Metric Matching| 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];
Lapiedra & Morales-Lladosa PRD(19)-a1910 [discontinuous source].
@ 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];
Huber EPJC(20)-a1908.
@ 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];
Chatterjee & Anand NPB(19)-a1810 [at fractal hypersurfaces].
> 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];
Olmo & Rubiera-García CQG(20)-a2007 [Palatini f(R) gravity];
Berezin et al CQG(21)-a2008,
PPN(20)-a2009 [shells in quadratic gravity];
Kolář et al PRD(21)-a2012 [infinite-derivative gravity].
@ Scalar-tensor theories:
Padilla & Sivanesan JHEP(12)-a1206 [generalized];
Avilés et al CQG(20)-a1910 [null or non-null, arbitrary dimensionality].
@ 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];
de la Cruz-Dombriz et al JCAP(14)-a1406 [extended teleparallel gravity];
Khakshournia & Mansouri IJMPD(20)-a2006 [Einstein-Cartan gravity].
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