Frame dragging and bending of light in Kerr and Kerr–(anti) de Sitter spacetimes

Abstract

The equations of general relativity in the form of time-like 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 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 time-like 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 (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.