Semiclassical General Relativity

In General > s.a. canonical quantum gravity; general relativity; semiclassical quantum gravity; quantum cosmology [decoherence].
* Idea: A theory describing quantized matter fields dynamically coupled to the metric treated as a classical field.
@ Proposal: Møller in(62); Rosenfeld NP(63).
@ General articles: Singh & Padmanabhan AP(89); Salehi CQG(92); Kiefer in(94)gq/93; Lifschytz et al PRD(96)gq/94; Ford gq/05-in [rev].
@ And quantum gravity: Page & Geilker PRL(81) [comments Hawkins PRL(82), Ballentine PRL(82), reply PRL(82), Whitaker JPA(85)], in(82) [test]; Duff in(81), Kibble in(81), Sonego pr(91) [need for quantum gravity]; Grishchuk & Rozhansky PLB(88); Pollock NPB(88); Habib PRD(90); Padmanabhan & Singh CQG(90); Keski-Vakkuri & Mathur PRD(96) [turning points]; Alberghi et al PRD(06)ht [scalar in dS from Born-Oppenheimer reduction of Wheeler-DeWitt equation]; López Nacir & Mazzitelli a0711 [new counterterms, from Einstein-ether].
@ Validity, consistency: Giulini & Kiefer CQG(95)gq/94; {> s.a. stability below}.
@ Related topics: Blencowe PRD(93) [electromagnetic model]; Kim JKPS(97)gq/96 [coherent state representation].

Usual Approach > s.a. quantum field theory in curved backgrounds; self-force.
* Idea: Like quantum field theory on a curved spacetime, but with back-reaction effects on the metric; A self-consistent framework in which one replaces the rhs of the Einstein equation by the renormalized expectation value of the stress-energy tensor for the quantum matter fields , but keeps the metric classical, and looks for quantum states |() which satisfy the Møller-Rosenfeld equation

G_ab(g) = 8G | T_ab(, g) | _ren .

* Remark: Some maintain that this is the correct approach and there is no quantum gravity, but this point of view seems to be inconsistent.
* Back-reaction: The influence of the matter T_ab on the metric, which cannot always be consistently treated as a fixed curved background.
* Issue: The change in the metric produced by back-reaction in turn changes T_ab, and so on; The iteration does not converge in general.
* Criticism: (& Sonego) If you average out quantum effects by using T_ab, it is not surprising that you get absurd results – the expectation value of position for e's in the Stern-Gerlach experiment gives no deflection!
* Limits of validity: Believed to be valid everywhere in regions of weak curvature (including horizons), as long as one takes into account the effects of back reaction (e.g., of Hawking radiation) on the background geometry; Metric fluctuations may limit the validity even before backreaction sets in.
@ Back-reaction: Padmanabhan CQG(89); Padmanabhan & Singh AP(93); Anderson PRL(95); Flanagan & Wald PRD(96) [and energy conditions]; Calzetta & Verdaguer PRD(99)gq/98; Altaie PRD(02) [Einstein universe, finite-T]; Plunien CQG(07) [1+1 scalar field toy model].
@ Effective action: Fischetti et al PRD(79) [and conformal anomaly]; Hartle & Hu PRD(79) [homogeneous, massless scalar], PRD(80) [anisotropy dissipation].
@ Limits of validity: Bose et al PRD(96) [2D dilatonic black holes]; Sriramkumar IJMPD(97)gq/95; Hu & Phillips gq/00-in.
@ Problems and tests: Eppley & Hannah FP(77), comment Mattingly PRD(06)gq; comments to Page & Geilker PRL(81); Unruh in(84); Boucher & Traschen PRD(88); Padmanabhan CQG(89) [back-reaction]; Anderson et al gq/02 [stability].

Stability of Minkowski Space
* Idea: There was a long debate about whether Minkowski space is stable or not; The problem is that quantum corrections to the Einstein equation introduce perturbative terms which are of higher order, and it can become like the problem of the charged particle with back-reaction, which has runaway solutions; It was solved by realizing that the unstable solutions are non-perturbative solutions to the perturbative problem, and are non-physical; There is no instability (& J Simon).
@ General references: Horowitz PRD(80); Gunzig & Nardone PLB(82) [massive scalar field, Minkowski-de Sitter phase transition]; Suen PRD(89) + comment Schmidt PRD(94)gq/01; Modanese PRD(99)gq/98 [euclidean]; Anderson et al PRD(03)gq/02; Hu et al PRD(04)gq, IJTP(04)gq/05; Verdaguer BJP(05)gq-in.
@ Fluctuations: Martín & Verdaguer PRD(00)gq.

Other Spacetimes
@ Semiclassical black holes: York PRD(85) [+ scalar]; Hiscock et al PRD(97) [interiors]; Stephens & Hu IJTP(01)gq [phase transitions]; Anderson et al gq/01-MG9 [T = 0]; Fabbri et al PRD(06)ht/05 [Schwarzschild corrections]; > s.a. black hole thermodynamics [back-reaction].
@ Other isolated objects: Gladush IJMPD(02)gq/00 [spherical dust shells]; > s.a. spacetime foam, wormholes.
@ FRW: Hartle PRD(81), in(81) [+ scalar+ radiaton, particle production]; Kim et al PRD(97)gq [+ scalar]; > s.a. cosmic acceleration.
@ de Sitter: Castagnino et al PLB(87) [graviton and topology contributions]; Isaacson & Rogers NPB(91), Rogers & Isaacson NPB(92) [dS + scalar, stability]; Busch a0803 [de Sitter + scalar, stability].
@ Bianchi I: Hartle PRD(80) [particle production and anisotropy]; Hu & Sinha PRD(95) [fluctuation-dissipation for classical geometry with quantum matter as environment]; Huang PLB(97), PRD(98)ht/02 [+ scalar, anisotropy]; Suresh IJTP(05)gq/03 [particle production]; Vitenti & Müller PRD(06) [numerical].
@ Other cosmological models: Kim PRD(97)gq/96 [and pilot wave]; Suresh IJTP(04)gq/03 [oscillatory inflation, and particle production].

Other Aspects and Approaches > s.a. action; newtonian gravitation [corrections]; quantum gravity phenomenology; regge calculus; time in gravity.
* Alternatives: One is a theory with a probability distribution P[g] for the metric (SS's "minimal theory").
@ Matter description: Naudts et al ht/02 [photons]; Moretti CMP(03)gq/01 [stress-energy operator]; Sahlmann & Thiemann CQG(06)gq/02, CQG(06)gq/02 [recovering quantum field theory in curved spacetime]; Anselmi & Halat ht/06 [renormalizable acausal theories].
@ Fluctuations: Calzetta & Hu PRD(94), et al PRD(97)gq; Martín & Verdaguer gq/97-in, PRD(99)gq; Visser PLB(97)gq, gq/97-in [reliability horizon]; Casadio IJMPD(00)gq/98 [minisuperspace]; Ford & Wu IJTP(03) ["passive quantum gravity"]; > s.a. Stochastic Gravity.
@ And decoherence: Paz & Sinha PRD(91); Kiefer PRD(93)gq; Martín & Verdaguer IJTP(99)gq/98; > s.a. quantum field theory effects in curved spacetime.
@ Related topics: Vanzella & Matsas PRD(00)gq/99 [astrophysical effects]; Nikolic gq/06 [and pilot wave theory and the cosmological constant]; Anderson & Fabbri PRD(07)gq/06 [far field limit, universality].
> Related topics: see collapse; decoherence; gravitational thermodynamics; energy conditions; renormalization; vacuum [polarization].

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