https://doi.org/10.1140/epjc/s10052-024-12880-w
Regular Article - Theoretical Physics
Mass, charge, and distance to Reissner–Nordström black hole in terms of directly measurable quantities
1
Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Ciudad Universitaria, CP 72570, Puebla, Puebla, Mexico
2
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla, Puebla, Mexico
3
Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, CP 58040, Morelia, Michoacán, Mexico
c mmomennia@ifuap.buap.mx, momennia1988@gmail.com
Received:
26
February
2024
Accepted:
3
May
2024
Published online:
24
May
2024
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.
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
