https://doi.org/10.1140/epjp/s13360-022-02803-7
Regular Article
Red and blue shift in spherical and axisymmetric spacetimes and astrophysical constraints
1
Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri 9, 62032, Camerino, Italy
2
Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via Alessandro Pascoli 23c, 06123, Perugia, Italy
3
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy
4
Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, 050040, Almaty, Kazakhstan
5
Dipartimento di Matematica e Fisica, Università degli Studi “Roma Tre”, Via della Vasca Navale, Roma, Italy
6
Istituto Nazionale di Fisica Nucleare (INFN), Laboratori Nazionali di Frascati, 00044, Frascati, Italy
Received:
6
April
2022
Accepted:
2
May
2022
Published online:
21
May
2022
We compute the red and blue shifts for astrophysical and cosmological sources. In particular, we consider low, intermediate and high gravitational energy domains. Thereby, we handle the binary system Earth–Mars as low energy landscape whereas white dwarfs and neutron stars as higher energy sources. To this end, we take into account a spherical Schwarzschild–de Sitter spacetime and an axially symmetric Zipoy–Voorhees metric to model all the aforementioned systems. Feasible outcomes come from modeling neutron stars and white dwarfs with the Zipoy–Voorhees metric, where quadrupole effects are relevant, and framing solar system objects using a Schwarzschild–de Sitter spacetime. In the first case, large 
parameters seem to be favorite, leading to acceptable bounds mainly for neutron stars. In the second case, we demonstrate incompatible red and blue shifts with respect to lunar and satellite laser ranging expectations, once the cosmological constant is taken to Planck satellite’s best fit. To heal this issue, we suggest coarse-grained experimental setups and propose Phobos for working out satellite laser ranging in order to get more suitable red and blue shift intervals, possibly more compatible than current experimental bounds. Implications to cosmological tensions are also debated.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
