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 + G2Q2/r2) dt2 + (1 – 2GM/r + G2Q2/r2)–1 dr2 + r22 .

* Singularities: For Q2 > M2, we get a naked singularity; For Q2 < M2, a regular black-hole solution with two horizons, at r = r+ = M ± (M2Q2)1/2, besides the true singularity at r = 0; For Q2 = M2, 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 = Qm sin 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.
@ Singularities: Giveon et al JHEP(04)ht [resolution, with scalar fields]; Abdel-Megied & Gad CSF(05)gq/04; Stoica PS(12)-a1111 [extension]; > 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 solution: 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. geodesics; klein-gordon fields; lensing; matter near black holes.
@ 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, a1304 [charged particles]; Pradhan Pra(16)-a1205, Pugliese et al EPJC(17)-a1304 [circular orbits]; Das et al a1609 [charged particles, Jacobi metric approach].
@ 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].

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 4 apr 2017