First order flow for non-extremal AdS black holes and mass from holographic renormalization

We derive both BPS and non-BPS first-order flow equations for magnetically charged black strings in five-dimensional N = 2 abelian gauged supergravity, using the Hamilton-Jacobi formalism. This is first done for the coupling to vector multiplets only and U(1) Fayet-Iliopoulos (FI) gauging, and then generalized to the case where also hypermultiplets are present, and abelian symmetries of the quaternionic hyperscalar target space are gauged. We then use these results to derive the attractor equations for near-horizon geometries of extremal black strings, and solve them explicitely for the case where the constants appearing in the Chern-Simons term of the supergravity action satisfy an adjoint identity. This allows to compute in generality the central charge of the two-dimensional conformal field theory that describes the black strings in the infrared, in terms of the magnetic charges, the CY intersection numbers and the FI constants. Finally, we extend the r-map to gauged supergravity and use it to relate our flow equations to those in four dimensions.

Section: Final Remarksmentioning

confidence: 93%

“…e.g. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] for an (incomplete) list of references. In particular, ref.…”

Section: Jhep01(2017)106mentioning

confidence: 99%

Black string first order flow in N = 2, d = 5 abelian gauged supergravity

Klemm

Petri

Rabbiosi

2017

“…2 see the interesting work [9] for work on holographic renormalization of finite temperature black holes in AdS4. 3 The Riemann surface Σg has genus g ≥ 0.…”

Section: N = 2 Fi-gauged Supergravitymentioning

confidence: 99%

On the on-shell: the action of AdS4 black holes

Halmagyi

Lal

2018

We compute the on-shell action of static, BPS black holes in AdS 4 from N = 2 gauged supergravity coupled to vector multiplets and show that for a certain class it is equal to minus the entropy of the black hole. Holographic renormalization is used to demonstrate that with Neumann boundary conditions on the scalar fields, the divergent and finite contributions from the asymptotic boundary vanish. The entropy arises from the extrinsic curvature on Σ g × S 1 evaluated at the horizon, where Σ g may have any genus g ≥ 0. This provides a clarification of the equivalence between the partition function of the twisted ABJM theory on Σ g × S 1 and the entropy of the dual black hole solutions. It also demonstrates that the complete entropy resides on the AdS 2 × Σ g horizon geometry, implying the absence of hair for these gravity solutions.

“…Although there has been a lot of progress constructing such flows -see, for example, [64][65][66][67][68][69][70][71] -a general understanding remains elusive. The existence of an "attractor" mechanism for a generic non-extremal solution may yield deeper understanding of first order flows and help in finding new solutions.…”

Section: Jhep01(2015)075mentioning

confidence: 99%

Hot attractors

Goldstein

Jejjala

Nampuri

2015

The product of the areas of the event horizon and the Cauchy horizon of a non-extremal black hole equals the square of the area of the horizon of the black hole obtained from taking the smooth extremal limit. We establish this result for a large class of black holes using the second order equations of motion, black hole thermodynamics, and the attractor mechanism for extremal black holes. This happens even though the area of each horizon generically depends on the moduli, which are asymptotic values of scalar fields. The conformal field theory dual to the BTZ black hole facilitates a microscopic interpretation of the result. In addition, we demonstrate that certain quantities which vanish in the extremal case are zero when integrated over the region between the two horizons. We corroborate these conclusions through an analysis of known solutions.