nLab black ring

Idea

The Einstein equations for gravity in dimension $\geq 5$ admit black hole solutions whose event horizon is not homeomorphic to an n-sphere, but has different topology. In particular in 5d-gravity and 5d supergravity there are solutions with topology $S^1 \times S^2$. These are called black rings.

Their KK-reduction down to 4 dimensions yields again ordinary black holes. This plays a central role in the discussion of black holes in string theory.

Related concepts

• black string

• D=5 Einstein-Maxwell theory

• D=5 Maxwell-Chern-Simons theory

• D=5 supergravity

References

The first black ring solution was found, in D=5 gravity, in

• Roberto Emparan, Harvey Reall, A rotating black ring in five dimensions, Phys. Rev. Lett.88:101101, 2002 (arXiv:hep-th/0110260)

The first black ring solution was found, in D=5 supergravity, in:

• Henriette Elvang, Roberto Emparan, David Mateos, Harvey Reall, Supersymmetric 4D Rotating Black Holes from 5D Black Rings, JHEP0508:042,2005 (arXiv:hep-th/0504125)

Review:

• Roberto Emparan, Harvey Reall, Black Rings, Class. Quant. Grav. 23:R169, 2006 (arXiv:hep-th/0608012)

Dimensional reduction to black holes in D=4 gravity:

• Davide Gaiotto, Andrew Strominger, Xi Yin, 5D Black Rings and 4D Black Holes, JHEP 0602:023, 2006 (arXiv:hep-th/0504126)

On non-uniqueness:

• Roberto Emparan, Rotating Circular Strings, and Infinite Non-Uniqueness of Black Rings, JHEP0403:064, 2004 (arXiv:hep-th/0402149)

• Iosif Bena, Simon Ross, Nicholas Warner, Coiffured Black Rings, Class.Quant.Grav. 31 (2014) 165015 (arXiv:1405.5217)

As intersecting black M5-branes wrapped on a 4-manifold times the black ring’s circle:

• Emparan-Reall 06, Sec. 4.1, 4.2, 6.1

• Castro-David-Kraus-Larsen 08, Sec 2.2

following

• Juan Maldacena, Andrew Strominger, Edward Witten, Black Hole Entropy in M-Theory, JHEP 9712:002, 1997 (arXiv:hep-th/9711053)

More in the context of D1-D5-brane bound states

• Iosif Bena, Per Kraus, Microscopic description of black rings in AdS/CFT JHEP 12 (2004) 070 (hep-th/0408186)

• Iosif Bena, Per Kraus, Microstates of the D1-D5-KK system Phys. Rev. D72 (2005) 025007 (hep-th/0503053)

• Alejandra Castro, Joshua L. Davis, Per Kraus, Finn Larsen, String Theory Effects on Five-Dimensional Black Hole Physics (arXiv:0801.1863)

See also:

• Pavan Dharanipragada, Gurmeet Singh Punia, Amitabh Virmani: Non-supersymmetric F1-P black rings [arXiv:2601.04623]

• Pavan Dharanipragada, Gurmeet Singh Punia, Amitabh Virmani: Index saddle for supersymmetric F1-P black ring [arXiv:2601.04624]