Schwarzschild Solution |
In General
> s.a. quantum black holes; spherical
solutions; schwarzschild geometry [including line element, curvature].
* Idea: The
1-parameter family of static, spherically symmetric solutions,
representing vacuum black holes; The first solution (other than Minkowski
space) in general relativity, found in 1916, and one of the most
important, equivalent to the Kepler problem in classical mechanics.
@ General references:
Schwarzschild VAG(00)-CQG(98),
SPAW(16)-GRG(03)phy/99,
SPAW(16)phy/99;
in Hawking & Ellis 73;
in Wald 84;
Gruber et al AJP(88)mar [derivation no-go];
Santander et al AJP(97)dec [curvature-based];
Visser IJMPD(05)gq/03 [heuristic];
Antoci phy/03-ch,
Gsponer phy/04 [history];
Schmidt GRG(05)gq/04 [Synge's contribution];
Bel a0709;
Berezin IJMPA(11)-a1006 [local formalism for global properties];
Cuzinatto et al AJP(11)jun-a1009 [Lenz-Sommerfeld argument];
Corda EJTP(11)-a1010 [Schwarzschild's original work];
Crater a1404 [with pointlike source?];
Zhang et al PRD(14)-a1412 [from thermodynamic considerations];
Heinicke & Hehl IJMPD(15)-a1503 [intro];
Grøn AJP(16)jul [centenary].
@ Pedagogical: Deser & Franklin AJP(05)mar-gq/04 [derivation];
Dadhich CS-a1206;
Kassner EJP(15)-a1502 [weak-field limit].
@ Characterization:
Ferrando & Sáez CQG(98);
Fernández-López et al JGP(03).
> Related topics:
see Birkhoff's Theorem; numerical black holes;
perturbations of the schwarzschild metric.
Specific Concepts > s.a. Irreducible Mass;
gravitational lensing; schwarzschild geometry
[including singularity and extensions]; yang-mills gauge theory.
@ Boosted (Aichelburg-Sexl): Barrabès & Hogan PRD(01)gq;
> s.a. solutions of general relativity.
@ Interior:
Som et al PLA(01) [matter];
Füzfa et al GRG(02) [Lemaître-Schwarzschild];
Doran et al FP(08)gq/06;
Helliwell & Konkowski GRG(11)-a1006 [with 2-sphere singularity];
Ellis a1203 [improved interior metric];
Beltracchi & Gondolo PRD(19)-a1902 [exact time-dependent solution];
> s.a. black holes.
@ Canonical approach: Varadarajan PRD(01)gq/00 [Kruskal variables].
@ Quantum corrections: Becker & Becker PRD(99) [11D matrix theory];
Vaz & Witten PRD(99)gq/98 [canonical];
Burić & Radovanović CQG(00);
Cavaglià & Ungarelli PRD(00)ht/99 [mass];
Cavaglià & Fabbri PRD(02)ht/01 [AdS2 and n-Schwarzschild];
Bjerrum-Bohr et al PRD(03)ht/02 [and Kerr];
Khriplovich & Kirilin JETP(04);
Fabbri et al JPCS(06)ht/05;
Kirilin PRD(07)gq/06;
Holstein gq/06 [spin-1, and Kerr];
Dasgupta JCAP(10)-a0910 [and unstable orbits];
Kim & Kim PLB(12) [phase transition];
Culetu a1508;
Farag Ali et al EPL-a1510 [from minimal length, and classical tests of gravity];
Bargueño et al EPL(17)-a1605;
Khodadi et al PLB(17)-a1702 [from minimal length];
Calmet & El-Menoufi EPJC(17)-a1704;
Ashtekar et al PRD(18)-a1806 [quantum extension];
Faraoni & Giusti Symm-a2006 [unsettling physics];
> s.a. black-hole entropy; covariant
quantum gravity; semiclassical general relativity.
@ With matter: Hartle in(72) [long-range neutrino forces];
Goncharov PLB(99)gq [twisted spinors];
Molnár & Elsässer PRD(03)gq [uniqueness of electrostatic solution];
Bormann & Antonsen IJTP(04) [0-point energy, scalar and fermion fields];
Doran et al PRD(05) [fermion absorption cross section];
Sharif & Sheikh GRG(07)-a0705 [cold plasma, dispersion relations];
Bergamin et al CQG(09) [vibrating systems].
