https://doi.org/10.1140/epjc/s10052-024-13028-6
Regular Article - Theoretical Physics
Relativistic periastron advance beyond Einstein theory: analytical solution with applications
1
Dipartimento di Fisica “E.R. Caianiello”, Università degli Studi di Salerno, Via G. Paolo II, 84084, Fisciano, Italy
2
Istituto Nazionale di Fisica Nucleare (INFN), Gruppo collegato di Salerno, Via G. Paolo II, 84084, Fisciano, Italy
a
antonio.tedesco.dt12@gmail.com
Received:
11
December
2023
Accepted:
14
June
2024
Published online:
13
August
2024
We find a new solution to calculate the orbital periastron advance of a test body subject to a central gravitational force field for relativistic theories and models beyond Einstein. This analitycal formula has general validity that includes all the post-Newtonian (PN) contributions to the dynamics and is useful for high-precision gravitational tests. The solution is directly applicable to corrective potentials of various forms, without the need for numerical integration. Later, we apply it to the scalar tensor fourth order gravity (STFOG) and noncommutative geometry, providing corrections to the Newtonian potential of Yukawa-like form 
, and we conduct the first analysis involving all the PN terms for these theories. The same work is performed with a Schwarzschild geometry perturbed by a Quintessence Field, leading to a power-law potential 
. Finally, by using astrometric data of the Solar System planetary precessions and those of the S2 star around Sgr A*, we infer new theoretical constraints and improvements in the bounds for 
. The resulting simulated orbits turn out to be compatible with general relativity.
The original online version of this article was revised: The arrangement of Figures 6, 7, 8, 9, and 10 has been updated, and the figures have been enlarged.
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