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The Gravitational Energy–Momentum Density of Radially Accelerated Observers in Schwarzschild Spacetime
Author(s) -
Formiga J. B.
Publication year - 2020
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.201900507
Subject(s) - physics , spacetime , gravitational energy , classical mechanics , quantum field theory in curved spacetime , schwarzschild radius , gravity probe a , linearized gravity , gravitation , schwarzschild metric , spherically symmetric spacetime , general relativity , quantum mechanics , quantum gravity , quantum
A hybrid machinery that is useful for calculations in teleparallel theories when the spacetime is spherically symmetric is developed. Using this machinery, the gravitational energy–momentum tensor density of the Schwarzschild spacetime is evaluated in a frame adapted to observers that accelerate in the radial direction. The energy density, the total energy, and the gravitational energy‐momentum flux are obtained. The regularization procedure and the limit where gravity is absent is discussed. It turns out that the regularized energy and energy–momentum flux are consistent in the whole spacetime. The continuity equation for the gravitational energy–momentum also holds for any point outside the black hole. Finally, the static and freely falling cases are discussed. It is found that a static observer measures a negative gravitational energy density, while a freely falling one measures a vanishing density.