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 −
(2GMr − Q 2)
ρ−2]
dt2 −
2a sin2θ
(2GMr−Q 2)
ρ−2dt dφ +
+
ρ2
Δ−1dr2
+ ρ2 dθ2
+ sin2θ
[r2 + a2
+ a2sin2θ
(2GMr−Q 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)2 − c2a2 − GQ 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];
Neznamov & Shemarulin G&C(18)-a1806 [half-integer-spin particle motion];
Zhang & Liu PLB(19)-a1812
[spinning charged particles, innermost stable circular orbit].
@ 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];
Giorgi a2002 [Teukolsky equations];
> 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 PRD(16)-a1512 [charged-test-particle motion];
Mukherjee et al EPJC(19)-a1807 [novel features].
@ Kerr-Newman-de Sitter: Shiromizu & Gen CQG(00)gq/99 [spinning test particle];
Engman & Santana a1007 [spectral geometry of event horizon];
Franzen & Girão a2008 [double null coordinates].
@ With cosmological constant, other: 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];
> s.a. dirac fields; Superradiance.
@ With cosmological constant, thermodynamics: Brown et al PRD(94)gq;
Caldarelli et al CQG(00);
Fujisaki NCB(01).
@ Kerr-Newman-Gödel:
Herdeiro CQG(03);
Pourhassan et al AP(18)-a1811 [thermodynamics].
@ 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];
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. black-hole analogs [optical analog];
optics [optical geometry].
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