Positive-Energy Theorem| Positive-Energy Theorem |
In General > s.a. energy conditions.
* Idea: If Σ is an
asymptotically flat non-singular spacelike hypersurface, and the dominant
energy condition is satisfied, then the total energy-momentum p
is a future-directed timelike or null vector; Furthermore, p = 0
iff the spacetime is flat in a neighborhood of Σ.
* Motivation:
Originally the motivation for a positive-energy theorem came from the
Newtonian physics observation that only positive masses are seen; A result
of this type is also required by the stability of the theory; Otherwise,
for example, in thermodynamics one could get a perpetual motion machine
by pumping energy out of a black hole (? : Nester).
* Rem: We do not have
positive-energy theorems for spacetimes with a positive cosmological constant.
> Online resources:
see Wikipedia page.
References > s.a. asymptotic flatness at null infinity
[positivity of the Trautman-Bondi mass]; Penrose Inequality.
@ Introductions and reviews: Dain in(14)-a1302;
Zhang IJMPA(15)-a1508-proc [spacetimes with non-zero cosmological constant].
@ Conjecture: Geroch in(78);
Geroch & Horowitz AP(79);
Brill & Jang in(80).
@ Schoen & Yau proof:
Schoen & Yau CMP(79),
PRL(79),
CMP(81),
CMP(81);
Choquet-Bruhat in(83).
@ Witten proof: Witten CMP(81);
Nester PLA(81);
Parker & Taubes CMP(82);
Reula JMP(82);
Bizoń & Malec CQG(86);
Dimakis & Müller-Hoissen CQG(90).
@ Other proofs:
Grisaru PLB(78);
Kijowski in(86);
Jezierski & Kijowski PRD(87);
Nester PLA(89);
Bergqvist CQG(92);
Penrose et al gq/93;
Nester et al CQG(94),
Nester & Tung PRD(94)gq;
Pelykh JMP(00) [equivalence Witten-Nester];
Chruściel & Galloway CQG(04)gq [and Lorentzian splitting theorem];
Chee et al PRD(05)gq [spinorial variables];
Sarıoğlu & Tekin a0709 [using asymptotic symmetries];
Bäckdahl & Valiente Kroon CQG(11) [invarianrt deviation from Minkowski space, approximate twistors];
Jezierski & Waluk BCP(16)-a1508 [using spacetime foliations].
@ Proofs for special cases: Jang JMP(76) [flat initial hypersurface],
JMP(78);
Chruściel CQG(04)gq [using null rigidity];
a1010
[Riemannian, manifolds that are graphs of smooth functions];
Grant & Tassotti a1205,
a1408 [low-regularity metrics];
Chruściel & Paetz CQG(14)
& CQG+
[positivity of the Trautman-Bondi mass for spacetimes containing complete smooth light cones, elementary proof];
Shyam a1408-wd
[maximally sliced, asymptotically flat spacetimes].
@ Related topics:
Jang & Wald JMP(77) [and cosmic censorship];
Bekenstein PRD(13)-a1310 [why is mass always positive, if vacuum energy can be negative?];
Carlotto et al IM(16)-a1503 [effective versions].
Extensions
> s.a. de sitter spacetime [asymptotically de Sitter];
energy [asymptotically FLRW spacetimes]; quasilocal
energy; teleparallel.
@ For black holes:
Gibbons, Hawking, Horowitz & Perry CMP(83);
Herzlich JGP(98);
Rogatko CQG(00) [in Einstein-Maxwell-dilaton].
@ Spacetimes with horizons and couplings: Finster et al JMP(00)gq;
Khuri & Weinstein JMP(13) [charged Dirac fields].
@ Asymptotically (locally) AdS spacetimes: Page et al PRL(02)ht [from boundary causality];
Cheng & Skenderis JHEP(05)ht;
Luo et al NPB(10).
@ Higher dimensions:
Witten NPB(82) [no, instability];
Lee & Sorkin CMP(88) [5D Kaluza-Klein theory];
Zhang JMP(99) [5D version of Witten's proof];
Ding JMP(08);
Choquet-Bruhat a1107 [arbitrary space dimension];
Shiromizu & Soligon a2007 [d+1 dimensional Kaluza-Klein];
Cameron a2010 [Penrose et al proof];
Nguyen a2102 [explicit negative-mass solutions].
@ 2+1 dimensions: Ashtekar & Varadarajan PRD(94)gq [and upper bound on energy];
Menotti & Seminara AP(95);
Wong a1202;
Barnich & Oblak CQG(14)-a1403 [holographic].
@ Manifolds with corners: Miao ATMP(02)mp;
McFeron & Székelyhidi CMP(12).
@ Lower bounds, Bogomolny-type inequalities:
Gibbons & Hull PLB(82);
Gibbons & Wells gq/93,
Gibbons CQG(99)ht/98 [asymptotically AdS, black holes].
@ Quantum version: Thiemann CQG(98)gq/97;
Smolin PRD(14)-a1406.
@ Other theories: Rogatko CQG(02) [Einstein-Maxwell-axion-dilaton];
Deser CQG(09)-a0907 [topologically massive gravity];
Garfinkle & Jacobson PRL(11)-a1108 [Einstein-aether and Hořava gravity];
Nozawa & Shiromizu NPB(14)-a1407 [extended supergravities];
> s.a. hořava gravity.
@ Conformal: Simon LMP(99)gq/00;
Tam & Wang a1607 [on asymptotically hyperbolic manifolds].
@ Manifolds with boundary: Kim DG&A(04) [with inner boundary];
Bryden et al JMP(19)-a1806 [in terms of angular momentum and charge];
Hirsch & Miao PJM-a1812;
Almaraz et al a1907 [initial data sets with non-compact boundary];
Galloway & Lee a2105.
@ Related topics:
Chruściel CQG(86);
Yip CMP(87);
Zhang & Zhang CMP(00) [time symmetric];
Zhang et al PRD(05) [with angular momentum contribution];
Okikiolu CMP(09) [negative-mass theorem for surfaces of positive genus];
Lee & LeFloch a1408,
Shibuya a1803
[manifolds with distributional curvature].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 24 may 2021