Positive Energy Theorem

In General > s.a. energy conditions.
* Idea: If 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 .
* Motivation: Originally from the Newtonian physics observation that only positive masses are seen; Required by thermodynamics, otherwise could get a perpetual motion machine by pumping energy out of a black hole (? : Nester).

References > s.a. Penrose Inequality.
@ Conjecture: Geroch in(78); Gerich & 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); Bizon & 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]; Chrusciel & Galloway CQG(04)gq [and Lorentzian splitting theorem]; Chee et al gq/05 [spinorial variables].
@ Proofs for special cases: Jang JMP(76) [flat initial hypersurface], JMP(78); Chrusciel CQG(04)gq [using null rigidity].
@ Related topics: Jang & Wald JMP(77) [and cosmic censorship].

Extensions > s.a. de Sitter [asymptotically dS]; energy [asymptotically FRW]; quasi-local; 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.
@ Asymptotically (locally) AdS spacetimes: Page et al PRL(02)ht [from bdry causality]; Cheng & Skenderis JHEP(05)ht.
@ Higher dimensions: Witten NPB(82) [no, instability]; Lee & Sorkin CMP(88) [5D Kaluza-Klein]; Zhang JMP(99) [5D version of Witten's proof]; Sarioglu & Tekin a0709; Ding JMP(08).
@ 2+1 dimensions: Ashtekar & Varadarajan PRD(94)gq [and upper bound on energy]; Menotti & Seminara AP(95).
@ 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.
@ Other: Chrusciel CQG(86); Yip CMP(87); Simon LMP(99)gq/00 [conformal]; Zhang & Zhang CMP(00) [time symmetric]; Miao ATMP(02)mp [with corners]; Rogatko CQG(02) [Einstein-Maxwell-axion-dilaton]; Kim DG&A(04) [manifolds with inner boundary]; Zhang et al PRD(05) [with angular momentum contribution].

Main page – Abbreviations – Journals – Comments – Other sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified 23 may 2008