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].

@ __Gravitational-wave-based tests__:
Thrane et al PRD(17)-a1706;
East & Pretorius PRL(17) [long-lived hair from superradiant instability, and gravitational-wave signature];
Carullo et al a1805 [ringdown phase of binary coalescence]

@ __Other phenomenology__: Lyutikov a1209-proc [astrophysical black holes];
Johannsen CQG(16)
+ CQG+,
Cardoso & Gualtieri CQG(16)-a1607 [electromagnetic tests, status];
Herdeiro & Radu CQG+(17).

@ __Related topics__: Dobkowski-Ryłko et al a1803 [local version].

__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(16)-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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