Gravitational Energy-Momentum| Gravitational Energy-Momentum |
In General
> s.a. energy-momentum tensors; expressions for gravitational
energy-momentum [including other theories]; stress-energy pseudotensors.
* Motivation: Just as in
Newtonian theory one gets mass from the gravitational field, in general
relativity it is reasonable to get also momentum and angular momentum;
If there is matter, the expressions we will write down give the total
(i.e., including matter) energy-momentum.
* Open universes: One
could try, bearing in mind the Einstein equation,
Pm = ∫Σ T m0 dv = \(1\over8\pi G\)∫Σ Gm0 dv ,
but, unless ...
* The situation: If spacetime
is stationary, one can get an energy-momentum from the stress-energy tensor
Tab, but otherwise one really
faces the gravitational field energy problem and finds at most pseudotensors;
In general, gavitational energy-momentum and related quantities cannot be given
by integrals of a local density; Rather, they are quasi-local (associated with a
closed 2-surface), have no unique formula, and have no reference-frame-independent
description.
* In closed universes: There is
no generally accepted definition, but this does not mean that there is no
evolution; 2012, Proposal by L B Szabados.
> Related topics:
see energy positivity; mass.
Specific Types of Spacetimes
> s.a. asymptotic flatness; gravitational radiation.
@ Asymptotically-flat spacetimes / isolated objects:
Chruściel CMP(88);
Dadhich & Narayan GRG(98)gq/97 [vanishing gravitational mass];
Sharif NCB(04)ht/03 [black hole];
Patashnick IJMPD(05)gq/04;
Sharif & Fatima NCB(05)gq [Weyl metrics];
Ge et al a1211;
> s.a. minkowski space; solitons;
teleparallel theories.
@ Spherical symmetry:
Sosnovskiy gq/05 [and cylindrical];
Mirshekari & Abbassi MPLA(09)-a0808 [comparing energy-momentum prescriptions].
@ FLRW spacetimes: Faraoni & Cooperstock ApJ(03)ap/02 [open];
Garecki gq/06-MGXI,
APPB(08)-a0708;
Mitra GRG(10).
@ Other cosmological spacetimes: Gerhardt ATMP(06)m.DG/04 [asymptotically FLRW];
Sharif & Fatima IJMPA(05) [Einstein-Maxwell];
Nester et al PRD(08)-a0803 [homogeneous];
Davis SA(10)jul [energy conservation and expansion-related redshift];
Penrose GRG(11)
[retarded mass/energy with a positive Λ];
Nourinezhad & Mehdipour IJP(12)-a1202 [Bianchi IX models];
Amsel & Gorbonos PRD(13)-a1209 [with a constant-curvature background, Wald-like formula];
Szabados & Tod IJMPD(18)-a1808 [with a positive cosmological constant];
> s.a. anti-de sitter spacetime [asymptotically AdS];
de sitter spacetime; quasilocal energy.
@ In closed universes: Szabados GRG(13)-a1212-proc [closed models, Bianchi I and IX];
Szabados CQG(13)-a1306 [with a positive cosmological constant].
@ With conical defects: Maluf & Kneip JMP(97)gq/95;
Nucamendi & Sudarsky CQG(97)gq/96 [ADM];
> s.a. singularities.
References
> s.a. charges; energy [self-energy].
@ General: Einstein PZ(14),
PZ(18);
Peters AJP(81)jun;
in Wald 84;
Ferraris & Francaviglia in(91);
Nissani & Leibowitz IJTP(91) [covariant, localized];
Gibbs gq/97 [covariant];
Katz CQG(05)gq;
Aldrovandi et al a0812
[gravitational and inertial, teleparallel gravity];
Jaramillo & Gourgoulhon ln(10)-a1001 [and angular momentum, rev];
Rodrigues RPMP(12)-a1109-conf;
Chen et al IJMPD(15)-a1507-in [covariant Hamiltonian formalism, and Poincaré gauge theories];
Padmanabhan GRG(15)-a1506 [momentum density of spacetime];
Shimizu MPLA(16)-a1601 [proposal];
Bičák & Schmidt PRD(16)-a1602 [uniqueness];
Wang a1605-conf [and center of mass];
Acquaviva et al CQG(18)-a1802 [and gravitational thermodynamics];
Goswami & Ellis CQG(18)-a1805 [energy-momentum transfer by the gravitational field];
Chen et al IJMPD(18)-a1805-GRF [it is well defined];
Curiel SHPMP-a1808;
Lopes de Lima et al a1811;
Wu & Zhang a1811-in;
Chen et al a1912,
a1912 [translation of 1918 papers by Felix Klein].
@ Conservation laws:
Palmer PRD(78);
Nissani & Leibowitz PLA(88),
IJTP(89);
Bondi PRS(90);
Wiesendanger a1102,
a1103,
a1103 [gravitational vs inertial energy-momentum];
Epp et al CQG(13) [local vs quasilocal];
Palese & Winterroth MG14(17)-a1601
[nature of the law of conservation of energy, a problem posed by Hilbert, and Noether's theorem];
Rowe a1912 [Emmy Noether's work];
> s.a. conservation laws;
gravity [theories with non-conserved energy-momentum].
@ And Noether's theorem: Bamba & Shimizu IJGMP(16)-a1506;
Deser a1902;
De Haro a2103 [and energy-momentum pseudo-tensor].
@ Doubting the reality: Infeld AP(59);
Zel'dovich & Grishchuk SPU(88) + refs [debate];
Cooperstock FP(92),
MPLA(99)gq,
AP(00)gq/99,
FP(01);
Hoefer SHPMP(00) [conceptual].
@ Other dimensionalities: Haslhofer JGP(11) [mass-decreasing flow in dimension three];
Barzegar et al PRD(17)-a1708 [higher-dimensional].
@ With boundaries:
Binz & Śniatycki CQG(86);
Francaviglia & Raiteri CQG(02)gq/01.
@ Negative energy density?
Bonnor & Cooperstock PLA(89).
@ The background question:
Bombelli et al NPB(87);
Hawking et al PRD(95) [Melvin];
Hawking & Hunter CQG(96)gq;
Katz & Lerer CQG(97)gq/96 [null infinity];
Lam PhSc(11) [need for a background structure].
@ Related topics: Geroch & Perng JMP(94)gq [arbitrary data];
Bozhkov & Rodrigues GRG(95) [definition of inertial mass].
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