On black holes in teleparallel torsion theories of gravity

Abstract

We first present an overview of the Schwarzschild vacuum spacetime within general relativity, with particular emphasis on the role of scalar polynomial invariants and the null frame approach (and the related Cartan invariants), that justifies the conventional interpretation of the Schwarzschild geometry as a black hole spacetime admitting a horizon (at $r=2M$ in Schwarzschild coordinates) shielding a singular point at the origin. We then consider static spherical symmetric vacuum teleparallel spacetimes in which the torsion characterizes the geometry, and the scalar invariants of interest are those constructed from the torsion and its (covariant) derivatives. We investigate the Schwarzschild-like spacetime in the teleparallel equivalent of general relativity and find that the torsion scalar invariants (and, in particular, the scalar $T$) diverge at the putative ``Schwarzschild'' horizon. In this sense the resulting spacetime is {\em not} a black hole spacetime. We then briefly consider the Kerr-like solution in the teleparallel equivalent of general relativity and obtain a similar result. Finally, we investigate static spherically symmetric vacuum spacetimes within the more general $F(T)$ teleparallel gravity and show that if a such a geometry admits a horizon, then the torsion scalar $T$ necessarily diverges there; consequently in this sense such a geometry also does {\em not} represent a black hole.

25 pages, no figures

References in corpus (19)

• Modified teleparallel gravity: inflation without inflaton
• Teleparallel Gravity: From Theory to Cosmology
• Static spherically symmetric black holes in weak f(T)-gravity
• Symmetry and Equivalence in Teleparallel Gravity
• Approaches to spherically symmetric solutions in f(T) gravity
• Geometric Horizons
• Identification of black hole horizons using scalar curvature invariants
• Exploring Axial Symmetry in Modified Teleparallel Gravity
• Spherically symmetric vacuum solutions in 1-Parameter New General Relativity and their phenomenology
• Scalarized Black Holes in Teleparallel Gravity
• A frame based approach to computing symmetries with non-trivial isotropy groups
• Symmetric Teleparallel Geometries
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Thick accretion disk configurations in the Born-Infeld teleparallel gravity
• Spherically symmetric teleparallel geometries
• Transforming singular black holes into regular black holes sourced by nonlinear electrodynamics
• General Teleparallel Modifications of Schwarzschild Geometry
• Static spherically symmetric solutions in New General Relativity
• Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity

Cited by in corpus (1)

• On black holes in new general relativity