Entropy Function Formalism Research Articles

Comments on Sen's classical entropy function for static and rotating AdS4 black holes

We consider various aspects of Sen's classical entropy function formalism for asymptotically AdS4 black holes with emphasis on its efficacy to capture higher derivative corrections to the Bekenstein-Hawking entropy. The formalism has the important advantage of being based on near-horizon symmetries and does not require knowledge of the full interpolating supergravity solution, nor of its AdS4 asymptotics. For the static case, we focus on applying the entropy function formalism in the presence of various higher derivative terms motivated in conformal supergravities; we find agreement with recently reported results utilizing the full black hole solutions and Wald's entropy formula. For the rotating case, we demonstrate that a modified version of the formalism generates a background that coincides precisely with the Bardeen-Horowitz limit of known rotating, electrically charged AdS4 black holes and provides a swift approach to the black hole entropy, including higher derivatives corrections. We conclude that Sen's classical entropy function formalism is a viable and highly efficient approach to capturing higher-derivative corrections to the entropy of asymptotically AdS4 black holes albeit naturally missing certain relations arising from global aspects of the full black hole solution.

Higher-derivative corrections to black hole entropy at zero temperature

There is a well-established connection between the higher-derivative corrections to the black hole entropy and the black hole extremality bound. The particular combination of effective field theory (EFT) coefficients ${c}_{i}$ that controls the mass shift at fixed charge and temperature also controls the entropy shift at fixed charge and mass, in the limit where the mass approaches the uncorrected value for the extremal mass. In this paper, we use the classical entropy function formalism to examine the entropy corrections at exactly zero temperature, or at the corrected value for the extremal mass. We find that the zero-temperature entropy shift (a) is unrelated to the mass shift, (b) is $\mathcal{O}({c}_{i})$ in the EFT coefficients, rather than $\mathcal{O}(\sqrt{{c}_{i}})$, as is the constant-mass entropy shift, and (c) is negative in the example of the EFT arising at low energies from QED plus gravity.

Entropy function from the Einstein boundary term

We show using the entropy function formalism developed by Sen (JHEP, 09 (2005) 038) that the boundary term which arises from the Einstein‐Hilbert action is sufficient to yield the Bekenstein‐Hawking entropy of a static extremal black hole which is asymptotically flat. However, for asymptotically AdS black holes, the bulk term also plays an important role due to the presence of the cosmological constant. Further, we show that for extremal rotating black holes, both the boundary and the bulk terms contribute non‐vanishing pieces to the entropy.

Logarithmic corrections to black hole entropy in matter coupled mathcal{N} \u2265 1 Einstein-Maxwell supergravity

We calculate the first three Seeley-DeWitt coefficients for fluctuation of the massless fields of a mathcal{N} = 2 Einstein-Maxwell supergravity theory (EMSGT) distributed into different multiplets in d = 4 space-time dimensions. By utilizing the Seeley-DeWitt data in the quantum entropy function formalism, we then obtain the logarithmic correction contribution of individual multiplets to the entropy of extremal Kerr-Newman family of black holes. Our results allow us to find the logarithmic entropy corrections for the extremal black holes in a fully matter coupled mathcal{N} = 2, d = 4 EMSGT, in a particular class of mathcal{N} = 1, d = 4 EMSGT as consistent decomposition of mathcal{N} = 2 multiplets ( mathcal{N} = 2 → mathcal{N} = 1) and in mathcal{N} ≥ 3, d = 4 EMSGTs by decomposing them into mathcal{N} = 2 multiplets ( mathcal{N} ≥ 3 → mathcal{N} = 2). For completeness, we also obtain logarithmic entropy correction results for the non-extremal Kerr-Newman black holes in the matter coupled mathcal{N} ≥ 1, d = 4 EMSGTs by employing the same Seeley-DeWitt data into a different Euclidean gravity approach developed in [17].

Attractor mechanism and nonrenormalization theorem in 6D (1, 0) supergravity

We compute the macroscopic entropy of the supersymmetric rotating dyonic strings carrying linear momentum in 6D (1, 0) supergravity with curvature squared corrections. Our calculation is based on Sen's entropy function formalism applied to the near-horizon geometry of the string solution taking the form of an extremal Ban\ifmmode \tilde{}\else \~{}\fi{}ados-Teitelboim-Zanelli $\ifmmode\times\else\texttimes\fi{}{S}^{3}$. The final entropy formula states that the two independent supersymmetric completions of Riemann tensor squared contribute equally to the entropy. A further ${S}^{3}$ compactification of the 6D theory results in a matter coupled 3D supergravity model in which the quantization condition of the ${\mathrm{SU}(2)}_{R}$ Chern-Simons level implies the horizon value of the dilaton is not modified by higher derivative interactions beyond supersymmetric curvature squared terms.

