Reissner-Nordström
Spacetime| Reissner-Nordström
Spacetime |
In General > s.a. black holes; black-hole
entropy, perturbations and
thermodynamics [including phase transitions].
$ Def: A family of solutions
of Einstein's equation representing a nonrotating black hole with nonzero electric
charge, depending on the parameters M (mass) and Q =
(Qe2 + Qm2)1/2 (electromagnetic
charges) [c = 1], and line element
ds2 = –(1 – 2GM/r +
G2Q2/r2)
dt2 +
(1 – 2GM/r + G2Q2/r2)–1 dr2
+ r2 d
2
.
* Singularities: For Q2 > M2,
we get a naked singularity; For Q2 < M2,
a regular black-hole solution with two horizons, at r = r+ = M 
(M2–Q2)1/2,
besides the true singularity at r = 0; For Q2 = M2,
extreme case.
* Electromagnetic field:
if Qm = 0, Aa =
(Qe/r, 0, 0, 0), F01
= –Qe/r2 ; if Qe =
0, Aa =
(0, –Qm sin 
,
0, 0), F23 = Qm sin .
* Symmetries: The only
conformal or projective vector fields it admits are its standard Killing vector
fields [@ Hall
CQG(00)].
* Fermat geometry: For P =
0, if q:= Q/M and
d2:= 1–q2 (the
horizon is at r/M = 1/d), then the Fermat geometry
is non-hyperbolic for r/M > 1
+ (d/2)2/3; can get arbitrarily
close to the horizon (
SS
1.12.1995).
@ General references: Reissner AdP(16);
Nordström PKNAW(18);
Klösch & Strobl
CQG(96)
[global coordinates]; Marsh FP-a0708.
@ Singularities: Giveon et al JHEP(04)ht [resolution, with scalar
fields]; Abdel-Megied & Gad CSF(05)gq/04.
> Note: The spelling
is Reissner-Nordström, not Reissner-Nordstrøm [@ see Brill & Dray
GRG(93)].
Special Topics > s.a. particle
models.
@ Interior solution: Bonanno et al PRS(95)gq/94; Ivanov PRD(02)gq [pfluid].
@ Mass: Hushwater gq/01;
Barbachoux et al IJMPD(02)gq;
Herrera et al GRG(03)gq [active mg].
@ The extremal limit:
Wang et al
PRD(98)gq [no-go
for physical process]; Carroll
et al a0901 [discontinuous
nature, and black-hole entropy].
@ Other topics: Couch & Torrence GRG(84)
[spatial inversion]; Abramowicz
et
al
CQG(02)gq [Fermat/optical
geometry]; Paranjape & Dadhich GRG(04)gq/03 [embedding
diagrams]; Reimann & Brügmann PRD(04)gq [maximal
slicing, late time]; Qadir et al NCB(07) [K-slicing].
Motion of Particles and Waves > s.a. klein-gordon
fields; lensing.
@ Particles: Dean GRG(99) [orbit precession].
@ Spinning particles: Ali & Ahmed AP(00); Mukhopadhyay CQG(00) [spin-1/2,
charged];
Bini et al PRD(00), IJMPD(05); Firsova MPLA(03) [scattering].
@ Scalar fields: Ori PRD(98)gq/97 [massless];
Wang & Huang
PRD(01)
[back-reaction]; Sini & Kuriakose IJMPD(09)-a0708 [WKB
approximation].
@ Electromagnetic fields: Torres del Castillo & Cartas-Fuentevilla PRD(96)
[and gravitational waves]; Crispino & Oliveira PRD(08)
[absorption
cross section].
@ Other fields: Goncharov PLB(99)gq [twisted
spinors]; > s.a. dirac fields.
@ Wave tails: Koyama & Tomimatsu PRD(01)
[massive scalar]; Blaksley & Burko PRD(07)-a0710 [same
as in Schwarzschild].
Similar and Modified Solutions > s.a. kerr-newman
spacetime;
teleparallel gravity;
wormholes.
@ RN-de Sitter: Brady et al PRD(97)
[tails of fields]; Stuchlík & Hledík APS(02)-a0803;
Ali GRG(03)
[spinning
particle];
Guo et al IJMPA(03), GRG(05)
[extreme, scalar field theory]; Brännlund GRG(04)gq/03 [conformal
isometry];
Astefanesei
et
al
JHEP(04)ht/03 [and
dS-cft]; Molina et al PRD(04)gq/03 [field
propagation]; > s.a. quantum black holes.
@ RN-de Sitter, thermodynamics: Cai et al CQG(98)gq/97;
Ren et al NCB(98); Wang & Huang CQG(02)
[York formalism]; Barlow et al PRD(05)gq [+
scalar].
@ RN-Anti de Sitter: Wang et al PRD(00)
[extreme], PRD(01)
[massless scalar]; Kim
et
al PRD(00)
[GEMS approach]; Wu PRD(00)
[critical phenomena]; Wang et al PRD(04)ht [massless
scalar quasi-normal modes].
@ RN-Anti de Sitter, thermodynamics: Louko & Winters-Hilt PRD(96);
Chamblin et al PRD(99);
Aman et al a0901-in.
@ In FRW models: Shah & Vaidya Tens(68);
Gao & Zhang PLB(04)gq,
GRG(06)gq/04 [higher-dimensional].
@ Double Reissner-Nordström: Manko PRD(07);
Paolino
& Pizzi IJMPD(08)
[electric field lines]; Manko et al a0811 [+ dilaton].
@ Other solutions: Robinson et al IJTP(69)
[generalized]; Rudolph et al
IJMPA(96)
[arbitrary
group and dimension];
Graf
CQG(01)
[extremal, weak extension].
@ In other theories: Macías & Socorro CQG(99)gq [metric-affine
gravity];
Bretón CQG(02)
[Born-Infeld]; Nashed & Shirafuji IJMPD(07)-a0704 [tetrad gravity].
@ Quantum corrections: Buric & Radovanovic CQG(99);
Donoghue et al
PLB(02)ht/01,
erratum PLB(05);
Holstein gq/06;
> s.a. non-commutative gravity.
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jul
2009