On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity

Abstract

We examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field $\xi$ and we consider two different options where $\xi$ is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained generalised freely falling frame with an arbitrary initial velocity. We also demonstrate how to determine the inertial spin connection for various tetrads used in our calculations, and find a certain ambiguity in the "switching off" gravity method where different tetrads can share the same inertial spin connection.

arXiv comment39 pages

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Cited by in corpus (14)

• Teleparallel Gravity: From Theory to Cosmology
• Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions
• Deflection angle and lensing signature of covariant f(T) gravity
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Conserved quantities in STEGR and applications
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• On the gravitational energy problem and the energy of photons
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• Bulk Action Growth for Holographic Complexity
• Phase space structure of symmetric teleparallel theory of gravity
• On the total energy conservation of the Alcubierre spacetime
• Mass and angular momentum for the Kerr black hole in TEGR and STEGR
• The irreducible mass of a regular rotating black hole