Near-horizon symmetries of extremal black holes

By Hari K. Kunduri, James Lucietti, Harvey Reall. 2007

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Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a near-horizon SO(2, 1) symmetry. We prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as known four- and five-dimensional solutions (including black rings). The result is valid for a general two-derivative theory of gravity coupled to Abelian vectors and uncharged scalars, allowing for a non-trivial scalar potential. We prove that it remains valid in the presence of higher-derivative corrections. We show that SO(2, 1)-symmetric near-horizon solutions can be analytically continued to give SU(2)-symmetric black hole solutions. For example, the near-horizon limit of an extremal 5D Myers–Perry black hole is related by analytic continuation to a non-extremal cohomogeneity-1 Myers–Perry solution.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ba662a7374d31a29b16a979de91ea08fa8321c46

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Citations in the corpus

Numerical methods for finding stationary gravitational solutions (2015, background): “In some cases, they exhibit universal criticality, which on the gravity side manifests itself through the existence of uniqueness theorems of geometries near regular extremal horizons [548–553].”
Essentials of blackfold dynamics (2009, background): “In this respect, we may say that a main part of our contribution is to (3)The approach to extremality in a black hole introduces a long length scale transverse to the horizon and allows to decouple a different sector of the physics, namely the near-horizon region [8].”
Near extremal black hole entropy as entanglement entropy via AdS 2 / CFT 1 (2007, background): “Recently, it has been shown that extremal (rotating) black holes always have the SO(2, 1) symmetry in the near horizon limit [2, 3, 4].”
A classification of near-horizon geometries of extremal vacuum black holes (2008, background): “One of the main results found in [22] is that the vanishing of the ρi and ρv components of the Ricci tensor of the full near-horizon geometry in these new (v, r, ρ, i) coordinates implies that k are constants and that A = A0Γ for some constant A0.”
CFT Duals for Extreme Black Holes (2008, background): “The central charge of the dual CFT is determined by two of the three charges (5)In fact, it was proved in [4,5] that a very general class of extremal black holes has a near horizon metric of this form.”
Black hole entropy function, attractors and precision counting of microstates (2007, background): “We now define a rotating extremal black hole solution to be one whose near horizon geometry has the symmetries of AdS2×S(1), – this holds for known extremal rotating black hole solutions [36,24] and has recently been proven in [23].”
Central charges in extreme black hole/CFT correspondence (2009, background): “Notice that the above metric for D = 5 can be obtained from the extremal black holes with a topologically S1 × S2 horizon and with a topologically S3 horizon [24].”
Kerr-AdS/CFT correspondence in diverse dimensions (2008, neutral): “(This result also appears, with l−1 = 0, in [16], and with l−1 > 0 in [17].”
Holographic Description of AdS_2 Black Holes (2008, background): “This is consistent with the universality of extremal black hole spacetimes [1].”
Local Fluid Dynamical Entropy from Gravity (2008, background): “While the area-form is a very natural object, all its physically important properties (most importantly the positivity of divergence) appear to be retained if we add to it the exterior derivative of a (d − 2)-form.”
Extremal Black Hole/CFT Correspondence in (Guaged) Supergravities (2008, background): “. The metric has n−1+ǫcopies of the Virasoro algebra. It has been shown that near-horizon geometries are generally of this form for classes of theories that are of interest in four and ﬁve dimensions [34], and also for cohomogeneity-1 horizons in arbitrary dimension [35]. We have veriﬁed for dimensi”