Comparison between the Gravitational Redshift in the Kerr and Schwarzschild Fields

The Schwarzschild and Kerr metrics are solutions of Einstein field equations of general relativity representing the gravitational fields of a non-rotating spherical mass and a rotating black hole respectively. Unlike the Kerr field, the gravitational redshift in the Schwarzschild field is well known. We employ the concept of stationary clocks to derive the gravitational redshift in the Kerr field demonstrating that frame dragging plays no role. We then calculate the Kerr gravitational redshift for the earth, sun, white dwarfs and neutron stars and compare them with the Schwarzschild gravitational redshift, showing that the gravitational redshift on earth and from the sun does not differ from the Schwarzschild gravitational redshift. For extreme cases of rapidly rotating white dwarfs and neutron stars there is a significant difference between the two gravitational redshifts. Unlike the Schwarzschild gravitational redshift, the Kerr gravitational redshift has to date not been put on a firm observational basis. We point out that the gravitational redshift in the Kerr field possess a latitude dependency, which cannot be confirmed through solar or terrestrial observations, but can be on rapidly rotating white dwarfs and neutron stars

Redshift of radiation of a point-like source moving in the external Kerr field

The method of calculation of redshift of light from a point-like source that moves in the gravitational field of the Kerr black hole as a function of time of observation is developed. The widely presented in literature methods for solving the boundary problem are based on a numerical selection of parameters of geodesics. In contrast, the proposed method is based on approximate analytical expressions for isotropic geodesics in the Kerr metric. The proposed method is illustrated by the example of a model problem with parameters corresponding to real stars moving in the immediate vicinity of a supermassive black hole located in the Center of our Galaxy. The same example shows the efficiency and good accuracy of this method.

A pseudo-Newtonian description of any stationary space-time

Since the first investigations into accretion onto black holes, astrophysicists have proposed effective Newtonian-like potentials to mimic the strong-field behavior of matter near a Schwarzschild or Kerr black hole. On the other hand, the fields of neutron stars or black holes in many of the alternative gravity theories differ from the idealized Schwarzschild or Kerr field which would require a number of new potentials. To resolve this, we give a Newtonian-like Hamiltonian which almost perfectly mimics the behavior of test particles in any given stationary space-time. The properties of the Hamiltonian are excellent in static space-times such as the Schwarzschild black hole, but become worse for space-times with gravito-magnetic or dragging effects such as near the Kerr black hole.