We set up a new version of black hole information paradox in an eternal Narayan black hole, a generic two-dimensional dilaton gravity theory with non-trivial on-shell bulk action and a product of dimensional reduction from higher-dimensional AdS black brane, joined to Minkowski bath on both sides. We also report both similarities as well as important differences between our model and the famous model of JT gravity coupled with baths. The contradiction of Hawking's result of entanglement entropy with unitarity is resolved by including a new saddle in the Euclidean gravitational path integral. As part of ongoing and developing research, we attempt, and have had partial success, to explicitly construct the replica wormhole geometry for our model to fully justify the quantum extremal surface calculations with Euclidean gravitational path integral, without using holography.
Using brick wall method the entropy of charged dilaton-axion black hole is determined for both asymptotically flat and non-flat cases. The entropy turns out to be proportional to the horizon area of the black hole confirming the Beckenstien, Hawking area-entropy formula for black holes. The leading order logarithmic corrections to the entropy are also derived for such black holes.
We study thermodynamics of (1+1) dimensional dilatonic black holes in global embedding Minkowski space scheme. Exploiting geometrical entropy correction we construct consistent entropy for the charged dilatonic black hole. Moreover, (1+1) dilatonic black holes with higher order terms are shown to possess (3+2) global flat embedding structures regardless of the details of the lapse function, and to yield a generic entropy.
In this paper we consider the holographic DC and Hall conductivity in Einstein-Maxwell-Dilaton in Gauss-Bonnet gravity with momentum dissipation. We analytically derived the DC conductivity and Hall conductivity from the black horizon data, and found that the conductivities are independent on the Gauss-Bonnet coupling. We also used the entropy function formalism to get the conductivities in terms of the charge of the black hole, even without knowing the explicit black hole solutions.
With Carlip's boundary conditions, a standard Virasoro subalgebra with corresponding central charge for stationary dilaton black hole obtained in the low-energy effective field theory describing string is constructed at a Killing horizon. The statistical entropy of stationary dilaton black hole yielded by standard Cardy formula agree with its Bekenstein-Hawking entropy only if we take period $ T$ of function $v$ as the periodicity of the Euclidean black hole. On the other hand, if we consider first-order quantum correction then the entropy contains a logarithmic term with a factor $-{1/2}$, wh…
Recently we showed that in semiclassical 2D dilaton gravity the regularity of a black hole horizon may be compatible with divergencies of Polyakov-Liouville stresses on it, the temperature deviating from its Hawking value. This makes the question about thermal properties of such solutions non-trivial. We demonstrate that, adding to gravitation-dilaton part of the action certain counterterms, which diverge on the horizon but are finite outside it, one may achieve finiteness of the effective gravitation-dilaton couplings on the horizon. This gives for the entropy S the Bekenstein - Hawking value…
Current cosmological models require the universe to be in a very smooth initial state before the onset of inflation, a situation to which Penrose ascribes a vanishingly small probability, leading to his proposal of a Conformal Cyclic Cosmology. We present an alternative paradigm, in which the Higgs plays the role of dilaton and resolves this problem by weakening gravity at very early times, thus providing a form of inflation that is compatible with observations and in which the inflaton is solidly related to tested particle physics.
We use complex semiclassical method to compute scattering amplitudes of a point particle in dilaton gravity with a boundary. This model has nonzero minimal black hole mass $M_{cr}$. We find that at energies below $M_{cr}$ the particle trivially scatters off the boundary with unit probability. At higher energies the scattering amplitude is exponentially suppressed. The corresponding semiclassical solution is interpreted as formation of an intermediate black hole decaying into the final-state particle. Relating the suppression of the scattering probability to the number of the intermediate black…
According to the gauge/gravity duality, the Van der Waals transition of charged AdS black holes in extended phase space is conjectured to be dual to a renormalization group flow on the space of field theories. So exploring the Van der Waals transition is potentially valuable for studying holographic properties of charged black hole thermodynamics. There are different transition behaviors for charged dilatonic AdS black holes in Einstein-Maxwell-dilaton (EMD) theory with string-inspired potential with different dilaton coupling constants in diverse dimensions. In this work, we find a special cl…
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.
We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page's time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a g…
Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extrema…
The area formula for entropy is extended to the case of a dilatonic black hole. The entropy of a scalar field in the background of such a black hole is calculated semiclassically. The area and cutoff dependences are normal {\it except in the extremal case}, where the area is zero but the entropy nonzero.
It has been proposed that a quantum group structure underlies de Sitter/Conformal field theory duality. These ideas are used to give a microscopic operator counting interpretation for the entropy of two-dimensional dilaton de Sitter space. This agrees with the Bekenstein-Hawking entropy up to a factor of order unity.
