Kerr-Newman Solutions  

In General > s.a. axisymmetry; cosmic censorship; gravitational energy; quasilocal energy.
* Idea: A 3-parameter (or 4-parameter, if we include magnetic charge) family of type II-II solutions of the Einstein equation, representing (the only) stationary electrovac black-hole solutions.
* Metric: In the standard coordinate system, the line element is

ds2 = –[1–(2GMrQ 2) ρ–2] dt2 – 2a sin2θ (2GMrQ 2) ρ–2dt dφ +
                   + ρ2 Δ–1dr2 + ρ2 dθ2 + sin2θ [r2+a2+a2sin2θ (2GMrQ 2) ρ–2] dφ2 ,

with Δ:= r2 – 2GMr + a2 + Q2, ρ2:= r2 + a2cos2θ; M is the mass, J:= Ma the angular momentum at infinity, and Q = (Qe2+Qm2)1/2 the electromagnetic charge (one usually sets Qm = 0).
* Singularities and horizons: They have a singularity at r = 0 and horizons at r = r±, where (restoring c and G)

r± = [GM ± ((GM)2c2a2GQ 2)1/2]/c2 ;

The condition for not having a naked singularity is M 2 > a2 + Q 2 (the case M 2 = a2 + Q 2 is the extreme Kerr-Newman black hole).
* Dipoles: The asymptotic electric and magnetic dipole moments are, respectively, Qea and Qma.
* Duality transformations: The metric is invariant under variations in Qe and Qm with Q 2 = constant.
* Uniqueness: They are the only stationary electrovac black-hole solutions.
@ General references: Newman et al JMP(65); Mazur JPA(82); Cohen & de Felice JMP(84) [effective mass]; Krori & Barua PRD(87); Kokkotas GRG(88) [ergosurface]; Andréka et al GRG(08)-a0708 [ring singularity and acausality]; Wong AHP(09)-a0807 [covariant characterization]; Meinel a1310-proc [physical derivation]; Adamo & Newman Sch-a1410 [rev].
@ Coordinates, geometry: Zhang & Zhao PLB(05) [and radiation]; Lin & Soo GRG(13)-a0905 [Painlevé-Gullstrand-type coordinates]; Rosquist GRG(09) [generalized Boyer-Lindquist form for the metric]; García-Compeán & Manko PTEP(15)-a1205 [physically inconsistency of maximal analytic extensions].
@ Quantum corrections: Donoghue et al PLB(02)ht/01, err PLB(05); Holstein PRD(06)gq.
@ Related topics: Kaiser JPA(04)gq/01-conf [Newman's complex formalism]; Berman gq/04 [energy]; Frolov PRD(06)gq [embedding of surface in E4]; Gong et al PRD(07) [Newman-Penrose constants]; Wang & Liu JHEP(10)-a1004, Chen et al PRD(10) [hidden conformal symmetries]; Modak & Samanta IJTP(12)-a1009 [Komar angular momentum]; > s.a. initial-value formulation; teleparallel theory.

Particles, Fields and Perturbations > s.a. tests of general relativity with light; types of geodesics.
@ Particles: Stuchlík & Hledík CQG(00)-a0803 [photons, equatorial]; Ivanov & Prodanov PLB(05)gq [charged, equatorial]; Dokuchaev CQG(11)-a1103 + news pw(11)may, G&C(12)-a1203 [stable orbits inside the black hole]; Pugliese et al PRD(13)-a1303 [neutral test particles in the equatorial plane]; Hackmann & Xu PRD(13)-a1304 [charged particles].
@ Fields: Batic & Schmid PTP(06)gq [Dirac propagator]; > s.a. dirac fields; klein-gordon fields; quantum fields in curved backgrounds.
@ Perturbations: Kalnins & Williams CQG(98) [integrability]; Cherubini & Ruffini NCB(00); Perjés & Vasúth ApJ(03)gq/02; Casals PhD(04)-a0802 [electromagnetic, quantum]; Engman & Cordero-Soto JMP(06) [spectral geometry of event horizon]; Pani et al PRL(13)-a1304 [gravito-electromagnetic perturbations], PRD(13)-a1307 [slow-rotation imit]; > s.a. quasinormal modes.
@ Stability: Reiris a1311 [electrovacuum instability]; Zilhão et al PRD(14)-a1410 [non-linear stability]; Dias et al PRL(15)-a1501 [linear stability within Einstein-Maxwell theory, non-extremal].

Thermodynamics > s.a. black-hole thermodynamics [phase transitions, Ruppeiner theory] and specific types.
@ General references: Kaburaki PRD(96); Belgiorno & Martellini IJMPD(04)gq/02 [third law]; Fujisaki NCB(07) [in Brans-Dicke theory]; Panković et al a0804 [simple "derivation"]; Panković et al SAJ(09)-a0811 [and dynamics]; Anderson GRG(12)-a1206 [state space].
@ Hawking radiation: Chen & Yang IJTP(07); Zhang & Zhao PLB(06)gq/05 [charged particles]; Umetsu IJMPA(10)-a0908 [tunneling approach].
@ Quantum: Mäkelä et al PRD(01)gq/00; Gour & Medved CQG(03)gq/02.

Similar Metrics and Other Topics > s.a. kerr spacetime; quantum black holes; semiclassical quantum gravity.
* Melvin-Kerr-Newman spacetimes: Black holes immersed in a distorting background magnetic field; Unlike the standard Kerr-Newman family, they are not asymptotically flat.
@ Kerr-Newman-NUT: Bini et al CQG(03)gq, PRD(03)gq [particles and fields]; Cebeci et al a1512 [charged-test-particle motion].
@ With cosmological constant: Shiromizu & Gen CQG(00)gq/99 [Kerr-Newman-de Sitter, spinning test particle]; Podolský & Griffiths PRD(06)gq [accelerating]; Aliev CQG(07) [Kerr-Newman-Anti-de Sitter, gyromagnetic ratio]; Sahay et al JHEP(10)-a1002 [thermodynamic geometry, phase transitions]; Engman & Santana a1007 [Kerr-Newman-de Sitter, spectral geometry of event horizon]; > s.a. dirac fields; Superradiance.
@ With cosmological constant, thermodynamics: Brown et al PRD(94)gq; Caldarelli et al CQG(00); Fujisaki NCB(01).
@ Other metrics: Quevedo & Mashhoon PRD(91) [axisymmetric deformations]; Gao & Shen CQG(02) [Kerr-Newman-Kasuya]; Burinskii a0704 [boosted, charged spinning lightlike solutions in Kerr-Schild form]; Booth et al CQG(15)-a1502 + CQG+ [Melvin-Kerr-Newman spacetimes].
@ Generalizations: Manko PLA(93) [magnetic]; Herdeiro CQG(03) [Kerr-Newman-Gödel]; Ansorg et al GRG(11) [distorted by arbitrary axisymmetric and stationary surrounding matter]; Dymnikova IJMPD(15)-a1510 [in non-linear electrodynamics]; Fan et al PRD(16)-a1512 [5D]; > s.a. black holes in generalized theories [f(R)] and in higher dimensions [rotating, charged]; Vaidya Metrics.
@ Related topics: Sidharth CSF(04) [and quantum electron, varying G, ...?]; Tahvildar-Zadeh a1410, Kiessling & Tahvildar-Zadeh JMP(15)-a1410 [zero-gravity limit]; > s.a. optics [optical geometry].

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