Photon sphere and perihelion shift in weak f(T) gravity

Abstract

Among modified theories of gravity, the teleparallel f (T ) gravity is an intensively discussed model in the literature. The best way to investigate its viability is to derive observable predictions which yield evidence or constraints for the model, when compared with actual observations. In this paper we derive the photon sphere and the perihelion shift for weak f (T ) perturbations of general relativity. We consistently calculate first order teleparallel perturbations of Schwarzschild and Minkowski spacetime geometry, with which we improve and extend existing results in the literature. * Electronic address: sbahamonde@ut.ee † Electronic address: kai.flathmann@uni-oldenburg.de ‡ Electronic address: christian.pfeifer@ut.ee

Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints

“…[94] which was further pursued in Ref. [95], the idea is to assume a static spherically symmetric geometry arising due to a spherically symmetric static source of mass M . Then, one solves the field equations Eq.…”

“…The effect of α for the power-law ansatz Lagrangian on perihelion precession has been investigated in great detail in Refs. [94,95]. Here, we shall only quote the results:[108] p = 2 ∆φ = 16παM 2 r c 4 (89)…”

Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity

“…It is still unclear if the solutions found might be astrophysically interesting. One can follow a similar approach as [30] and study possible effects such as the photon sphere and perihelion shift of those solutions. Another study that can be done is to analyse the accretion process of these solutions [26,65].…”

“…The first solutions were found using perturbation theory [28,29]. In a recent paper, more general perturbed spherically symmetric solutions were found [30]. Still, there are few exact spherically symmetric solutions in modified Teleparallel gravity.…”

A metric-affine version of the Horndeski theory

“…There is currently a growing interest in the metric-affine scalar-tensor theories. [11][12][13][14][15][16][17][18][19] In most of the previously studied cases the Levi-Civita covariant derivatives of the scalar field have been replaced by the covariant derivatives with respect to the independent connection in the "minimal" way:…”