We study the corrections to the entropy of Einstein-Maxwell dilaton-axion black holes beyond semiclassical approximations. We consider the entropy of the black hole as a state variable and derive these corrections using the exactness criteria of the first law of thermodynamics. We note that from this general frame-work the entropy corrections for "simpler" black holes like Schwarzschild, Reissner-Nordström and anti-de Sitter-Schwarzschild black holes follow easily. This procedure gives us the modified area law as well.
By investigating the critical behavior appearing at the extremal limit of the non-dilatonic, black p-branes in (d+p) dimensions, we find that some critical exponents related to the critical point obey the scaling laws. From the scaling laws we obtain that the effective spatial dimension of the non-dilatonic black holes and black strings is one, and is p for the non-dilatonic black p-branes. For the dilatonic black holes and black p-branes, the effective dimension will depend on the parameters in theories. Thus, we give an interpretation why the Bekenstein-Hawking entropy may be given a simple …
The quantum contribution of a scalar field to entropy of a dilatonic black hole is calculated in the brick wall model by the WKB method and analyzed by a high-temperature expansion. If the cutoff distance from the horizon approaches zero, the leading divergent piece of entropy turns out to be proportional to the "area" of the horizon surface (which has (N-1)-dimensional extension in (N+1)-dimensional space-time) and independent of other properties of black holes even in the case of general dilaton coupling. There is also qualitative argument with the known result of subleading divergence for N…
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 …
We introduce a new attractor mechanism to find the entropy for spherically symmetric extremal black holes. The key ingredient is to find a two-dimensional (2D) dilaton gravity with the dilaton potential $V(ϕ)$. The condition of an attractor is given by $\nabla^2ϕ=V(ϕ_0)$ and $\bar{R}_2=-V^{\prime}(ϕ_0)$ and for a constant dilaton $ ϕ=ϕ_0$, these are also used to find the location of the degenerate horizon $r=r_{e}$ of an extremal black hole. As a nontrivial example, we consider an extremal regular black hole obtained from the coupled system of Einstein gravity and nonlinear electrodynamics. Th…
We investigate non-dilatonic p-branes in the near-extremal, near-horizon regime. A two-dimensional gravity model, obtained from dimensional reduction, gives an effective description of the brane. We show that the AdS_p+2/CFT_p+1 correspondence at finite temperature admits an effective description in terms of a AdS_2/CFT_1 duality endowed with a scalar field, which breaks the conformal symmetry and generates a non-vanishing central charge. The entropy of the CFT_1 is computed using Cardy formula. Fixing in a natural way a free, dimensionless, parameter introduced in the model by a renormalizati…
We find broad classes of exact 4-dimensional asymptotically flat black hole solutions in Einstein-Maxwell theories with a non-minimally coupled dilaton and its non-trivial potential. We consider a few interesting limits, in particular, a regular generalization of the dilatonic Reissner-Nordstr{ö}m solution and, also, smooth deformations of supersymmetric black holes. Further examples are provided for more general dilaton potentials. We discuss the thermodynamical properties and show that the first law is satisfied. In the non-extremal case the entropy depends, as expected, on the asymptotic va…
We present the new agegraphic dark energy model by introducing the quantum corrections to the entropy-area relation in the setup of loop quantum gravity. Employing this new form of dark energy, we investigate the model of interacting dark energy and derive its equation of state. We study the correspondence between the tachyon, K-essence and dilaton scalar field models with the interacting entropy-corrected new agegraphic dark energy model in the non-flat FRW universe. Moreover, we reconstruct the corresponding scalar potentials which describe the dynamics of the scalar field models.
