Observables in Classical Gravity |

**In General** > s.a. 3D gravity; canonical
general relativity [diffeomorphisms]; parametrized
theories; unimodular relativity.

* __Physical observables__: Diffeomorphism-invariant functions of the dynamical field variables (configuration space or phase space).

* __Rem__: In an abstract
sense, observables are as defined above; But this
may not be very useful physically, so (as emphasized by Ehlers) keep in mind
that the *real* observables are those related to proper times and lengths,
and things one can actually measure.

* __Requirement on the set of observables__: Observables should be "local" (space or spacetime integrals of quantities expressed in terms of the metric field and its derivatives) and the set should be "large" (it should separate the points of physical phase space).

* __Problem__: Gravity does not admit any local (gauge invariant) observables.

* __Chaos and observables__: Because general relativity is likely chaotic, observables have to be generalized to non-differentiable or even discontinuous ones, which do not admit a standard quantization; Dittrich et al propose to use a polymer-type spacetime topology so that enough observables become continuous.

* __How to find observables__:
One way to define observables is to deparametrize the theory and obtain a preferred
time; But this cannot be done in the full theory, only in some sectors; Another
approach is that of relational observables, proposed by Rovelli and generalized
to field theory by Dittrich; Given a function *f* on
phase space and a "clock" function *T*, the observable *F* gives
the value of *f* when *T* has some given value *τ*.

@ __Reviews__: Giesel IJMPA(08)-proc.

@ __General references__: Bergmann RMP(61),
in(65); Ohta & Kimura NCB(91);
Rovelli CQG(91);
Torre CQG(91), gq/94-conf;
Anderson gq/92;
Efroimsky & Lazarian CQG(93);
Torre PRD(93)gq [no known ones for closed spacetimes]; Lusanna & Pauri GRG(06)gq/04 [Bergmann
vs Dirac observables]; Pons et al MPLA(09)-a0902,
CQG(10)-a1001-proc; Anderson Sigma(14)-a1312 [and beables, in classical and quantum gravity];
Dittrich et al PLB(17)-a1602 [continuity of observables, chaos and spacetime topology]; Pitts a1609 [and change, for equivalent theories].

@ __And gauge, diffeomorphism invariance__: Husain in(94) [and diffeomorphism invariance];
Pons CQG(01)gq [and
gauge]; Khavkine CQG(15)-a1503 & CQG+ [generalized local gauge-invariant observables]; Donnelly & Giddings PRD(16)-a1507 [diffeomorphism-invariant observables, non-local algebra].

@ __Related topics__: Lusanna gq/02-conf
[and non-inertial observers], gq/03-conf
[and Einstein's hole argument].

> __Related topics__: see Event; gauge
transformations; riemann tensor [invariants]; time
in gravitation.

**Types of Observables**

@ __Relational__: Westman & Sonego FP(08)-a0708,
AP(09)-a0711 [and
symmetries, coordinates]; Girelli & Poulin PRD(08)
[and deformed symmetries]; Tambornino Sigma(12)-a1109 [rev]; Dapor et al PRD(13)-a1305 [general formulation]; > s.a. FLRW quantum cosmology.

@ __Evolving constants, t-dependent invariants:__
Page & Wootters PRD(83);
Anderson gq/05;
Pons & Salisbury PRD(05)gq;
Gambini et al PRD(09)-a0809 [and relational time];
Pitts FP(18)-a1803.

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**Special Systems** > s.a. Lemaître-Tolman-Bondi
Spacetimes; minisuperspace; spin-foam models.

@ __Types of spacetimes__: Neville CQG(93)
[plane waves]; Husain PRD(94)gq, PRD(97)gq [2-Killing vector field reduction];
Salisbury et al GRG(08)gq/05 [Bianchi I + scalar, time-dependent invariants].

@ __Gravitating bodies__: Damour et al PRD(00)gq/99 [2-body];
Rovelli gq/01 [general relativity + particles].

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send feedback and suggestions to bombelli at olemiss.edu – modified 31 mar 2018