In General > s.a. types of
metrics.
* Idea:
Establish 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: Israel NCB(66), NCB(67); in Misner et al 73, #21.13;
Ipser
& Sikivie
PRD(84)
[domain walls]; Fayos et al PRD(96)
[spherical symm].
@ Spacelike/timelike, beyond thin wall: Garfinkle & Gregory PRD(90).
@ Null: 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: 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-in [distributional matter, shocks].
@ Perturbations:
Mukohyama CQG(00)ht;
Mars et al CQG(07);
Copeland & Wands JCAP(07) [and cosmology].
@ Special types: Israel PRS(58) [spherically symmetric]; Grøn & Rippis GRG(03)gq [Schwarzschild-FRW];
Kirchner CQG(04)
[spherically symmetric]; Copeland & Wands ht/06 [cosmological].
@ And energy conditions: Goldwirth & Katz CQG(95)gq/94;
Marolf & Yaida PRD(05)gq.
@ Other topics: Schmidt GRG(84)gq/01 [and
surface tension]; Khakshournia & Mansouri
ht/99; Taylor CQG(04) [at a corner].
@ 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]; Deruelle et al PTP(08)-a0711 [f(R)
gravity].
> Related topics: see
constraints and solutions
in general relativity [gluing of solutions].
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
20 jun 2008