Kerr-Newman Solutions  

In General > s.a. axisymmetry; 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.
* Line element:

ds2 = –[1–(2GMr–Q2) –2] dt2 – 2a sin2 (2GMr–Q2) –2dt d +
                   + 2 –1dr2 + 2 d2 + sin2 [r2+a2+a2sin2 (2GMr–Q2)–2] d2 ,

with := r2 – 2GMr + a2 + Q2, 2:= r2 + a2cos2; 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)2–c2a2–GQ2)1/2]/c2 ;

The condition for not having a naked singularity is M2 > a2 + Q2 (the case M2 = a2 + Q2 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 Q2 = 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].
@ Coordinates, geometry: Zhang & Zhao PLB(05) [and radiation]; Lin & Soo a0905 [Painlevé-Gullstrand-type coordinates]; Rosquist GRG(09) [generalized Boyer-Lindquist form for the metric].
@ Quantum corrections: Donoghue et al PLB(02)ht/01, err PLB(05) [quantum corrections]; Holstein gq/06.
@ Related topics: Kaiser JPA(04)gq/01-in [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]; > s.a. teleparallel theory.

Particles, Fields and Perturbations > s.a. black-hole perturbations.
@ Particles: Stuchlík & Hledík CQG(00)-a0803 [photons, equatorial]; Ivanov & Prodanov PLB(05)gq [charged, equatorial].
@ Scalar field: Furuhashi & Nambu PTP(04)gq [massive, instability].
@ Other fields: Batic & Schmid PTP(06)gq [Dirac propagator]; > s.a. dirac fields in curved spacetime.
@ 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].

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]; Pankovic et al a0804 [simple "derivation"]; Pankovic et al a0811 [and dynamics].
@ Hawking radiation: Chen & Yang IJTP(07); Zhang & Zhao PLB(06)gq/05 [charged particles]; Umetsu 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.
@ Kerr-Newman-NUT: Bini et al CQG(03)gq, PRD(03)gq [particles and fields].
@ With cosmological constant: Shiromizu & Gen CQG(00)gq/99 [Kerr-Newman-de Sitter, spinning test particle]; Podolsky & Griffiths PRD(06)gq [accelerating]; Aliev CQG(07) [Kerr-Newman-AdS, gyromagnetic ratio]; > 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: Gao & Shen CQG(02) [Kerr-Newman-Kasuya]; Burinskii a0704 [boosted, charged spinning lightlike solutions in Kerr-Schild form].
@ Generalizations: Quevedo & Mashhoon PRD(91) [axisymmetric deformations]; Manko PLA(93) [magnetic]; Herdeiro CQG(03) [KN-Gödel].
@ Related topics: Sidharth CSF(04) [and quantum electron, varying G, ...?]; > s.a. optics [optical geometry].

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