Gravitational Entropy  

In General > s.a. decoherence; lanczos potential; particle effects; spacetime foam.
* Goals: (i) Give a thermodynamical meaning to particle creation in gravitational fields; (ii) Generalize the second law to cosmology; (iii) Define an entropy for the gravitational field (Penrose: square of the Weyl tensor).
* Hints: One can define an entropy in ways that seem to be related to a gravitational arrow of time, e.g., one related to particle production, by using the Weyl tensor, or one related to inhomogeneity and clustering.
@ General references: Tolman PR(30); Davies 74, in(81); Davies et al PRD(86); Marolf et al PRD(04)ht/03 [observer dependence]; Fatibene et al IJGMP(09) [from Holst Lagrangian]; Smoot IJMPD(10)-a1003 [entropy flow and holography]; Clifton et al CQG(13)-a1303 [based on the Bel-Robinson tensor]; Lewkowycz & Maldacena JHEP(13)-a1304 [generalized, for euclidean solutions]; Ruchin et al EPJC(17)-a1312 [Perelman's W-entropy]; Fursaev a1406; Kothawala & Padmanabhan PLB(15)-a1408 [and emergent gravity, zero-point length]; Camps & Kelly JHEP(15)-a1412 [without replica symmetry]; Chen et al a1506 [thermofield dynamics approach].
@ Weyl tensor: Penrose in(79); Smolin GRG(85) [matter to gravitational radiation]; Husain PRD(88); Pelavas & Lake PRD(00)gq/98 [self-similar spacetimes]; Grøn & Hervik gq/02; Amarzguioui & Grøn PRD(05)gq/04 [collapsing matter]; Rudjord et al PS(08) [and black holes]; Belgiorno & Catino CQG(20)-a2005 [candidate Weyl entropy density]; > s.a. Lemaître-Tolman-Bondi Solutions; Weyl Curvature Hypothesis.
@ And gravitational action: Banerjee & Majhi PRD(10)-a1003; Astaneh et al a1411, Dong & Miao JHEP(15)-a1510 [and total derivative terms]; Tuveri et al a1604.
@ Phase space approach: Rothman & Anninos PLA(97), PRD(97)gq/96; Rothman GRG(00)gq/99.
@ Noether approach: Fatibene et al AP(00)gq/99 [and Taub-Bolt]; Garfinkle & Mann CQG(00)gq [and Taub-Bolt].
@ Upper bound: Bousso JHEP(99)ht [conjecture]; Flanagan et al PRD(00)ht/99; Low CQG(02)gq/01; Frampton & Kephart JCAP(08)-a0711 [and dark matter]; Hsu & Reeb MPLA(09)-a0908 [monsters].
@ Spacetime regions or subsets: Mäkelä & Peltola gq/04 [spacelike 2-surfaces]; Pabmanabhan IJMPD(12) [and distortion of null surfaces in spacetime]; Baccetti & Visser CQG(14)-a1303 [for arbitrary bifurcate null surfaces]; Balasubramanian et al JHEP(13)-a1305 [entropy of a hole in spacetime]; Pesci Ent(15)-a1404 [matter entropy flux across horizons].
@ Covariant, geometrical meaning: Hawking & Hunter PRD(99)ht/98; Lowe JHEP(99)ht; Mäkelä gq/05 [arbitrary spacelike 2-surface].

Specific Types of Manifolds / Metrics > s.a. black-hole entropy and thermodynamics; de sitter space; LTB Solutions.
@ Cosmology: Frautschi Sci(82)aug; Gibbons NPB(87), NPB(88); Prigogine IJTP(89); Prigogine et al GRG(89); Brandenberger et al PRD(93) [density perturbations in inflation]; Barrow NA(99)ap; Grøn & Hervik CQG(01)gq/00 [Bianchi I]; Obregón et al PRD(03)ht [from Cardy-Verlinde formula]; Pelavas & Coley IJTP(06)gq/04 [Szekeres & Bianchi VIh]; Nielsen & Ninomiya IJMPA(06)ht [and periodic universe]; Hernández & Quevedo GRG(07)gq [Bianchi I and V, and Cardy-Verlinde construction]; Frampton et al CQG(09)-a0801; Pavón et al a1212-MG13 [the generalized second law in inflationary cosmology]; Sussman AN(14)-a1408 [and cosmic expansion]; Sussman & Larena CQG(15)-a1503 [local cosmic voids]; Kiessling a1905-in; Saha IJMPA-a1910 [Viaggiu entropy]; Chakraborty et al a1912 [models]; > s.a. cosmological acceleration.
@ Collapsing spacetimes: Maiella & Stornaiolo IJMPA(10)-a1007 [spherical symmetric, Cardy-Verlinde formula]; > s.a. gravitational collapse.
@ Topology: Liberati & Pollifrone NPPS(97)ht/95 [manifolds with boundary, mathematical].
@ Boundaries / horizons: Carlip CQG(99)gq; Brustein PRL(01)ht/00 [causal horizon in FLRW models]; Mäkelä & Peltola gq/02 [Rindler]; Padmanabhan CQG(02)gq, GRG(02)gq [spherical symmetry], CQG(04)gq/03 [and density of states]; Chatterjee & Majumdar Pra(04)gq-conf; Lemos & Zaslavskii PRD(10)-a0904 [quasiblack holes]; Romero et al IJTP(12)-a1109 [black holes and wormholes]; > s.a. horizons.
@ Singularities: Anastopoulos & Savvidou CQG(12)-a1103.
@ In other theories of gravity: Camps JHEP(14)-a1310 [curvature-squared theories, extension of the Ryu-Takayanagi prescription]; > s.a. Gauss-Bonnet Gravity.

And Quantum Theory > s.a. quantum gravity phenomenology [limitations to spacetime measurements].
@ Entanglement entropy: Fursaev PRD(08); Jacobson a1204-GRF [finiteness]; Cooperman & Luty JHEP(14)-a1302 [renormalization, and effective action]; Gyongyosi a1403 [quantum gravity and smooth entanglement entropy transfer]; Bhattacharyya & Sharma JHEP(14)-a1405 [higher-derivative gravity]; Nomura & Weinberg JHEP(14)-a1406 [semiclassical spacetime]; Kastor et al a1604 [Lovelock gravity, extended first law].
@ Particle creation: Hu PLA(83), & Kandrup PRD(87); Kandrup IJTP(88); Prigogine et al PNAS(88); Nesteruk pr(91); Rau in(95)ht/94.
@ Loop quantum gravity: Krasnov PRD(97)gq/96 [boundaries]; Livine & Terno NPB(08)-a0706 [bulk entropy and holographic regime].
@ Quantum gravity: Kandrup CQG(88) [second law and quantum cosmology]; Garattini PLB(99)ht [spacetime foam]; Balasubramanian et al JHEP(07)-a0705 [AdS-cft and half-BPS universes]; Kothawala et al PRD(08)-a0807 [quantization, various gravity theories]; > s.a. entropy in quantum theory.

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