Mass and angular momentum for the Kerr black hole in TEGR and STEGR

Abstract

We study the energy-momentum characteristics of the rotating black hole - Kerr solution of general relativity in the Teleparallel Equivalent of General Relativity (TEGR) and the Symmetric Teleparallel Equivalent of General Relativity (STEGR). The previously constructed spacetime covariant and Lorentz invariant expressions for conserved Noether currents, superpotentials and charges are used. The Noether charges describe total energy, momentum or angular momentum of gravitating system depending on a choice of the displacement vector $\xi$. To define covariant and invariant conserved quantities both in TEGR and in STEGR on needs to use external fields which are flat teleparallel connections. To determine the non-dynamical connections in TEGR and STEGR we use the unified ``turning off'' gravity principle. Besides, to analyse the Noether conserved quantities in these theories, we use the concept of ``gauges''. The gauge changing can affect the Noether conserved quantities. We highlight two ways to turn off gravity - by $M\to 0$ and by $M\to 0,a\to 0$ which gives us different gauges in TEGR and STEGR. In both kind of gauges we get the expected values of black hole mass and angular momentum. Our attempts to find gauges which could lead to a correspondence to Einstein's equivalence principle for the Kerr solution where unsuccessful both in TEGR and STEGR. However, these exercises helped us to find a related gauge for the Schwarzschild solution in STEGR that is a novelty.

References in corpus (39)

• f(T) teleparallel gravity and cosmology
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• The teleparallel equivalent of general relativity
• Cosmology in $f(Q)$ geometry
• Teleparallel Gravity: From Theory to Cosmology
• On Born-Infeld Gravity in Weitzenbock spacetime
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• "Teleparallel" Dark Energy
• On the covariance of teleparallel gravity theories
• Relativistic conservation laws and integral constraints for large cosmological perturbations
• Comparing Equivalent Gravities: common features and differences
• A new form of the Kerr solution
• Energy and angular momentum of the gravitational field in the teleparallel geometry
• New classes of modified teleparallel gravity models
• General Teleparallel Quadratic Gravity
• Energy-Momentum Complex in Møller's Tetrad Theory of Gravitation
• Regularizing role of teleparallelism
• On reference frames in spacetime and gravitational energy in freely falling frames
• Covariance properties and regularization of conserved currents in tetrad gravity
• Local symmetries and physical degrees of freedom in $f(T)$ gravity: a Dirac Hamiltonian constraint analysis
• Teleparallel theories of gravity as analogue of non-linear electrodynamics
• Kerr-Newman Solution and Energy in Teleparallel Equivalent of Einstein Theory
• Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence
• Conformally invariant teleparallel theories of gravity
• The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity
• Kerr geometry in f(T) gravity
• Charged Black Holes in Generalized Teleparallel Gravity
• Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity
• Gravitational energy of rotating black holes
• On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity
• Conserved Currents and Superpotentials in Teleparallel Equivalent of General Relativity
• Difficulties of Teleparallel Theories of Gravity with Local Lorentz Symmetry
• Conserved quantities in STEGR and applications
• Gravitational Energy of Kerr and Kerr Anti-de Sitter Space-times in the Teleparallel Geometry
• Energy of general 4-dimensional stationary axisymmetric spacetime in the teleparallel geometry
• A novel approach to autoparallels for the theories of symmetric teleparallel gravity
• Degrees of Freedom in modified Teleparallel Gravity
• The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity