Metric Matching  

In General > s.a. types of metrics.
* Idea: Establish junction / matching conditions that a metric and its derivatives must satisfy across a hypersurface in order for conditions such as field equations to be satisfied at least in a distributional sense, e.g., distributional sources corresponding to thin matter shells in general relativity.
* Lichnerowicz conditions: In general relativity, the Lorentzian metric gab and its first derivatives ∂a gbc must be continuous across a discontinuity surface; Higher derivatives need not be.
* Note on validity: Metrics are known with thin shell matter for which the metric is not continuous across the corresponding hypersurface; Marolf and Yaida have conjectured that in general relativity, in all positive-energy spacetimes, the metric is continuous across hypersurfaces.

References > s.a. action for general relativity [singular hypersurfaces]; gravitating matter; models in canonical general relativity.
@ Spacelike / timelike hypersurface: Israel NCB(66), NCB(67); in Misner et al 73, #21.13; Ipser & Sikivie PRD(84) [domain walls]; Fayos et al PRD(96) [spherical symmetry].
@ Spacelike / timelike, beyond thin wall: Garfinkle & Gregory PRD(90).
@ Null hypersurface: Penrose in(72) [spinors]; Redmount ["contranormal" coordinates]; Dray & 't Hooft CMP(85) [two Schwarzschild metrics separated by null shell]; Clarke & Dray CQG(87); Gemelli GRG(02) [rev, timelike/null]; Poisson gq/02.
@ General hypersurface: Barrabès CQG(89); Mars & Senovilla CQG(93)gq/02; Ferraris et al in(96); Nozari & Mansouri JMP(02); Vera CQG(02)gq [and symmetries]; Raju a0804-MG5 [distributional matter, shocks].
@ Perturbations: Mukohyama CQG(00)ht; Mars et al CQG(07); Copeland & Wands JCAP(07) [and cosmology].
@ Lemaître-Tolman-Bondi solutions: Khakshournia & Mansouri G&C(08) [and FLRW spacetimes]; Khakshournia GRG(10)-a0907 [and Vaidya exterior solution].
@ Other special types: Israel PRS(58) [spherically symmetric]; Grøn & Rippis GRG(03)gq [Schwarzschild-FLRW spacetimes]; Kirchner CQG(04) [spherically symmetric]; Copeland & Wands JCAP(07)ht/06 [cosmological]; Mena & Natário JGP(09) [stationary].
@ And energy conditions: Goldwirth & Katz CQG(95)gq/94; Marolf & Yaida PRD(05)gq.
@ At spacetime singularities: Khakshournia & Mansouri ht/99 [spherically symmetric, with singular hypersurface]; Rosenthal a1011.
@ Other topics: Schmidt GRG(84)gq/01 [and surface tension]; Taylor CQG(04) [at a corner].
> Related topics: see boundaries in field theory; constraints and solutions in general relativity [gluing of solutions].

In Modified Gravity Theories
@ Higher-order gravity: Deruelle et al PTP(08)-a0711 [f(R) gravity]; Senovilla PRD(13)-a1303, CQG(14)-a1402 [for f(R)-gravity, and consequences]; Reina et al CQG(16)-a1510 [junction conditions in quadratic gravity].
@ Other theories: Bressange CQG(00)gq [shells in Einstein-Cartan theory]; Macías et al PRD(02) [metric-affine gravity]; Giacomini et al PRD(06)gq [with spinning sources]; Padilla & Sivanesan JHEP(12)-a1206 [generalized scalar-tensor theories]; de la Cruz-Dombriz et al JCAP(14)-a1406 [extended teleparallel gravity].

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