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Energy and angular momentum of charged rotating black holes
General Relativity and Quantum Cosmology · Submitted 3 Jan 1995
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that the pseudotensors of Einstein, Tolman, Landau and Lifshitz, Papapetrou, and Weinberg (ETLLPW) give the same distributions of energy, linear momentum and angular momentum, for any Kerr-Schild metric.
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We show that the pseudotensors of Einstein, Tolman, Landau and Lifshitz, Papapetrou, and Weinberg (ETLLPW) give the same distributions of energy, linear momentum and angular momentum, for any Kerr-Schild metric. This result generalizes a previous work by G\"urses and G\"ursey that dealt only with the pseudotensors of Einstein and Landau and Lifshitz. We compute these distributions for the Kerr-Newman and Bonnor-Vaidya metrics and find reasonable results. All calculations are performed without any approximation in Kerr-Schild Cartesian coordinates. For the Reissner-Nordstr\"{o}m metric these definitions give the same result as the Penrose quasi-local mass. For the Kerr black hole the entire energy is confined to its interior whereas for the Kerr-Newman black hole, as expected, the energy is shared by its interior as well as exterior. The total energy and angular momentum of the Kerr-Newman black hole are $M$ and $ M a$, respectively ($M$ is the mass parameter and $a$ is the rotation parameter). The energy distribution for the Bonnor-Vaidya metric is the same as the Penrose quasi-local mass obtained by Tod.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that the pseudotensors of Einstein, Tolman, Landau and Lifshitz, Papapetrou, and Weinberg (ETLLPW) give the same distributions of energy, linear momentum and angular momentum, for any Kerr-Schild metric. | result 0.91 | 0.93 | 0.87 | asserted 1.00 |
| s1 | This result generalizes a previous work by G\"urses and G\"ursey that dealt only with the pseudotensors of Einstein and Landau and Lifshitz. | background 0.63 | 0.15 | 0.06 | asserted 0.99 |
| s2 | We compute these distributions for the Kerr-Newman and Bonnor-Vaidya metrics and find reasonable results. | result 0.61 | 0.97 | 0.10 | asserted 1.00 |
| s3 | All calculations are performed without any approximation in Kerr-Schild Cartesian coordinates. | method 1.00 | 0.94 | 0.03 | asserted 1.00 |
| s4 | For the Reissner-Nordstr\"{o}m metric these definitions give the same result as the Penrose quasi-local mass. | result 1.00 | 0.80 | 0.07 | asserted 1.00 |
| s5 | For the Kerr black hole the entire energy is confined to its interior whereas for the Kerr-Newman black hole, as expected, the energy is shared by its interior as well as exterior. | result 0.93 | 0.89 | 0.09 | asserted 1.00 |
| s6 | The total energy and angular momentum of the Kerr-Newman black hole are $M$ and $ M a$, respectively ($M$ is the mass parameter and $a$ is the rotation parameter). | result 1.00 | 0.90 | 0.15 | asserted 1.00 |
| s7 | The energy distribution for the Bonnor-Vaidya metric is the same as the Penrose quasi-local mass obtained by Tod. | result 1.00 | 0.76 | 0.06 | asserted 1.00 |
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Original abstract
We show that the pseudotensors of Einstein, Tolman, Landau and Lifshitz, Papapetrou, and Weinberg (ETLLPW) give the same distributions of energy, linear momentum and angular momentum, for any Kerr-Schild metric. This result generalizes a previous work by G\"urses and G\"ursey that dealt only with the pseudotensors of Einstein and Landau and Lifshitz. We compute these distributions for the Kerr-Newman and Bonnor-Vaidya metrics and find reasonable results. All calculations are performed without any approximation in Kerr-Schild Cartesian coordinates. For the Reissner-Nordstr\"{o}m metric these definitions give the same result as the Penrose quasi-local mass. For the Kerr black hole the entire energy is confined to its interior whereas for the Kerr-Newman black hole, as expected, the energy is shared by its interior as well as exterior. The total energy and angular momentum of the Kerr-Newman black hole are $M$ and $ M a$, respectively ($M$ is the mass parameter and $a$ is the rotation parameter). The energy distribution for the Bonnor-Vaidya metric is the same as the Penrose quasi-local mass obtained by Tod.
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How the literature uses it
7 arXiv papers cite this in 10 sentences
Papers citing it · 7 sentences without a confident label
Compares with it 1 paper
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The corresponding conserved charges are obtained from [equation] and we compute $P_ρ= (-m,-m,0, 2/3 m a)$ (using that $M = G m$) and $P̃_ρ= (-m,0,0,-m a)$, where the latter again agrees with [ref] taking into account the different conventions, as well as the result in Einstein gravity [ref] .
Kerr-Schild metrics in teleparallel gravity · Asymptotic form · 1.00
Cites it as background 2 papers
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Energy-momentum pseudotensors have been studied previously in [ref] , [ref] .
Quasinormal modes as a distinguisher between general relativity and f(R) gravity: Charged black-holes · Energy-Momentum pseudotensor of perturbation · 0.98
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Some examples of different pseudotensors can be found in Refs. [ref] .
Teleparallelism: A New Insight Into Gravity · Gravitational Energy-Momentum Density · 0.84
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