https://doi.org/10.1140/epjc/s10052-024-12933-0
Regular Article – Theoretical Physics
Schwarzschild black hole and redshift rapidity: a new approach towards measuring cosmic distances
1
Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla, Puebla, Mexico
2
Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, CP 58040, Morelia, Michoacán, Mexico
3
Indian Institute of Technology, 721302, Kharagpur, India
a mmomennia@ifuap.buap.mx, momennia1988@gmail.com
Received:
24
March
2024
Accepted:
20
May
2024
Published online:
6
June
2024
Motivated by recent achievements of a full general relativistic method in estimating the mass-to-distance ratio of supermassive black holes hosted at the core of active galactic nuclei, we introduce the new concept redshift rapidity in order to express the Schwarzschild black hole mass and its distance from the Earth just in terms of observational quantities. The redshift rapidity is also an observable relativistic invariant that represents the evolution of the frequency shift with respect to proper time in the Schwarzschild spacetime. We extract concise and elegant analytic formulas that allow us to disentangle mass and distance to black holes in the Schwarzschild background and estimate these parameters separately. This procedure is performed in a completely general relativistic way with the aim of improving the precision in measuring cosmic distances to astrophysical compact objects. Our exact formulas are valid on the midline and close to the line of sight, having direct astrophysical applications for megamaser systems, whereas the general relations can be employed in black hole parameter estimation studies. We also computed the frequency shift and the redshift rapidity for emitter eccentric orbits and calculated their relative error with respect to their numerical exact value for different eccentricities.
© The Author(s) 2024
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