Reissner-Nordström Spacetimes| Reissner-Nordström Spacetimes |
In General > s.a. black holes;
generalized reissner-nordström spacetimes.
> Note: The spelling is
Reissner-Nordström, not Reissner-Nordstrøm [@ see Brill &
Dray GRG(93)].
$ Def: A family of solutions
of Einstein's equation representing a non-rotating black hole with non-zero
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 + GQ2 /r2) dt2 + (1 − 2GM/r + GQ2 /r2)−1 dr2 + r2 dΩ2 .
* Singularities:
For Q2 > GM2,
we get a naked singularity; For Q2 <
GM2, a regular black-hole solution with
two horizons, at r = r±
= GM ± (G2M2
− GQ2)1/2
(from grr = 0), besides the true
singularity at r = 0; For Q2
= GM2, the extreme case.
* Electromagnetic field:
if Qm = 0, Aa = (Qe/r, 0, 0, 0), F01 = −Qe/r2 ; if Qe = 0, Aa = (0, −Qm sin θ, 0, 0), F23 Qmsin θ .
* 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; One 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(08)-a0708;
Riazuelo IJMPD(19)-a1812.
@ Singularities: Giveon et al JHEP(04)ht [resolution, with scalar fields];
Abdel-Megied & Gad CSF(05)gq/04;
Stoica PS(12)-a1111 [extension];
Chesler et al a1902 [from charged scalar field collapse];
> s.a. perturbations [without singularities].
> Online resources:
see Wikipedia page.
Special Topics
> s.a. black-hole entropy; particle models;
perturbations [including stability]; spherical
symmetry; thermodynamics [including phase transitions].
@ Interior: Bonanno et al PRS(95)gq/94 [mass inflation];
Ivanov PRD(02)gq [pfluid];
Lemos & Zanchin PRD(11)-a1104 [de Sitter];
Hansraj et al IJTP(14).
@ Mass: Hushwater gq/01-wd;
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 JHEP(09)-a0901 [discontinuous nature, and black-hole entropy].
@ Embeddings: Paranjape & Dadhich GRG(04)gq/03 [embedding diagrams];
Paston & Sheykin Sigma(14)-a1304 [global embeddings in flat space].
@ Foliations: Reimann & Brügmann PRD(04)gq [maximal slicing, late time];
Qadir et al NCB(07) [K-slicing];
Tuite & Ó Murchadha a1307 [constant-mean-curvature slices].
@ Other related topics:
Couch & Torrence GRG(84) [spatial inversion];
Abramowicz et al CQG(02)gq [Fermat/optical geometry];
Chen & Sun JHEP(10) [hidden conformal symmetry];
Bengtsson et al CQG(14)-a1406 [the \(Q\to0\) and \(Q\to M\) limits];
Crispino et al EPJC-a1602 [tidal forces].
Motion of Particles and Waves
> s.a. klein-gordon fields; lensing;
matter near black holes; types of geodesics.
@ Particles: Dean GRG(99) [orbit precession];
Pradhan & Majumdar PLA(11)-a1001 [extremal, ISCOs];
Pugliese et al a1003-MG12 [circular motion];
Misra & Levin PRD(10)-a1007 [taxonomy of orbits];
Grunau & Kagramanova PRD(11)-a1011 [charged particles];
Pugliese et al PRD(11)-a1012 [neutral particles, circular geodesics],
PRD(11)-a1103,
EPJC(17)-a1304 [charged particles];
Pradhan Pra(16)-a1205,
Pugliese et al EPJC(17)-a1304 [circular orbits];
Das et al a1609 [charged particles, Jacobi metric approach];
Hong a1709 [test particles].
@ Spinning particles: Ali & Ahmed AP(00);
Mukhopadhyay CQG(00) [spin-1/2, charged];
Bini et al PRD(00),
IJMPD(05)-a1408;
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];
Babichev et al JETP(11)-a0806 [and perfect fluid];
Matyjasek et al PRD(10)-a1005 [quantum, vacuum polarization];
Aretakis a1006 [wave equation on extreme solution];
Chen & Jing PRD(10)-a1007;
Dain & Dotti CQG(13) [wave equation on the extreme Reissner-Nordström solution];
Franzen a1407 [boundedness in the interior].
@ Electromagnetic fields:
Torres del Castillo & Cartas-Fuentevilla PRD(96) [and gravitational waves];
Crispino & Oliveira PRD(08),
Crispino et al PRD(09) [absorption cross section].
@ Other fields: Goncharov PLB(99)gq [twisted spinors];
> s.a. dirac fields in curved spacetime.
@ Wave tails:
Koyama & Tomimatsu PRD(01) [massive scalar];
Blaksley & Burko PRD(07)-a0710 [same as in Schwarzschild spacetime].
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