We consider near horizon fall-off conditions of stationary black holes in Einstein-Maxwell-Dilaton theory and find conserved charge conjugate to symmetry generator that preserves near horizon fall-off conditions. Subsequently, we find supertranslation, superrotation and multiple-charge modes. We apply the obtained results on a typical static dilaton black hole and on a charged rotating black string, as examples. In this case, supertranslation double-zero-mode charge $\mathcal{T}_{(0,0)}$ is not equal to black hole entropy times Hawking temperature. This may be seen as a problem but it is not, …
We explore several extensions of the generalized entropy construction of Lewkowycz and Maldacena, including a formulation that does not rely on preserving replica symmetry in the bulk. We show that an appropriately general ansatz for the analytically continued replica metric gives us the flexibility needed to solve the gravitational field equations beyond general relativity. As an application of this observation we study Einstein-Gauss-Bonnet gravity with a small Gauss-Bonnet coupling and derive the condition that the holographic entanglement entropy must be evaluated on a surface which extrem…
We study generic two-dimensional dilaton gravity with a Maxwell field and prove its triviality for constant dilaton boundary conditions, despite of the appearance of a Virasoro algebra with non-zero central charge. We do this by calculating the canonical boundary charges, which turn out to be trivial, and by calculating the quantum gravity partition function, which turns out to be unity. We show that none of the following modifications changes our conclusions: looser boundary conditions, non-linear interactions of the Maxwell field with the dilaton, inclusion of higher spin fields, inclusion o…
We have found that for extreme dilaton black holes an inner boundary must be introduced in addition to the outer boundary to give an integer value to the Euler number. The resulting manifolds have (if one identifies imaginary time) topology $S^1 \times R \times S^2 $ and Euler number $χ= 0$ in contrast to the non-extreme case with $χ=2$. The entropy of extreme $U(1)$ dilaton black holes is already known to be zero. We include a review of some recent ideas due to Hawking on the Reissner-Nordström case. By regarding all extreme black holes as having an inner boundary, we conclude that the entrop…
In this note we do the analysis of entanglement entropy more carefully when the non-conformal theory flows to a non-trivial IR fixed point. In particular we emphasize the role of the trace of the energy-momentum tensor in these calculations. We also compare the current technique for evaluating the entanglement entropy, particularly the Green's function method for gaussian theories, with the dilaton effective action approach and show that they compute identical quantities. As a result of this, the dilaton effective action approach can be thought of as an extension of Green's function technique …
We calculate the entanglement entropy between two (maximally-extended) spacetime regions of static black hole, seperated by horizon. As a first case, we consider the Schwarzschild black hole, and then we extend the calculations to the charged Reissner- Nordstrom and Schwarzschild-de Sitter black holes with more than one horizon. The case for static and spherically-symmetric solution to the more general F (R) gravity is also considered. The calculation of the entanglement entropy is performed using the replica trick by obtaining the explicit form of the metric which corresponds to the replica s…
We study the islands and the Page curve in the 1+1-dimensional eternal dilaton black hole models. Without islands, the entanglement entropy of the radiation grows linearly at late time. However with an island, its growth stops at the value of almost twice of the black hole entropy. Therefore an island emerges at the late time, and the entanglement entropy of the radiation shows the Page curve.
The entropy for two-dimensional black holes is obtained through the entropy function with the condition that the geometry approaches an $AdS_2$ spacetime in the near horizon limit. It is shown that the entropy is universal and proportional to the value of the dilaton field at the event horizon as expected. We find this universal behavior holds even after the inclusion of higher derivative terms, only modifying the proportional constant. More specifically, a variety of models of the dilaton gravity in two dimensions are considered, in which it is shown that the universal entropy coincides with …
We present a detailed calculation of the entropy and action of $U(1)~2$ dilaton black holes, and show that both quantities coincide with one quarter of the area of the event horizon. Our methods of calculation make it possible to find an explanation of the rule $S = A/4$ for all static, spherically symmetric black holes studied so far. We show that the only contribution to the entropy comes from the extrinsic curvature term at the horizon, which gives $S = A/4$ independently of the charge(s) of the black hole, presence of scalar fields, etc. Previously, this result did not have a general expla…
I present the ``Chern--Simons'' formulation of generalized 2d dilaton gravity, summarize its Hamiltonian quantization (reduced phase space and Dirac quantization) and briefly discuss the statistical mechanical entropy of 2d black holes. Focus is put on the close relation to finite dimensional point particle systems.
A generalized second law in string cosmology accounts for geometric and quantum entropy in addition to ordinary sources of entropy. The proposed generalized second law forbids singular string cosmologies, under certain conditions, and forces a graceful exit transition from dilaton-driven inflation by bounding curvature and dilaton kinetic energy.
