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.

* __Rem__: The action of gravity should include fourth derivative terms
to provide renormalizability in the vacuum sector.

@ __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];
Fewster & Liberati GRG-a1402 [GR20 report];
Hu JPCS(14)-a1402 [rev]; Tilloy & Diósi PRD(16)-a1509 [consistent theory of (stochastic) semiclassical gravity].

@ __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].

@ __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 *φ*, but keeps the metric classical,
and looks for quantum states |*ψ*(*φ*)\(\rangle\),
which satisfy the Møller-Rosenfeld equation

*G*_{ab}(*g*)
= 8π*G* \(\langle\)*ψ* | *T*_{ab}(*φ*, *g*)
| *ψ*\(\rangle\)_{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 *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 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 a1704.

@ __Fluctuations__: Martín & Verdaguer PRD(00)gq.

**Other Spacetimes** > s.a. de sitter space;
semiclassical cosmology.

@ __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];
> s.a. black-hole thermodynamics [back-reaction].

@ __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 a1602 [lightcone fluctuations from stress tensor fluctuations]; > 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.

@ __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__: Nikolić gq/06 [and pilot-wave theory and the cosmological constant];
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].

> __Related topics__:
see collapse; decoherence;
gravitational thermodynamics; energy conditions;
renormalization; vacuum [polarization].

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