Boundary value problem for five-dimensional stationary rotating black holes

Morisawa, Yoshiyuki; Ida, Daisuke

doi:10.1103/physrevd.69.124005

Cited by 84 publications

(95 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This leads us to conclude that this near-horizon geometry does not correspond to that of an asymptotically flat black hole. It should also be noted that in the non-extremal case it has been shown [51] that the Myers-Perry black hole is the unique asymptotically flat black hole with two rotational symmetries and S 3 topology horizon and one expects this result to go over in the extremal case (and its near-horizon geometry is in fact given by our other class of S 3 horizon geometries). Another useful aspect of this analysis is that the explicit metrics for the various nearhorizon geometries appear simple in the coordinates we have derived.…”

Section: Discussionmentioning

confidence: 99%

“…This latter solution implies Γ and Q are both constants -this is incompatible with having a compact H and therefore we discount it. Therefore Γ must be given by (51) and since by definition σ is only defined up to an additive constant, without loss of generality we will set σ 0 = 0. We can now integrate easily for Q using (37) to find:…”

Section: Four Dimensionsmentioning

confidence: 99%

See 1 more Smart Citation

A classification of near-horizon geometries of extremal vacuum black holes

Kunduri

Lucietti

2009

Journal of Mathematical Physics

134

221

View full text Add to dashboard Cite

We consider the near-horizon geometries of extremal, rotating black hole solutions of the vacuum Einstein equations, including a negative cosmological constant, in four and five dimensions. We assume the existence of one rotational symmetry in 4d, two commuting rotational symmetries in 5d and in both cases non-toroidal horizon topology. In 4d we determine the most general near-horizon geometry of such a black hole, and prove it is the same as the near-horizon limit of the extremal Kerr-AdS 4 black hole. In 5d, without a cosmological constant, we determine all possible near-horizon geometries of such black holes. We prove that the only possibilities are one family with a topologically S 1 × S 2 horizon and two distinct families with topologically S 3 horizons. The S 1 × S 2 family contains the near-horizon limit of the boosted extremal Kerr string and the extremal vacuum black ring. The first topologically spherical case is identical to the near-horizon limit of two different black hole solutions: the extremal Myers-Perry black hole and the slowly rotating extremal Kaluza-Klein (KK) black hole. The second topologically spherical case contains the near-horizon limit of the fast rotating extremal KK black hole. Finally, in 5d with a negative cosmological constant, we reduce the problem to solving a sixth-order non-linear ODE of one function. This allows us to recover the near-horizon limit of the known, topologically S 3 , extremal rotating AdS 5 black hole. Further, we construct an approximate solution corresponding to the near-horizon geometry of a small, extremal AdS 5 black ring.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Four Dimensionsmentioning

confidence: 99%

A classification of near-horizon geometries of extremal vacuum black holes

Kunduri

Lucietti

2009

Journal of Mathematical Physics

134

221

View full text Add to dashboard Cite

show abstract

“…Our proof mostly relied on the known σ-model formulation of the reduced Einstein equation [25,26], combined with basic arguments clarifying the global structure of the factor manifold of symmetry orbits.…”

Section: Resultsmentioning

confidence: 99%

“…Following [26] (see also [25]), this is done as follows in 5 dimensions. On M, we first define the two twist 1-forms…”

Section: The Factor Spacemmentioning

confidence: 99%

Uniqueness Theorem for 5-Dimensional Black Holes with Two Axial Killing Fields

Hollands

Yazadjiev

2008

Commun. Math. Phys.

179

350

View full text Add to dashboard Cite

We show that two stationary, asymptotically flat vacuum black holes in 5 dimensions with two commuting axial symmetries are identical if and only if their masses, angular momenta, and their "rod structures" coincide. We also show that the horizon must be topologically either a 3-sphere, a ring, or a Lens-space. Our argument is a generalization of constructions of Morisawa and Ida (based in turn on key work of Maison) who considered the spherical case, combined with basic arguments concerning the nature of the factor manifold of symmetry orbits.

show abstract

“…4 exhaust the allowed phases of rotating black holes with a single angular momentum in thermal equilibrium (see, however, [62]). Work related to the classification of the five-dimensional phases can be found in [63,64]. The main properties of the phases in Fig.…”

Section: The "Finesse" Of Five Dimensionsmentioning

confidence: 99%

Phases of Higher Dimensional Black Holes

Niarchos

2008

Mod. Phys. Lett. A

View full text Add to dashboard Cite

We review some of the most striking properties of the phase diagrams of higher dimensional black holes in pure gravity. We focus on static black hole solutions with KaluzaKlein asymptotics and stationary black hole solutions in flat Minkowski space. Both cases exhibit a rich pattern of interconnected phases and merger points with topology changing transitions. In the first case, the phase diagram includes uniform and non-uniform black strings, localized black holes and sequences of Kaluza-Klein bubbles. In the latter case, it includes Myers-Perry black holes, black rings, black saturns and pinched black holes.

show abstract

Boundary value problem for five-dimensional stationary rotating black holes

Cited by 84 publications

References 24 publications

A classification of near-horizon geometries of extremal vacuum black holes

A classification of near-horizon geometries of extremal vacuum black holes

Uniqueness Theorem for 5-Dimensional Black Holes with Two Axial Killing Fields

Phases of Higher Dimensional Black Holes

Contact Info

Product

Resources

About