In this paper, we study topological AdS black branes of $(n+1)$-dimensional Einstein-Maxwell-dilaton theory and investigate their properties. We use the area law, surface gravity and Gauss law interpretations to find entropy, temperature and electrical charge, respectively. We also employ the modified Brown and York subtraction method to calculate the quasilocal mass of the solutions. We obtain a Smarr-type formula for the mass as a function of the entropy and the charge, compute the temperature and the electric potential through the Smarr-type formula and show that these thermodynamic quantit…
We show that four-dimensional Einstein-Maxwell-Dilaton-Gauss-Bonnet gravity admits asymptotically flat black hole solutions with a degenerate event horizon of the Reissner-Nordström type $AdS_2\times S^2$. Such black holes exist for the dilaton coupling constant within the interval $0\leq a^2<a^2_{\rm cr}$. Black holes must be endowed with an electric charge and (possibly) with magnetic charge (dyons) but they can not be purely magnetic. Purely electric solutions are constructed numerically and the critical dilaton coupling is determined $a_{\rm cr}\simeq 0.488219703$. For each value of the di…
We relate various black hole solutions in the near-horizon region to black hole solutions in two-dimensional dilaton gravity theories in order to argue that thermodynamics of black holes in D>=4 can be effectively described by thermodynamics of black holes in two-dimensional dilaton gravity theories. We show that the Bekenstein-Hawking entropies of single-charged dilatonic black holes and dilatonic p-branes with an arbitrary dilaton coupling parameter in arbitrary spacetime dimensions are exactly reproduced by the Bekenstein-Hawking entropy of the two-dimensional black hole in the associated t…
In this talk some essential features of stringy black holes are described. We consider charged four-dimensional axion-dilaton black holes. The Hawking temperature and the entropy of all solutions are shown to be simple functions of the squares of supercharges, defining the positivity bounds. Spherically symmetric and multi black hole solutions are presented. The extreme solutions have some unbroken supersymmetries. Axion-dilaton black holes with zero entropy and zero area of the horizon form a family of stable particle-like objects, which we call holons. We discuss the possibility of splitting…
We propose that Strominger's method to derive the BTZ black hole entropy is in fact applicable to other asymptotically AdS_3 black holes and gives the correct functional form of entropies. We discuss various solutions in the Einstein-Maxwell theory, dilaton gravity, Einstein-scalar theories, and Einstein-Maxwell-dilaton theory. In some cases, solutions approach AdS_3 asymptotically, but their entropies do not have the form of Cardy's formula. However, it turns out that they are actually not "asymptotically $AdS_3$" solutions. On the other hand, for truly asymptotically AdS_3 solutions, their e…
The a-theorem is demonstrated for the RG flows of entanglement entropy in two and four dimensions. In four dimensions we relate it to the term quadratic in intrinsic derivative of the dilaton along the entangling surface in the dilaton entropy. The a-theorem, similarly to the c-theorem in two dimensions, then follows from the positivity of the 2-point function of stress-energy tensor. We suggest that the a-theorem, provided it is properly reformulated in terms of the entanglement entropy, may follow from the c-theorem.
We consider the Hamiltonian dynamics and thermodynamics of the two-dimensional vacuum dilatonic black hole in the presence of a timelike boundary with a fixed value of the dilaton field. A~canonical transformation, previously developed by Varadarajan and Lau, allows a reduction of the classical dynamics into an unconstrained Hamiltonian system with one canonical pair of degrees of freedom. The reduced theory is quantized, and a partition function of a canonical ensemble is obtained as the trace of the analytically continued time evolution operator. The partition function exists for any values …
The Bekenstein-Hawking ``entropy'' of a Kerr-Newman dilaton black hole is computed in a perturbative expansion in the charge-to-mass ratio. The most probable configuration for a gas of such black holes is analyzed in the microcanonical formalism and it is argued that it does not satisfy the equipartition principle but a bootstrap condition. It is also suggested that the present results are further support for an interpretation of black holes as excitations of extended objects.
The z=3 Lifshitz black hole is an exact black hole solution to the new massive gravity in three dimensions. In order to understand this black hole clearly, we perform a dimensional reduction to two dimensional dilaton gravity by utilizing the circular symmetry. Considering the linear dilaton, we find the same Lifshitz black hole in two dimensions. This implies that all thermodynamic quantities of the z=3 Lifshitz black hole could be obtained from its corresponding black hole in two dimensions. As a result, we derive the temperature, mass, heat capacity, Bekesnstein-Hawking entropy, and free en…
A static black hole with spherical symmetry is obtained and examined in the framework of Einstein-Yang-Mills-dilaton theory. The obtained black hole solution allowed us to derive and investigate entropy, temperature and heat capacity. To better examine the thermodynamics of the black hole extended phase space is also used. On this ground the equation of state is obtained and studied. We have also investigated the Gibbs free energy and it is shown that below the critical temperature the system demonstrates phase transitions of the first as well as of the zeroth order which is notable feature fo…
In this note it is shown that near-extremal four dimensional dyonic black holes, where the dilaton is not constant, can be described by a microscopic model consisting of a one-dimensional gas of massless particles.
