Gravitational Instantons  

In General
* Idea: Non-singular, complete solutions to the Euclideanized vacuum Einstein equation with or without a cosmological constant, i.e., regular, real, Ricci-flat or Einstein Riemannian manifolds; They are used for calculating tunneling probability amplitudes in semiclassical quantum cosmology, for example in scenarios in which the universe tunnels out of nothing.
* Applications: Since they represent local minima of the Euclideanized action, they are used in the path-integral approach to approximate amplitudes by perturbing around them; They are also used to deduce thermodynamic properties of black holes.

Special Solutions > s.a. BF theory [Plebański gravity]; boundary proposals in quantum cosmology.
@ Taub-Bolt: Mars & Simon JGP(99)gq/98 [uniqueness]; Fatibene et al AP(00)gq/99 [entropy]; Garfinkle & Mann CQG(00) [entropy]; Awad CQG(06) [higher-dimensional].
@ Inflationary universes: Firouzjahi et al JHEP(04)ht [modified Hartle-Hawking wave function in brane world].
@ Bianchi models: Barrow et al CQG(00)gq/99 [VI0 and VII0]; Saffin PLB(99)gq [IX]; Page a0912 [1978 conference talk].
@ Asymptotically flat: Etesi PLB(06) [topology]; Etesi & Jardim CMP(09) [moduli spaces of self-dual connections]; Cho & Teo PLB(11)-a1107 [two-parameter family].
@ Black hole pair creation: Branoff & Brill gq/98-fs; Booth & Mann PRL(98)gq, NPB(99)gq/98 [charged, rotating]; > s.a. quantum black holes.
@ With matter / Kaluza-Klein theory: Copeland et al JHEP(00)ht [scalar]; Gray & Copeland JHEP(01)gq [scalar + form in higher dimensions].
@ In quantum cosmology: Bousso & Linde PRD(98)gq; Garriga PRD(00)ht/98, ht/98; Turok PLB(99)gq [stability of Minkowski spacetime]; Blanco-Pillado et al JCAP(12)-a1104 [quantum creation of an open universe from nothing].
@ Torsional instantons: Kaul & Sengupta PRD(14)-a1411 [Giddings-Strominger wormhole and Nieh-Yan topological index]; > s.a. dark energy models.
@ Singular instantons: Vilenkin PRD(98)ht; Hashimoto PRD(01) [action]; Kirklin et al PRD(01) [made regular]; > s.a. inflation [from quantum cosmology].
@ In supergravity: Hawking & Pope NPB(78); Kaya JHEP(99)ht [AdS]; Chiodaroli & Gutperle PRD(09)-a0901 [N = 2].
@ Related topics: D'Auria & Regge NPB(82); Nergiz & Saclioglu PRD(96)ht/95 [and foam]; Nutku PRL(96) [and minimal surfaces]; Nutku et al CQG(97); Hunter PRD(99)gq/98 [U(1) symmetry, NUT charge]; Nutku & Sheftel gq/01 [axisymmetric, "heavenly"]; Demetrian PS(06)gq/04 [Coleman-de Luccia, second-order]; Yang & Salizzoni PRL(06)ht/05 [from non-commutative gauge theory instantons]; Bourliot et al PRD(10)-a0906 ["spatially homogeneous"], CQG(10) [G3-homogeneous]; Biquard & Minerbe CMP(11)-a1005; Mercuri PRD(11)-a1007 [with the Holst action, and gravitational parity violation]; Birkandan IJMPC(08)-a0711 [Maple11+GRTensorII symbolic calculator using the Newman-Penrose formalism].

References > s.a. null infinity [BMS group]; unimodular gravity.
@ General: Gibbons & Hawking PRD(77); Hawking PLA(77), in(79); Gibbons & Perry PRD(80); Pope in(81); Rubakov & Tinyakov PLB(88); Mellor & Moss CQG(89); Lorenz-Petzold PTP(89); 't Hooft NPB(89); Ó Murchadha & Shanahan PRL(93); Marathe & Martucci NCB(98).
@ New variables: Samuel CQG(88); Capovilla et al CQG(90); Torre PLB(90); Chang & Soo ht/92; Ishihara et al IJMPA(96)gq/95.
@ NP formalism: Goldblatt GRG(94); Aliev & Nutku gq/98 [hyper-Kähler structure].
@ Entropy, topology: Liberati & Pollifrone PRD(97)ht.
@ And black-hole radiation: Massar & Parentani PRL(97)gq.
@ Uniqueness results: Simon CQG(95)gq [Kerr spacetime].
@ Perturbations: Torre PRD(90); Dunne & Wang PRD(06) [bounce with scalar field].
@ And the cosmological constant: Xue IJMPA(09)ht/06; Cyriac a1511.
@ Applications: Moss PLB(92); Allen AIP(99)ap [in cosmology]; Marochnik G&C(13)-a1204 [tunneling from "nothing" into de Sitter space and dark energy].
@ Related topics: Jibu & Yasue PLA(92) [and Euclidean quantum mechanics]; Brill & Pirk in(93)gq [pictures]; Bakas et al PLB(98) [octonionic]; Ratcliffe & Tschantz CQG(98) [constant curvature], CQG(00) [spin and complex structures], CQG(00)gq [growth with V and Hartle-Hawking wave function].
> Related topics: see quantum field theory in curved backgrounds [particle creation].

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