Semiclassical Gravity

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.
* Rem: The action of gravity should include fourth derivative terms to provide renormalizability in the vacuum sector.
@ Textbooks, reviews: Hu & Verdaguer 20.
@ Proposals: Møller in(62); Rosenfeld NP(63); Oppenheim a1811 [including gravitational collapse of the wave function].
@ 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]; Fewster & Liberati GRG-a1402 [GR20 report]; Hu JPCS(14)-a1402 [rev]; Tilloy & Diósi PRD(16)-a1509 [consistent theory of (stochastic) semiclassical gravity]; Kent a1808.
@ 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 field in de Sitter space from Born-Oppenheimer reduction of Wheeler-DeWitt equation]; López Nacir & Mazzitelli PRD(08)-a0711 [new counterterms, from Einstein-ether].
@ Other theories of gravity: Casadio et al JCAP(19)-a1903 [f(R) gravity, de Sitter space is excluded].
@ Effective theory: Paszko PhD(06)-a0801, Paszko & Accioly CQG(10); Tomozawa a1107 [corrections to gravity]; Codello & Jain CQG(16)-a1507 [covariant].
@ Validity, consistency: Giulini & Kiefer CQG(95)gq/94; Pinamonti CMP(11)-a1001 [initial conditions and existence of solutions]; {> s.a. stability below}.
@ Related topics: Blencowe PRD(93) [electromagnetic model]; Kim JKPS(97)gq/96 [coherent-state representation].

Usual Approach > s.a. QED in curved spacetime; 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 \(\phi\), but keeps the metric classical, and looks for quantum states |ψ(φ)\(\rangle\), øller-Rosenfeld equation

G_ab(g) = 8πG \(\langle\psi | T_{ab}(\phi,g) | \psi\rangle_{\rm ren}\) .

* 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 \(\langle T_{ab} \rangle\) 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 \(\langle T_{ab} \rangle\), and so on; The iteration does not converge in general.
* Criticism: (& Sonego) If you average out quantum effects by using \(\langle T_{ab} \rangle\), it is not surprising that you get absurd results – the expectation value of position for electrons 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 IJTP(00)gq-conf.
@ 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); 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-conf; Dvali a1107; Carneiro & Borges GRG(18)-a1704.
@ Fluctuations: Martín & Verdaguer PRD(00)gq.

Other Spacetimes > s.a. de sitter space.
@ 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]; Brustein & Medved JHEP(13)-a1304 [information-loss paradox and other controversies]; Abedi & Arfaei JHEP(16)-a1506 [removing the singularity with quantum field theory effects, before quantum gravity]; Ho et al a1912; Arrechea et al PRD(20)-a1911 [Schwarzschild, internal structure]; > s.a. black-hole thermodynamics [back-reaction].
@ Cosmological spacetimes: Matsui & Watamura PRD(20)-a1910 [FLRW instability]; Meda et al a2007 [existence and uniqueness of solutions]; > s.a. semiclassical cosmology [semiclassical states in quantum cosmology].
@ Other isolated objects: Gladush IJMPD(02)gq/00 [spherical dust shells]; Carlson et al PRD(10)-a1008; Doplicher et al JGP(13)-a1201 [spherically symmetric solution with massless scalar field]; > s.a. spacetime foam; wormholes.

Other Aspects / Approaches > s.a. action; 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: Sanyal IJMPA(95)-a1703 [non-minimally coupled scalar field]; 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 CQG(07)ht/06 [renormalizable acausal theories].
@ Fluctuations: Calzetta & Hu PRD(94), et al PRD(97)gq; Martín & Verdaguer gq/97-MG8, PRD(99)gq; Visser PLB(97)gq, gq/97-MG8 [reliability horizon]; Casadio IJMPD(00)gq/98 [minisuperspace]; Ford & Wu IJTP(03) ["passive quantum gravity"]; Bessa et al PRD(16)-a1602 [lightcone fluctuations from stress tensor fluctuations]; Satin PRD(19)-a1812 [matter fluctuations, semiclassical and classical]; > s.a. Stochastic Gravity.
@ Based on pilot-wave theory: Nikolić gq/06 [and the cosmological constant]; Struyve in(17)-a1902 [new approach].
@ 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.
@ Astrophysical effects: Vanzella & Matsas PRD(00)gq/99; Carballo-Rubio PRL(18)-a1706 [stellar equilibrium]; > s.a. Tolman-Oppenheimer-Volkoff Equation.
@ Other phenomenology: Bessa et al PRD(14)-a1402 [analog model for light propagation]; Calmet et al EPJC(15)-a1505 [non-local effects for matter]; Crowell a1601 [on a proposal for photon emisson by atoms]; > s.a. newtonian gravity [corrections]; quantum-gravity phenomenology.
@ Related topics: Anderson & Fabbri PRD(07)gq/06 [far field limit, universality]; Lima & Vanzella PRL(10)-a1003 [and quantum vacuum energy density dominance]; Di Criscienzo et al a1010-fs [Hamilton-Jacobi approach]; Yargic et al PRD(20)-a2001 [only part of the stress-energy tensor gravitates].
> Related topics: see collapse; decoherence; gravitational thermodynamics; energy conditions; renormalization; vacuum [polarization].

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