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

15 pages with 4 captioned figures. Comments are welcome; V2: Minor changes to match the published version

References in corpus (16)

• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• The Megamaser Cosmology Project. XIII. Combined Hubble constant constraints
• Equatorial circular orbits in the Kerr-de Sitter spacetimes
• Precise analytic treatment of Kerr and Kerr-(anti) de Sitter black holes as gravitational lenses
• The Megamaser Cosmology Project. VI. Observations of NGC 6323
• Deriving accurate peculiar velocities (even at high redshift)
• The Megamaser Cosmology Project.IX. Black hole masses for three maser galaxies
• Obtaining mass parameters of compact objects from red-blue shifts emitted by geodesic particles around them
• The Megamaser Cosmology Project. XI. A geometric distance to CGCG 074-064
• Dynamics of Particles Near Black Hole with Higher Dimensions
• Toward the Gravitational Redshift Detection in NGC 4258 and the Estimation of its Black Hole Mass-to-Distance Ratio
• A general relativistic mass-to-distance ratio for a set of megamaser AGN black holes
• Probing a polymerized black hole with the frequency shifts of photons
• Redshift of light emitted by particles orbiting a black hole immersed in a strong magnetic field
• How to Detect Inclined Water Maser Disks (and Possibly Measure Black Hole Masses)

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