@ Other: Karlhede et al GRG(82) [horizon and Karlhede invariant];
Abrams CJP(89)gq/01 [??];
Quirós gq/99 [spurious??];
Nikishov gq/00 [energy-momentum pseudotensor];
Krasnov & Solodukhin ATMP(04)ht [stringy description];
Antoci & Liebscher in(06)gq/04 [surface is singular??].
> With matter:
see black-hole phenomenology [including appearance to an observer];
particles in schwarzschild spacetime; waves and fields.
> Related topics:
see green functions; metric matching;
perturbations; Phantom Field;
self-force; Weyl-Lanczos Equations.
> Other: see boundaries
[extensions?]; cosmic strings; regge calculus;
sources of gravitational waves.
Similar Solutions > s.a. black-hole solutions
and higher-dimensional black holes [including Schwarzschild-Tangherlini];
gravitational instanton [Euclidean].
* In cosmological
backgrounds: Solutions which represent a black hole or local system
in an asymptotically FLRW spacetime, or other cosmological background.
* Conformal gravity: Replace
1 − (2GM/r) \(\mapsto\) 1 − (2GM/r)
+ γr − kr2 in line
element above (γ, k are integration constants).
@ Schwarzschild-FLRW solutions:
Gautreau PRD(84);
Grøn & Rippis GRG(03)gq;
Gao CQG(04) [arbitrary D];
Senevirathne & de Silva a0812;
> s.a. McVittie Metric.
@ In other backgrounds: Nayak et al PRD(01) [Einstein universe].
@ Non-commutative:
Nasseri GRG(05)ht,
comment Li ht/05;
Nicolini et al PLB(06)gq/05 [and evaporation];
Nasseri IJMPD(06);
Batic & Nicolini PLB(10)-a1001 [stability of the interior and horizon effects];
Arraut et al JMP(10)-a1001 [maximal extension];
Gangopadhyay JPCS(12)-a1212 [and the Voros product].
@ With other fields: Ren & Lichun NCB(01) [sourrounded by radiation];
in Kastor & Traschen CQG(17)-a1607 [Janis-Newman-Winicour, with massless scalar field]
@ Other theories: Federbush gq/00 [quadratic curvature];
Zet gq/03 [teleparallel gravity with torsion];
López-Domínguez et al PRD(09)-a0910 [supersymmetric];
De Felice et al PRD(11)-a1102 [in f(R,G) gravity, stability];
Cognola et al PRD(11) [covariant renormalizable gravity theory];
Nashed EPL(14)-a1501 [extended teleparallel gravity];
Chamseddine & Mukhanov EPJC(17)-a1612 [limited-curvature theory];
> s.a. branes; dilaton gravity;
massive gravity.
@ Other modifications: Abrams PRD(79)gq/02 [Droste-Weyl-Schwarzschild];
Dadhich et al Pra(98)gq/97 [with global monopole charge];
Aichelburg & Balasin CQG(98),
CQG(00) [ultrarelativistic];
Gen & Shiromizu JMP(99) [asymptotically Schwarzschild];
de Felice & Sorge CQG(03) [with magnetic field, orbits];
Martínez-Morales gq/05;
Al-Badawi & Halilsoy GRG(06) [+ Robinson-Bertotti, and NUT parameter];
Hackmann et al PRD(10)-a0912 [pierced by a cosmic string, geodesics];
Gaete et al PLB(10)-a1005 [un-gravity corrections];
Anastasiei & Gottlieb a1104 [Schwarzschild-like metric];
Belletête & Paranjape IJMPD(13)-a1304-GRF [negative-mass];
Banik & Guendelman a1510 [topological deformation];
Kinyanjui & Wamalwa a1703 [in post-Riemannian Finsler spacetime];
> s.a. holonomy [Schwarzschild-Droste]; modified
black-hole solutions; perturbations [including M < 0].
> Other related metrics: see FLRW
spacetimes; kerr spacetime; metric matching;
reissner-nordström spacetime; schwarzschild-de sitter spacetime
[including M < 0].
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