Kerr Solutions  

In General > s.a. black holes; solutions with symmetries; particles and fields [including geodesics].
* Idea: A two-parameter family of solutions to Einstein's equation, representing (the only) stationary vacuum black-hole solutions.
* Line element: In Boyer-Lindquist coordinates, with ρ2(r,θ):= r2 + a2 cos2θ and Δ(r):= r2 – 2GMr + a2,

ds2 = ρ2 (dr2/Δ + dθ2) + (r2+a2) sin2θ dφ2– dt2 + (2GMr/ρ2) (a sin2θ dφ – dt)2 = ηab dxa dxbλ la lb dxa dxb ,

where λ = 2GMr3/(r 4+a2z2), and la = (1, (rx+ay)/(a2+y2), (ryax)/(a2+y2), z/r) is null with respect to ηab; > s.a. Kerr-Schild Solutions.
* Parameters: M represents the mass and Ma the angular momentum measured at infinity.
* Inequalities: The three parameters that characterize the Kerr black hole (M, a and horizon area) satisfy several important inequalities, some of which remain valid also for dynamical black holes; > s.a. black-hole geometry.
@ General references: Kerr PRL(63); Kerr & Schild in(65), re GRG(09); O'Neill 95; Deser & Franklin AJP(07)mar-gq/06 [and time-independence, pedagogical]; Visser in(09)-a0706 [introduction]; Kerr in(09)-a0706, Dautcourt GRG(09)-a0807 [historical]; Wiltshire et al ed-09; Teukolsky CQG(15)-a1410 [overview]; Heinicke & Hehl IJMPD(15)-a1503 [intro].
@ Derivations: Carter in(73) [nice, based on wave equation separability]; Deser & Franklin GRG(10)-a1002 [pedagogical]; Dadhich GRG(13)-a1301.
> Generalizations: see black-hole perturbations [including instability]; generalized kerr metrics; numerical models [collapse]; quantum black holes.

Coordinates and Geometry > s.a. Ergosphere; horizons; Hypersurfaces; petrov classification; Smarr Formula.
* Singularities and horizons: They have a singularity at r = 0, horizons at r = r±, and an ergosurface at r = r0, where

r± = GM ± [(GM)2a2]1/2 ,   r0 = GM + [(GM)2a2cos2θ]1/2 .

* Killing tensor: The tensor Kab = Δ l(a l'b) + r2gab [@ Ludvigsen]; > s.a. killing tensors [and Killing-Yano tensor].
* Boyer-Lindquist coordinates: A coordinate system that allows to maximally extend the Kerr solution.
* Light-like limit: The gravitational field relative to a distant observer moving at high speed rectilinearly in an arbitrary direction is an impulsive plane gravitational wave with a singular point on its wave front.
@ Coordinates and extensions: Boyer & Lindquist JMP(67); Doran PRD(00)gq/99; Herberthson GRG(01) [extension at spi]; Fletcher & Lun CQG(03), Bishop & Venter PRD(06) [generalized Bondi-Sachs]; Hayward PRL(04)gq [Kruskal-like, dual null]; Bini et al CQG(05)gq [static observers, Fermi coordinates]; Natário GRG(09)-a0805 [generalized Painlevé-Gullstrand]; Novello & Bittencourt G&C(11)-a1004 [Gaussian coordinate systems]; García-Compeán & Manko PTEP(15)-a1205 [physically inconsistency of maximal analytic extensions]; Dennison et al PRL(14)-a1409 [new family of analytical coordinate systems, trumpet slices].
@ Papapetrou gauge: Bergamini & Viaggiu CQG(04); Moreno & Núñez GRG(05).
@ Light-cone structure: Pretorius & Israel CQG(98); Bai et al PRD(07)gq [near null infinity].
@ Other geometric properties: Jerie et al CQG(99), comment Hall & Keane CQG(00) [symmetries]; Marsh gq/07 [infinite-redshift surfaces]; Jacobson & Soong CQG(09)-a0809 [ergosurface]; Castro et al PRD(10)-a1004 [hidden conformal symmetry]; Schinkel et al CQG(14)-a1310 [constant-mean-curvature slices].
@ Invariants, intrinsic characterization: Lake GRG(03)gq, GRG(04)gq/03; Ferrando & Sáez CQG(09)-a0812; Abdelqader & Lake PRD(15)-a1412 [horizon, M, a].
@ Extreme case, geometry: Wang et al PRD(98); Åman et al CQG(12)-a1206 [Killing-vector behavior].

Physical Properties and Related Topics > s.a. black-hole thermodynamics [phase transitions]; energy.
@ General references: Cohen JMP(68) [angular momentum]; Berti et al PRL(16)-a1605 [testing the Kerr nature of a black hole with spectroscopy]; > s.a. black-hole uniqueness and hair.
@ Stability: Beyer CMP(01)ap/00; Finster & Smoller a1609 [outline of proof].
@ Quantum corrections: Reuter & Tuiran PRD(11)-a1009; > s.a. schwarzschild space.
@ Other topics: Ge & Leng PLA(94) [approximations]; de Felice & Preti CQG(99) [separation constants]; Mars CQG(99)gq [characterization]; Loinger gq/99/NCB [?]; Camargo & Socolovsky a1405 [Rindler approximation]; Gralla et al PRD(16)-a1602 [magnetosphere]; Hernández-Pastora & Herrera PRD(17)-a1701 [interior solution]; > s.a. initial-value formulation; lanczos potential.
> Phenomenology: see black-hole phenomenology; particles and fields in kerr spacetimes.


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