Black hole entropy function and the attractor mechanism in higher derivative gravity

By Ashoke Sen. 2005

556 citations recorded by the source corpus.

We study extremal black hole solutions in D dimensions with near horizon geometry AdS2 ? SD?2 in higher derivative gravity coupled to other scalar, vector and anti-symmetric tensor fields. We define an entropy function by integrating the lagrangian density over SD?2 for a general AdS2 ? SD?2 background, taking the Legendre transform of the resulting function with respect to the parameters labelling the electric fields, and multiplying the result by a factor of 2?. We show that the values of the scalar fields at the horizon as well as the sizes of AdS2 and SD?2 are determined by extremizing this entropy function with respect to the corresponding parameters, and the entropy of the black hole is given by the value of the entropy function at this extremum. Our analysis relies on the analysis of the equations of motion and does not directly make use of supersymmetry or specific structure of the higher derivative terms.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/22eae9228973521718fd160411fee38e6072de23

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Ashoke Sen
2. S. Trivedi
3. R. Kallosh
4. I. Bena
5. N. Warner
6. Andrei Linde
7. S. Sachdev
8. A. Dabholkar

In Nuclear and High Energy Physics

1. Ashoke Sen
2. S. Trivedi
3. R. Kallosh
4. I. Bena
5. N. Warner
6. A. Dabholkar
7. S. Sachdev
8. Frederik Denef

In Statistical and Nonlinear Physics

1. Ashoke Sen
2. S. Trivedi
3. N. Warner
4. I. Bena
5. A. Dabholkar
6. S. Murthy
7. B. Pioline
8. Yuji Tachikawa

Citations in the corpus

• Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates (2011, background): “In the extremal limit this leads to a simple algebraic procedure for determining the near horizon field configurations and the entropy [5, 6].”
• Black hole entropy in the presence of Chern–Simons terms (2006, methodology): “The entropy function formalism [21] devised by Sen is more convenient in that respect because it automatically incorporates both sources of corrections via the extremalization of the entropy function.”
• Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity (2011, background): “Some references pertaining to the attractor mechanism are, [26], [41], [42], [43], [44], and more recently [45].”
• Holographic Description of AdS_2 Black Holes (2008, background): “12) is the natural starting point for computation of higher derivative corrections to the central charge, in the spirit of [30, 31, 8].”
• Holography of charged dilaton black holes (2009, background): “Some references on attractors without supersymmetry are [18, 19, 20, 21, 22].”
• Lectures on black holes, topological strings and quantum attractors (2006, background): “17) In fact, there are now general arguments [91, 89] to the effect that the BekensteinHawking-Wald entropy is equal the Legendre transform of the Lagrangian evaluated on the near-horizon geometry; in the case of N = 2 supergravity, the equality of this Lagrangian with the topological free energy F(”
• The Non-BPS black hole attractor equation (2006, methodology): “3 In [ 7 ] an argument was given as to why extremal black holes are attractive and non-extremal ones are”
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, background): “udied the full asymptotically AdS 5 black hole solution in the context of the AdS 5/CFT 4 correspondence, rather than the near-horizon AdS 2/CFT 1 correspondence as in Sen’s entropy function approach [75]. In fact, the entropy of BPS AdS 5 black holes has been studied in [76{78] in the entropy funct”
• The Lovelock Black Holes (2008, background): “Sen [106] within the context of the attractor mechanism, works nicely for the case of Lovelock black holes.”
• Wald's entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling (2007, methodology): “3 Small black holes in heterotic string theory Sen has defined the BH entropy function [16] and used it [17, 8] to find the near horizon geometry of extremal BH solutions in the four dimensional low energy effective action of heterotic string theory on M ×S(1) × S̃1.”
• Black hole microstates in AdS4 from supersymmetric localization (2015, unknown): “similarities with Sen’s entropy function formalism [51], of which we might provide a supersymmetric version.”
• Large rotating AdS black holes from fluid mechanics (2007, unknown): “As an application of this observation, let us recall the suggestion [31–33] that the attractor mechanism for black holes implies the non-renormalisation of the entropy of all extremal configurations, as a function of the ’t Hooft coupling λ.”
• Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions (2011, methodology): “The classical entropy function method [66], applied to the near horizon geometry with the action (4.”