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; gravitational phenomenology).

@ __References__: Rosen FP(91);
Rugh & Zinkernagel SHPMP(09)-a0805
[cosmic time]; Yahalom IJMPD(09) [existence of time from gravity]; Ludwin & Horwitz MPLA(11) [and covariant dynamics]; Ciufolini EJPW-a1306-ch [time travel, clock puzzles, and tests]; Anderson NYAS(14)-a1306 [Machian strategy].

@ __In cosmology__:
Balbi a1304-proc; Anderson a1403 [slightly inhomogeneous, problem of time]; Rugh & Zinkernagel a1603-in [limits of the concept of time].

> __Effects__: see chaos
in the metric; doppler effect; tests
of general relativity [time dilation].

> __Related topics__: see dynamical wave-function collapse.

**Time Functions **> s.a. gauge
choice; Paneitz Operator and unimodular
gravity [spacetime volume].

* __Cosmological time function__:
The function *τ*(*q*):=
sup_{p < q}
*d*(*p*,* q*); It is called regular iff *τ*(*q*) < ∞ for
all *q* and *τ* → 0
along every past inextendible causal curve; If *τ* is
regular, (*M*,* g*) has several pleasant properties.

* __York time__: The parameter *T* = (1/12π *G*) *K*, proportional to the trace of the extrinsic curvature of a spatial hypersurface; This leads to using spatial slices of constant mean curvature, whose importance has been known at least since York's solution of the initial-value problem of general relativity.

* __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.

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**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-proc,
ap/95-proc,
ap/95-proc
[Hamilton-Jacobi]; Giulini & Kiefer CQG(95)gq/94 [Tomonaga-Schwinger].

**General References** > s.a. causality and
causality conditions; cosmology; time
in
quantum gravity.

@ __Timeless gravity__: Barbour gq/03-proc [in shape dynamics]; Shyam & Ramachandra a1209 [phase-space reformulation of Barbour's theory].

@ __Clocks__: Teyssandier & Tucker CQG(96) [def]; Goy gq/97, gq/97-conf [synchronization].

@ __Relation to quantum theory__: Kitada & Fletcher Ap(96)gq/01;
Macías & Camacho PLB(08)
[incompatibility].

@ __Initial singularity__: Lévy-Leblond AJP(90)feb
[beginning of time]; Minguzzi IJMPD(09)-a0901-FQXi
[and global existence of time].

@ __Two-time physics__: Bars & Kounnas PLB(97);
Bars AIP(02)ht/01;
Nieto ht/05 [and
Ashtekar variables]; Bars PRD(08)-a0804; Piceno et al EPJP(16)-a1512 [fundamental constraints]; > s.a. modified general relativity; time.

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