Time in Gravity

In Classical General Relativity > s.a. canonical general relativity; parametrized theories.
* Multi-fingered nature of time: In general relativity, there is no single naturally-defined time function, but an infinity of them; In asymptotically flat spaces, there is an asymptotic time translation group which is a symmetry, for a given spacelike hypersurface, and any asymptotic time translation can be extended in infinitely many ways to the interior; However, this causes no problems in the classical theory; In the symplectic formulation, each extension gives rise to a different Hamiltonian, which generates a different canonical transformation.
* Frozen formalism: An expression that refers to the fact that, for a compact spacelike hypersurface, the Hamiltonian of general relativity vanishes on the constraints; This does not happen in the asymptotically flat case.
* Arrow of time: One can physically be associated with gravitational clustering (> see arrow of time, phenomenology).
@ References: Rosen FP(91); Rugh & Zinkernagel a0805-SHPMP [cosmic time].
> Effects: see chaos in the metric; doppler; tests of general relativity [t dilation].

Special Choices > s.a. gauge choice; unimodular gravity [spacetime volume].
* Cosmological time function: The function (q):= sup_{p < q} d(p, q); It is called regular iff (q) < for all q and → 0 along every past inextendible causal curve; If is regular, (M, g) has several pleasant properties.
* Epoch function: A scalar field P on spacetime, constructed from R_abcd and its covariant derivatives, which reflects the Weyl curvature and is monotonically increasing along almost all timelike trajectories for non conformally flat spacetimes.
@ Cosmic time: Hawking PRS(68); Seifert GRG(77); Qadir & Wheeler in(85); Andersson et al CQG(98)gq/97; Wegener FP(04).
@ Epoch function: Pelavas & Lake PRD(00)gq/98 [and Weyl tensor/entropy].
@ From special lapse/shift: Maia gq/96; Gyngazov et al GRG(98)gq [and Higgs].
@ For 2+1 gravity: Benedetti & Guadagnini NPB(01)gq/00.
@ Other proposals: Kummer & Basri IJTP(69) [initial surface]; Salopek & Stewart PRD(93) [and fluids]; Tiemblo & Tresguerres gq/96 [from gauge fixing], GRG(98) [Frobenius foliation], GRG(02); Pulido et al GRG(01)gq/00; Bernal & Sánchez CMP(05), LMP(06) [smoothness in globally hyperbolic spacetimes]; Thiemann ap/06 [from phantom/K-essence Lagrangian]; Farajollahi IJTP(07)-a0801.

In Semiclassical Gravity
* Results: Tomonaga-Schwinger time does not exist on Riem(M), but it does on Riem(M)/Diff(M); However, different foliations give rise to unitarily non-equivalent theories.
@ References: Halliwell PRD(87); Brout & Venturi PRD(89); Venturi CQG(90); Kiefer in(94)gq; Salopek ap/94, PRD(95)ap, ap/95-in, ap/95-in, ap/95-in [Hamilton-Jacobi]; Giulini & Kiefer CQG(95)gq/94 [Tomonaga-Schwinger].

General References > s.a. time in quantum gravity.
@ And scale/shape: Barbour gq/03-in.
@ Clocks: Teyssandier & Tucker CQG(96) [def]; Goy gq/97, gq/97 [synchronization].
@ Relation to quantum theory: Kitada & Fletcher Ap(96)gq/01; Macías & Camacho PLB(08) [incompatibility].
@ Beginning of time: Lévy-Leblond AJP(90).
@ Two-time physics: Bars & Kounnas PLB(97); Bars ht/01; Nieto ht/05 [and Ashtekar variables]; Bars PRD(08); > s.a. time.

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