Frame dragging and bending of Light in Kerr and Kerr-(anti) de Sitter spacetimes

TL;DR

This paper derives exact solutions for geodesics in Kerr and Kerr-(anti) de Sitter spacetimes, applying them to analyze frame dragging, light bending, and orbital precession around rotating black holes, including the galactic center.

Contribution

It provides new exact solutions for null and timelike geodesics in Kerr spacetimes with cosmological constant, enabling precise calculations of gravitational effects.

Findings

Exact expression for photon deflection angle in Kerr spacetime

Analytical formula for perihelion precession in Kerr spacetime

Calculation of frame dragging effects for photons near galactic center

Abstract

The equations of general relativity in the form of timelike and null geodesics that describe motion of test particles and photons in Kerr spacetime are solved exactly including the contribution from the cosmological constant. We then perform a systematic application of the exact solutions obtained to the following cases. The exact solutions derived for null, spherical, polar and non-polar orbits are applied for the calculation of frame dragging (Lense-Thirring effect) for the orbit of a photon around the galactic centre, assuming that the latter is a Kerr black hole for various values of the Kerr parameter including those supported by recent observations. Unbound null polar orbits are investigated, and an analytical expression for the deviation angle of a polar photon orbit from the gravitational Kerr field is derived. In addition, we present the exact solution for timelike and null equatorial orbits. In the former case, we derive an analytical expression for the precession of the point of closest approach (perihelion, periastron) for the orbit of a test particle around a rotating mass whose surrounding curved spacetime geometry is described by the Kerr field. In the latter case, we calculate an exact expression for the deflection angle for a light ray in the gravitational field of a rotating mass (the Kerr field). We apply this calculation for the bending of light from the gravitational field of the galactic centre for various values of the Kerr parameter and the impact factor.