Unimodular Relativity

In General
* Idea: A generalization of general relativity, in which the cosmological constant appears as a variable, but is then seen to be a constant of the motion.
* Motivation: Possible approach to the problem of time in quantum gravity, and to the cosmological constant problem.

Classical Theory
* Unit metric determinant version:
* Fixed volume element version:
* Fixed total volume version:
* Variation – time as past volume of a point: V(p) is the volume of the past of p; It is strictly increasing along timelike curves iff (M, g) is chronological; If (M, g) is strongly causal, then it is strictly increasing along causal curves; If the latter is true, then (M, g) is causal; If (M, g) is globally hyperbolic, then V(p) is continuous everywhere.
@ General references: [in Geroch JMP(70)]; Dieckmann GRG(88); Sorkin pr(88); Brown & York PRD(89); Henneaux & Teitelboim PLB(89); Unruh PRD(89); Ng & Van Dam IJMPD(01)ht/99-in [variable cosmological constant]; Abbassi & Abbassi FPL(01)gq/00; Bock IJTP(03)gq [equations for null cones and volume element].
@ From coupling to 3-form field: Henneaux & Teitelboim PLB(84); Teitelboim PLB(85) [and black holes]; Brooks NPB(94)ht/99.
@ Metric from gauge structure and volume: Wilczek PRL(98)ht.
@ Other topics: Nishino & Rajpoot PLB(02)ht/01 [and supergravity]; Bock a0704, a0704 [modified energy momentum conservation, and dark matter / dark energy].

Quantum Theory > s.a. path integral formulation of quantum gravity.
@ General references: Ng & van Dam PRL(90); Gamboa & Mendez NPB(01)ht/00 [3D, strong coupling, path integral]; Álvarez JHEP(05)ht [vs general relativity, quadratic (Fierz-Pauli) regime]; Calmet EPL(07)ht/05 [and non-commutative spacetime], MPLA(07)-a0704 [and fundamental length].
@ In quantum cosmology: Daughton et al gq/93-in [k = 1, initial conditions and unitarity].
@ Instantons, unitarity: Daughton et al PRD(98)gq.

Other References > s.a. cosmological constant; gravitational thermodynamics; modifications of general relativity.
@ Unit determinant version: Buchmüller & Dragon PLB(89); Kreuzer CQG(90); Ng & van Dam PRL(90), JMP(91) [has refs]; Petrov MPLA(91); Ng IJMPD(92); Álvarez & Faedo PRD(07)ht [and coupling of KE and PE to gravity].
@ Unit determinant version, canonical: Unruh PRD(89); Unruh & Wald PRD(89).
@ Fundamental volume element: Anderson & Finkelstein AJP(71); Finkelstein et al JMP(01)gq/00.
@ Time = Volume: Bombelli in(91); Sorkin IJTP(94).
@ Time = Volume, canonical: Bombelli, Couch & Torrence PRD(91).
@ Energy-momentum conservation: Tiwari JMP(93), gq/03/JMP.
@ Against: Kuchar PRD(91).
@ Time, other: Hosoya & Soda PTP(90); Bertolami IJMPD(95); Earman SHPMP(03) [and cosmological constant, conceptual]; Farajollahi GRG(05)-a0801, IJTP(08) [and observables].
@ Variations: Abbassi & Abbassi a0706 [unimodular tensor density].

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 12 jun 2008