Kerr black hole in de Sitter spacetime and observational redshift: Toward a new method to measure the Hubble constant

TL;DR

This paper proposes a new method to measure the Hubble constant by analyzing redshift from particles orbiting Kerr black holes in de Sitter spacetime, linking observable redshift to spacetime parameters.

Contribution

It introduces a novel general relativistic approach connecting redshift measurements to the Hubble constant using Kerr-de Sitter black hole models.

Findings

Derived formulas for redshift in Kerr-de Sitter spacetime.

Expressed the Hubble constant in terms of observable redshift.

Provided exact relations for Schwarzschild black holes and Hubble constant.

Abstract

We extract the Hubble law by the frequency-shift considerations of test particles revolving the Kerr black hole in asymptotically de Sitter spacetime. To this end, we take into account massive geodesic particles circularly orbiting the Kerr-de Sitter black holes that emit redshifted photons towards a distant observer which is moving away from the emitter-black hole system. By considering this configuration, we obtain an expression for redshift in terms of the spacetime parameters, such as mass, angular momentum, and the cosmological constant. Then, we find the frequency shift of photons versus the Hubble constant with the help of some physically motivated approximations. Finally, some exact formulas for the Schwarzschild black hole mass and the Hubble constant in terms of the observational redshift of massive bodies circularly orbiting this black hole are extracted. Our results suggest a new independent general relativistic approach to obtaining the late-time Hubble constant in terms of observable quantities.