in the Equatorial Plane of a Kerr Black Hole

TL;DR

This paper derives an explicit formula for the bending angle of light in the equatorial plane of a Kerr black hole, showing how spin affects light deflection differently for direct and retrograde orbits, impacting gravitational lensing.

Contribution

It provides a detailed, spin-dependent expression for light bending angles in Kerr black holes, highlighting the asymmetry introduced by black hole spin on gravitational lensing.

Findings

Bending angle depends on the light's direction relative to black hole spin.

Higher spins cause more pronounced differences in light deflection.

Spin influences the apparent position of lensed images.

Abstract

We present here a detailed derivation of an explicit spin-dependent expression for the bending angle of light as it traverses in the equatorial plane of a spinning black hole. We show that the deflection produced in the presence of the black hole angular momentum explicitly depends on whether the motion of the light ray is in the direction, or opposite to the spin. Compared to the zero-spin Schwarzschild case, the bending angle is greater for direct orbits, and {\em smaller} for retrograde orbits, confirming our physical intuition about the loss of left-right symmetry from a lensing perspective. In addition, we show that for higher spins, the effect is more pronounced resulting in tighter winding of direct orbits with respect to the axis of rotation, and a higher degree of unwinding of retro orbits. A direct consequence of this effect is a shift in image positions in strong gravitational lensing.