Logarithmic correction to the entropy of extremal black holes in mathcal{N} = 1 Einstein-Maxwell supergravity

We study one-loop covariant effective action of “non-minimally coupled” mathcal{N} = 1, d = 4 Einstein-Maxwell supergravity theory by heat kernel tool. By fluctuating the fields around the classical background, we study the functional determinant of Laplacian differential operator following Seeley-DeWitt technique of heat kernel expansion in proper time. We then compute the Seeley-DeWitt coefficients obtained through the expansion. A particular Seeley-DeWitt coefficient is used for determining the logarithmic correction to Bekenstein-Hawking entropy of extremal black holes using quantum entropy function formalism. We thus determine the logarithmic correction to the entropy of Kerr-Newman, Kerr and Reissner-Nordström black holes in “non-minimally coupled” mathcal{N} = 1, d = 4 Einstein-Maxwell supergravity theory.

Einstein-Maxwell-scalar black holes: classes of solutions, dyons and extremality

Spherical black hole (BH) solutions in Einstein-Maxwell-scalar (EMS) models wherein the scalar field is non-minimally coupled to the Maxwell invariant by some coupling function are discussed. We suggest a classification for these models into two classes, based on the properties of the coupling function, which, in particular, allow, or not, the Reissner- Nordström (RN) BH solution of electrovacuum to solve a given model. Then, a comparative analysis of two illustrative families of solutions, one belonging to each class is performed: dilatonic versus scalarised BHs. By including magnetic charge, that is considering dyons, we show that scalarised BHs can have a smooth extremal limit, unlike purely electric or magnetic solutions. In particular, we study this extremal limit using the entropy function formalism, which provides insight on why both charges are necessary for extremal solutions to exist.

Dilaton black hole entropy from entropy function formalism

It has been shown that the entropy function formalism is an efficient way to calculate the entropy of black holes in string theory. We check this formalism for the extremal charged dilaton black hole. We find the general four-derivative correction on the black hole entropy from the value of the entropy function at its extremum point.

S-duality, entropy function and transport in AdS4/CMT3

In this paper we consider Abelian vector plus scalar holographic gravity models for 2+1 dimensional condensed matter transport, and the effect of S-duality on them. We find the transport coefficients from the electric and heat currents via usual membrane paradigm-type calculations, and the effect of S-duality on them. We study the same system also by using the entropy function formalism in the extremal case, and the formalism of holographic Stokes equations, in the case of one-dimensional lattices. We study a few generalizations that appear when considering a supergravity-inspired model, and apply the entropy function method for them.

Seeley-DeWitt coefficients in mathcal{N} = 2 Einstein-Maxwell supergravity theory and logarithmic corrections to mathcal{N} = 2 extremal black hole entropy

We investigate the heat kernel method for one-loop effective action following the Seeley-DeWitt expansion technique of heat kernel with Seeley-DeWitt coefficients. We also review a general approach of computing the Seeley-DeWitt coefficients in terms of background or geometric invariants. We, then consider the Einstein-Maxwell theory em-bedded in minimal mathcal{N} = 2 supergravity in four dimensions and compute the first three Seeley-DeWitt coefficients of the kinetic operator of the bosonic and the fermionic fields in an arbitrary background field configuration. We find the applications of these results in the computation of logarithmic corrections to Bekenstein-Hawking entropy of the extremal Kerr-Newman, Kerr and Reissner-Nordström black holes in minimal mathcal{N} = 2 Einstein-Maxwell supergravity theory following the quantum entropy function formalism.

Weak Gravity Conjecture and extremal black holes

Motivated by the desire to improve our understanding of the Weak Gravity Conjecture, we compute the one-loop correction of charged particles to the geometry and entropy of extremal black holes in 4D. We use the entropy function formalism to extend previous analysis that dealt with neutral particles, and obtain the corrections to the horizon entropy for different regimes of black hole masses. These corrections are small in general. They are furthermore reduced when supersymmetry is present, and disappear in N = 4 supergravity. We provide some speculative arguments that in a theory with only sub-extremal particles, classical Reissner-Nordstrom black holes actually possess an infinite microcanonical entropy, though only a finite amount is visible to an external observer, as shown by the horizon entropy computation.

Quantum phase transition of the static extremal black hole coupled to a Stückelberg scalar

We show that a static extremal black hole in 4D gravity, non-linearly coupled to a massive Stückelberg scalar, can exhibit a quantum phase transition due to electric charge variations. The critical point exists only if the spacetime possesses cosmological constant (positive or negative) and the mass of the scalar is non-vanishing. In that case, around the critical point, two solutions coexist: Reissner-Nordström (A)dS black hole and the hairy (A)dS black hole. A near-critical expansion reveals that the entropy and its derivative are continuous functions at the critical point. Obtained results are analytical and based on the entropy function formalism.

