Mass, charge, and distance to Reissner-Nordström black hole in terms of directly measurable quantities
arXiv:2401.07112 · doi:10.1140/epjc/s10052-024-12880-w
Abstract
In this paper, we employ a general relativistic formalism and develop new theoretical tools that allow us to analytically express the mass and electric charge of the Reissner-Nordström black hole as well as its distance to a distant observer in terms of few directly observable quantities, such as the total frequency shift, aperture angle of the telescope, and redshift rapidity. Our analytic and concise formulas are valid on the midline, and the redshift rapidity is a relativistic invariant observable that represents the evolution of the frequency shift with respect to the proper time in the Reissner-Nordström spacetime. This procedure is applicable for particles undergoing circular motion around a spherically symmetric and electrically charged black hole, which is the case for accretion disks orbiting supermassive black holes hosted at the core of active galactic nuclei. Although this type of black hole is expected to be electrically neutral, our results provide a novel method to measure the electric charge of the Reissner-Nordström black hole, hence can shed some light on this claim. Besides, these results allow us to measure the mass of the black hole and its distance from the Earth, and we can employ the general formulas in black hole parameter estimation studies.
10 pages with 3 captioned figures. Comments are welcome; V2: Published version
References in corpus (10)
- Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A
- No-hair theorem for Black Holes in Astrophysical Environments
- 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
- Kerr black hole in de Sitter spacetime and observational redshift: Toward a new method to measure the Hubble constant
- Toward the Gravitational Redshift Detection in NGC 4258 and the Estimation of its Black Hole Mass-to-Distance Ratio
- Mass parameter and the bounds on redshifts and blueshifts of photons emitted from geodesic particle orbiting in the vicinity of regular black holes
- 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
- Observational redshift from general spherically symmetric black holes