General Teleparallel Modifications of Schwarzschild Geometry

Abstract

Teleparallel theories of gravity are described in terms of the tetrad of a metric and a flat connection with torsion. In this paper, we study spherical symmetry in a modified teleparallel theory of gravity which is based on an arbitrary function of the five possible scalars constructed from the irreducible parts of torsion. This theory is a generalisation of the so-called New General Relativity theory. We find that only two scalars are different to zero in spherical symmetry and we solve the corresponding field equations analytically for conformal Teleparallel gravity, and then perturbatively around Schwarzschild geometry for the general perturbative theory around GR. Finally, we compute phenomenological effects from the perturbed solutions such as the photon sphere, perihelion shift, Shapiro delay, and the light deflection. We find their correspondent correction to the standard GR contribution and their dependence on the three model parameters.

17 pages; v2 has some new additions matching the published version

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• Deflection angle and lensing signature of covariant f(T) gravity
• Scalarized Black Holes in Teleparallel Gravity
• Testing Born-Infeld $f(T)$ teleparallel gravity through Sgr A${}^{\star }$ observations
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Thick accretion disk configurations in the Born-Infeld teleparallel gravity
• Gravitational Wave Propagation and Polarizations in the Teleparallel analog of Horndeski Gravity
• On black holes in teleparallel torsion theories of gravity
• On black holes in new general relativity
• Interference effects and modified Born rule in the presence of torsion