Extremal black holes, Stueckelberg scalars and phase transitions

We calculate the entropy of a static extremal black hole in 4D gravity, non-linearly coupled to a massive Stueckelberg scalar. We find that the scalar field does not allow the black hole to be magnetically charged. We also show that the system can exhibit a phase transition due to electric charge variations. For spherical and hyperbolic horizons, the critical point exists only in presence of a cosmological constant, and if the scalar is massive and non-linearly coupled to electromagnetic field. On one side of the critical point, two extremal solutions coexist: Reissner-Nordström (A)dS black hole and the charged hairy (A)dS black hole, while on the other side of the critical point the black hole does not have hair. A near-critical analysis reveals that the hairy black hole has larger entropy, thus giving rise to a zero temperature phase transition. This is characterized by a discontinuous second derivative of the entropy with respect to the electric charge at the critical point. The results obtained here are analytical and based on the entropy function formalism and the second law of thermodynamics.

Conductivities from attractors

In the context of applications of the AdS/CFT correspondence to condensed matter physics, we compute conductivities for field theory duals of dyonic planar black holes in 3+1-dimensional Einstein-Maxwell-dilaton theories at zero temperature. We combine the near-horizon data obtained via Sen’s entropy function formalism with known expressions for conductivities. In this way we express the conductivities in terms of the extremal black hole charges. We apply our approach to three different examples for dilaton theories for which the background geometry is not known explicitly. For a constant scalar potential, the thermoelectric conductivity explicitly scales as αxy ∼ N3/2, as expected. For the same model, our approach yields a finite result for the heat conductivity κ/T ∝ N3/2 even for T → 0.

Dyonic AdS 4 black hole entropy and attractors via entropy function

Using the Sen's entropy function formalism, we compute the entropy for the extremal dyonic black hole solutions of theories in the presence of dilaton field coupled to the field strength and a dilaton potential. We solve the attractor equations analytically and determine the near horizon metric, the value of the scalar fields and the electric field on the horizon, and consequently the entropy of these black holes. The attractor mechanism plays a very important role for these systems, and after studying the simplest systems involving dilaton fields, we propose a general ansatz for the value of the scalar field on the horizon, which allows us to solve the attractor equations for gauged supergravity theories in $AdS_4$ spaces. In particular, we derive an expression for the dyonic black hole entropy for the $\mathcal{N}=8$ gauged supergravity in 4 dimensions which does not contain explicitly the gauge parameter of the potential.

A logarithmic correction in the entropy functional formalism

The entropy functional formalism allows one to recover general relativity, modified gravity theories, as well as the Bekenstein–Hawking entropy formula. In most approaches to quantum gravity, the Bekenstein–Hawking’s entropy formula acquires a logarithmic correction term. As such terms occur almost universally in most approaches to quantum gravity, we analyze the effect of such terms on the entropy functional formalism. We demonstrate that the leading correction to the micro-canonical entropy in the entropy functional formalism can be used to recover modified theories of gravity already obtained with an uncorrected micro-canonical entropy. Furthermore, since the entropy functional formalism reproduces modified gravity, the rise of gravity-dependent logarithmic corrections turns out to be one way to impose constraints on these theories of modified gravity. The constraints found here for the simple case of an [Formula: see text]-gravity are the same as those obtained in the literature from cosmological considerations.

Modified gravity from an entropy functional

We extend Padmanabhan's entropy functional formalism to show that, in addition to the Gauss–Bonnet (GB) or the entire series of Lanczos–Lovelock Lagrangians already obtained, more general higher-order corrections to General Relativity, i.e. the so-called modified gravity theories, also emerge naturally from this formalism. This extension shows that the formalism constitutes a valuable tool to investigate, at each order in the curvature, the possible structure the higher-order modified gravity theories might have. As an application, the extended formalism is used to evaluate the horizon entropy in a modified gravity theory of the second-order in the curvature. Our findings are in agreement with previous results from the literature.

Quantum corrections to extremal black brane solutions

We discuss quantum corrections to extremal black brane solutions in N=2 U(1) gauged supergravity in four dimensions. We consider modifications due to a certain class of higher-derivative terms as well as perturbative corrections to the prepotential. We use the entropy function formalism to assess the impact of these corrections on singular brane solutions and we give a few examples. We then use first-order flow equations to construct solutions that interpolate between quantum corrected fixed points of the associated potentials.

On attractor mechanism of [formula omitted] black holes

We construct a general family of exact non-extremal 4-dimensional black holes in AdS gravity with U(1) gauge fields non-minimally coupled to a dilaton and a non-trivial dilaton potential. These black holes can have spherical, toroidal, and hyperbolic horizon topologies. We use the entropy function formalism to obtain the near horizon data in the extremal limit. Due to the non-trivial self-interaction of the scalar field, the zero temperature black holes can have a finite horizon area even if only the electric field is turned on.

Thermodynamic consistency and fast dynamics in phase-field crystal modeling

A general formulation is presented to derive the equation of motion and demonstrate thermodynamic consistency for several classes of phase-field (PF) and PF crystal (PFC) models. It can be applied to models with a conserved and non-conserved phase-field variable, describing either locally uniform or periodic stable states, and containing slow as well as fast thermodynamic variables. The approach is based on an entropy functional formalism previously developed in the context of PF models for locally uniform states [P. Galenko and D. Jou, Phys. Rev. E 71 (2005) p.046125] and thus allows to extend several properties of the latter to PF models for periodic states, i.e., PFC models.