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];
Anderson a1809 [proposed solution to the problem of time].

@ __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 GRG(07)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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