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].

__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].

main page – abbreviations
– journals – comments
– other sites – acknowledgements

send feedback and suggestions to bombelli at olemiss.edu – modified
26 jul 2017