Cosmological redshift of a Schwarzschild-de Sitter black hole: Towards estimating the Hubble constant

TL;DR

This paper develops a relativistic model to estimate black hole parameters and the Hubble constant by analyzing photon redshifts in accretion disks within expanding universe frameworks, applied to megamaser galaxy data.

Contribution

It introduces a novel general relativistic approach incorporating cosmic expansion into black hole parameter estimation from astrophysical observations.

Findings

Cosmic expansion influences photon frequency-shifts in black hole environments.

Bayesian inference yields estimates for Hubble constant and black hole parameters.

The model provides a relativistic alternative to the standard Hubble law.

Abstract

In this work we estimate the parameters of several astrophysical black holes hosted at the core of active galactic nuclei by studying the kinematics of test objects in their accretion disk. First, we derive expressions for the redshift and blueshift of photons emitted by a massive particle circularly orbiting a Schwarzschild-de Sitter black hole, and detected by a distant receding observer. The frequency-shift depends on the mass and distance of the black hole, the orbital radius of the photon source, as well as the Hubble constant, directly relating these quantities to astrophysical observables, namely, the redshift and the angular position of the emitting particle on the sky. We apply for the first time this theoretical model, which accounts for the universe expansion through the Schwarzschild-de Sitter metric, to real astrophysical systems using megamaser galaxies within the Hubble flow, namely UGC 3789, NGC 5765b, NGC 6264, NGC 6323, and CGCG 074-064. Bayesian inference based on Markov Chain Monte Carlo methods is employed to estimate the mass-to-distance ratio, the product of the Hubble constant with the distance, and the black hole angular position. Additionally, by assuming a Gaussian prior on the Hubble constant, the mass, distance, and the Hubble constant are also estimated. Furthermore, we find that cosmic expansion is embedded in the gravitational contribution of the frequency-shift within this spacetime metric. Therefore, our results introduce a general relativistic framework that accounts for cosmic expansion and differs from the standard empirical Hubble law.