Black-Hole Uniqueness and Hair  

No-Hair and Uniqueness Results > s.a. astrophysical tests of general relativity; black-hole perturbations; kerr spacetime; multipole moments.
* Idea: "Hair" denotes one or more parameters characterizing a black hole that are not associated with conserved quantities at infinity; The expression "black holes have no hair," introduced by Wheeler, means that a stationary black hole is characterized just by the value of those multipoles that cannot be radiated away; There are no bifurcations from the Kerr-Newman family of solutions; In particular, uniqueness theorems prove that there are no other families of solutions of the Einstein equation with the same parameters; These are global results, and are shown using Green-like identities and integrals.
* Results: 1984, Established first for electrovac solutions; They hold also in scalar-tensor theories and supergravity; There are no static, spherically symmetric Einstein-Dirac-Maxwell or Einstein-Yang-Mills-Dirac solutions with non-trivial spinors; 2015, Extended by Gürlebeck to certain types of astrophysical black holes; 2016, Soft-hair results by Hawking, Perry and Strominger.
* Exceptions: Scalar hair in Einstein-Yang-Mills-Higgs systems (but unstable), and higher-curvature (Gauss-Bonnet, string inspired) gravity (but no new conserved quantum number).
* No-short-hair theorem: If a spherically-symmetric static black hole has hair, then this hair must extend beyond 3/2 the horizon radius; The theorem fails beyond the regime of spherically-symmetric static black holes.
@ Books, reviews: Mazur in(87)ht/01; Chruściel CM(94)gq; Bekenstein gq/96-conf; Heusler HPA(96)gq, 96, LRR(98); Carter gq/97-MG8; Chruściel et al LRR(12)-a1205.
@ General references: Etesi CMP(98)ht/97 [stationary black holes]; Vigeland PRD(10)-a1008 [multipole moments of bumpy black holes]; Bhattacharya PRD(13)-a1307 [massive forms and spin-1/2 fields]; Gürlebeck PRL(15) + viewpoint Ashtekar Phy(15)-a1504 [static axisymmetric black holes with surrounding matter].
@ Phenomenology: Lyutikov a1209-proc [astrophysical black holes]; Johannsen CQG(16) + CQG+, Cardoso & Gualtieri CQG(16)-a1607 [electromagnetic tests, status]; Herdeiro & Radu CQG+(17); Thrane et al a1706 [tests with gravitational waves]; East & Pretorius PRL(17) [long-lived hair from superradiant instability, and gravitational-wave signature].

blue bullet Related topics: see results and solutions for specific types of hair \ black-hole solutions.

Modified Theories > s.a. scalar-tensor theories.
* In higher dimensions: In more than four dimensions, the conventional uniqueness theorem for asymptotically flat spacetimes does not hold, i.e., black objects cannot be classified only by their mass, angular momentum and charge.
@ In general: Ayón-Beato et al PRD(00)gq/99 [metric-affine gravity]; Vigeland et al PRD(11)-a1102 [bumpy black holes]; Skákala & Shankaranarayanan PRD(14)-a1312 [Lovelock gravity].
@ Proca field: Ayón-Beato in(02)gq; Zilhão et al CQG(15)-a1505 [very long-lived Proca field condensates]; Herdeiro et al a1603; Fan JHEP-a1606.
@ Higher-dimensional: Mazur & Bombelli JMP(87) [5D Kaluza-Klein theory]; Gibbons et al PRL(02)gq; Kol ht/02; Reall PRD(03) [supersymmetric, 5D]; Rogatko PRD(03)ht, PRD(04) [5D sigma-models, stationary], PRD(06); Hollands et al CMP(07)gq/06 [stationary rotating implies axisymmetric]; Hollands & Jazadjiev CQG(08) [5D Einstein-Maxwell]; Hollands & Yazadjiev CMP(11)-a0812 [D-dimensional stationary Kaluza-Klein black holes]; Figueras & Lucietti CQG(10)-a0906; Mizuno et al PRD(10)-a0911 [and Penrose inequality]; Yazadjiev PRD(10) [5D Einstein-Maxwell gravity], JHEP(11)-a1104 [5D Einstein-Maxwell-dilaton gravity]; Anabalón et al PRD(11)-a1108 [with gravitational hair]; Hollands CQG(12)-a1204 [uniqueness and new thermodynamic identities in 11D supergravity]; Hollands & Ishibashi CQG(12)-a1206 [rev].
@ 5D supergravity: Gutowski JHEP(04)ht; Tomizawa et al PRD(09)-a0901; Armas & Harmark JHEP(10) [multiple disconnected horizons]; Tomizawa PRD(10)-a1007.
@ Generalized no-hair / uniqueness theorems: Wells gq/98 [superstring black holes]; Hod PRD-a1612 [spherically symmetric reflecting stars].
@ Hairy situations: Dubovsky et al JHEP(07)-a0706 [Lorentz-violating theories of massive gravity]; Brito et al PRD(13)-a1309 [massive graviton hair].


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