Spacetime Geometry in Quantum Gravity  

Geometry in General > s.a. quantum gravity; quantum spacetime; semiclassical quantum gravity.
* Idea: Taking into account fluctuations around classical spacetimes is expected to lead to blurring of spacetime events and metric, fuzziness in causal relations and smearing of singularities; From a general quantum history or configuration extracting a classical one may not be possible because the ones with a classical interpretation are expected to be a very small subset.
* Evidence: Area of quantum black holes, with ΔAmin ~ 4 ln2 lP2; Indications of UV cutoff from the existence of a fixed point for G; Arguments re quantum uncertainty and black holes.
@ General references: Motoyoshi NCB(93); Sonego PLA(95) [interpretation]; Amelino-Camelia Nat(99)gq/98, PLB(00)gq/99; Major CQG(10) [observational effects of atoms of space]; Berenstein & Miller PRL(17)-a1605 [spacetime topology and geometry are not the result of an operator measurement]; Calmet PLB(18)-a1810 [no second-order curvature corrections to vacuum solutions of Einstein's equation]; Becker et al PRL(20)-a1911 [fractal properties].
@ Effective geometry: Hu JPCS(09)-a0903 [emergent spacetime]; Hogan a1204 [covariant macroscopic quantum geometry]; Cirilo-Lombardo & Prudêncio IJGMP(14)-a1309 [emergent metric]; Pesci PRD(20)-a1911 [zero-point length and the role of \(R_{ab}\,l^al^b\) for null \(l^a\)].
@ Spacetime symmetries: Lehnert gq/07-MGXI; Brunekreef & Reitz a2012 [and fluctuations].
@ Limitations in geometry extraction: Downes et al a1108 [quantum limit to estimation of the spacetime metric]; Bonder et al FP(18)-a1706; Nomura et al PRD(18)-a1705 [in holography].
@ Deformed algebras, non-commutativity: Amelino-Camelia et al CQG(04)ht/03 [κ-Poincaré algebra]; Smolin NPB(06)ht/05 [energy-dependent metric, and DSR]; Amelino-Camelia et al PRD(13)-a1304 [physical characterization, from spacetime non-commutativity].
> Various approaches: see discrete spacetime phenomenology; higher-dimensional theories; non-commutative geometry; quantum cosmology; regge calculus.

Metric Fluctuations > s.a. deformed uncertainty relations; spacetime symmetries.
* Rem: In the linearized theory they can be treated similarly to the electric and magnetic field fluctuations in Maxwell theory, but the gravitational probability distribution for fluctuations diverges when the temperature goes to zero.
@ General references: Acebal et al PLB(98), Miller JMP(99) [stochastic]; Ahluwalia Nat(99)gq; Ellis et al GRG(99)gq-GRF [general]; Hu et al IJTP(04) [semiclassical stability]; Kazakov G&C(04) [and the correspondence principle]; Requardt MPLA(07)gq/05 [and the holographic hypothesis]; Shalyt-Margolin a1306, Ent(16)-a1603 [and minimal length]; Amelino-Camelia et al a1309 [scale invariance, and UV reduction to dimension 2]; Parkinson & Ford PRD(14)-a1311 [non-cancellation of quantum geometry fluctuations]; Nomura et al JHEP(15)-a1412 [spacetime-matter duality and frame dependence]; Białynicki-Birula CQG(15)-a1501 [zero-point fluctuations at finite temperature, using the Wigner function]; Wetterich PRD(17)-a1603 [correlation function for the metric].
@ Superpositions of geometries: Mathur IJMPD(17)-a1705-GRF [spacetime thickness, spread of wave function in superspace]; Sahebdivan a1905 [optomechanical techniques]; Singh a1912 [absence in the classical limit]; > s.a. indefinite causal structures [superpositions].
@ Consequences, models: Redington gq/97; Rosales & Sánchez-Gómez gq/97 [conformal, and decoherence]; Acebal et al PLB(98), Miller GRG(00) [stochastic model]; Frenkel FP(02)qp/00 [Károlyházy]; Ford IJTP(05)gq-conf [test-particle Brownian motion]; Crowell 05; Hu & Roura in(07)gq/06 [around a black hole]; Hogan PRD(08)-a0712 [holographic noise and interferometers]; Hogan PRD(08)-a0806 [based on wave optics]; Fröb et al JCAP(14)-a1403 [Riemann correlator in de Sitter spacetime]; Dzhunushaliev et al EPJC(15)-a1501 [modified gravity]; Ng JPCS(17)-a1701 [holographic principle, the cosmological constant, gravitational thermodynamics, and the dark sector]; Carlip et al PRD(20)-a1809 [and the causal structure of spacetime]; Matsui a1901 [spacetime instability].
@ Light-cone fluctuations: Neves et al PRL(10)-a1012 [and causality]; Ford et al AP(13) [non-linear optics analog]; Hu & Yu PRD(19)-a1907 [due to thermal fluctuations in a medium]; > s.a. non-commutative field theory.
@ Experiments: Hogan a1208-proc [interferometry]; Wiens et al PRL(16) + news PhysOrg(17)jan [optical resonator]; Verlinde & Zurek a1902 [interferometry]; Afshordi a1911 [and the LIGO "mystery" noise]; Parikh et al IJMPD(20)-a2005-GRF, Zurek a2012 [detector arm-length fluctuations].
@ Black holes, other: Aurilia & Spallucci a1309-GRF [uncertainty principle and Planck-scale black holes]; Casadio et al a1405-in [and minimum length]; Davila a1409 [limits on observation]; Giddings & Psaltis PRD(18)-a1606 [time dependence of the shape and size of the black-hole shadow]; Barrau et al PLB(17)-a1606 [bouncing black holes and the Fermi gamma-ray excess]; Barceló et al CQG(17)-a1607, Ashtekar et al PRL(18), PRD(18) [transition to white hole]; Ikeda et al a2103 [microstate spectroscopy]; > s.a. black-hole entropy and origin.

Related Topics > s.a. quantum-gravity effects in gravity and astrophysics and cosmology [including singularity avoidance].
@ General references: Bethke & Magueijo CQG(12)-a1108 [complex Immirzi parameter and chiral asymmetry]; Haggard PRD(13)-a1211 [pentahedral volume and chaos]; Hogan PRD(17)-a1509 [exotic rotational correlations].
> Black-hole related: see black-hole thermodynamics; black-hole types; quantum black holes [black-to-white-hole tunneling]; reissner-nordström solutions.
> Specific types of spacetimes: see differentiable manifolds; manifolds; singularities in quantum gravity; spacetime foam.
> Other related topics: see chaos in classical gravity; differential geometry [generalizations]; dimensionality of spacetime [dimensional reduction]; lorentzian geometry [analogs]; quantum geometry.

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 4 apr 2021