We calculate the pressure, entropy density, trace anomaly and speed of sound of the gluon plasma using the dilaton potential of Ref. arXiv:0911.0627[hep-ph] in the dilaton-gravity theory of AdS/QCD. The finite temperature observables are calculated from the Black Hole solutions of the Einstein equations, and using the Bekenstein-Hawking equality of the entropy with the area of the horizon. Renormalization is well defined, because the T=0 theory has asymptotic freedom. Comparison with lattice simulations is made.
We construct charged black hole solutions with hyperscaling violation in the infrared(IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear viscosity to the entropy density. When translational symmetry breaking is relevant in the IR, the power law of the ratio is testified numerically at low temperature $T$, namely, $η/s\sim T^κ$, where the values of exponent $κ$ coincide with the analytical results. We also find that the exponent $κ$ is not affected by irrelevant current, but is reduced by the relevant current.
Dilaton black holes with a pure electric charge are considered in a framework of a grand canonical ensemble near the extreme state. It is shown that there exists such a subset of boundary data that the Hawking temperature smoothly goes to zero to an infinite value of a horizon radius but the horizon area and entropy are finite and differ from zero. In string theory the existence of a horizon in the extreme limit is due to the finiteness of a system only.
We study the Page curve in the four dimensional asymptotically flat eternal Garfinkle-Horowitz-Strominger dilaton black holes by applying the "quantum extremal surface" prescription. The results demonstrate that without island, the entanglement entropy of Hawking radiation is proportional to time and divergent at late times. While taking account of the emergence of the island extending slightly outside the event horizon, the entanglement entropy of Hawking radiation stops growing and eventually reaches a saturation value, which is twice of the Bekenstein-Hawking entropy and consistent with the…
The most general two-dimensional dilaton gravity theory coupled to an Abelian gauge field is considered. It is shown that, up to spacetime diffeomorphisms and $U(1)$ gauge transformations, the field equations admit a two-parameter family of distinct, static solutions. For theories with black hole solutions, coordinate invariant expressions are found for the energy, charge, surface gravity, Hawking temperature and entropy of the black holes. The Hawking temperature is proportional to the surface gravity as expected, and both vanish in the case of extremal black holes in the generic theory. A Ha…
The quantum mechanics of black holes in generic 2-D dilaton gravity is considered. The Hamiltonian surface terms are derived for boundary conditions corresponding to an eternal black hole with slices on the interior ending on the horizon bifurcation point. The quantum Dirac constraints are solved exactly for these boundary conditions to yield physical eigenstates of the energy operator. The solutions are obtained in terms of geometrical phase space variables that were originally used by Cangemi, Jackiw and Zwiebach in the context of string inspired dilaton gravity. The spectrum is continuous i…
We investigate the thermodynamics of Einstein-Maxwell(-Dilaton) theory for an asymptotically flat spacetime in a quasilocal frame. We firstly define a quasilocal thermodynamic potential via the Euclidean on-shell action and formulate a quasilocal Smarr relation from Eulerian theorem. Then we calculate quasilocal energy and surface pressure by employing Brown-York quasilocal method along with Mann-Marolf counterterm and find entropy from the quasilocal thermodynamic potential. These quasilocal variables are consistent with Tolman temperature and the entropy in a quasilocal frame turns out to be…
We discuss the new class of static axially symmetric black hole solutions obtained recently in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory. These black hole solutions are asymptotically flat and they possess a regular event horizon. The event horizon is almost spherically symmetric with a slight elongation along the symmetry axis. The energy density of the matter fields is angle-dependent at the horizon. The static axially symmetric black hole solutions satisfy a simple relation between mass, dilaton charge, entropy and temperature. The black hole solutions are characterized by …
The properties of static spherically symmetric black holes, which are either electrically or magnetically charged, and which are coupled to the dilaton in the presence of a cosmological constant, are considered. It is shown that such solutions do not exist if the cosmological constant is positive (in arbitrary spacetime dimension >= 4). However, asymptotically anti-de Sitter black hole solutions with a single horizon do exist if the cosmological constant is negative. These solutions are studied numerically in four dimensions and the thermodynamic properties of the solutions are derived. The ex…
The information paradox can be realized in anti-de Sitter spacetime joined to a Minkowski region. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirements of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as complexified wormholes connecting different copies of the black hole. As the replica number $n \to 1$, the presence of these wormholes leads to the island rule for the computation of the fine-grained gravitational entropy. We discuss these repl…
Quantum gravity (QG) on two-dimensional anti-de Sitter spacetime (AdS_2) takes always the form of a chiral conformal field theory (CFT). However, the actual content of the CFT, and in particular its central charge, depends on the background values of the dilaton and Maxwell field. We review the main features of AdS_2 QG with linear dilaton and of AdS_2 QG with constant dilaton and Maxwell field. We also show that the 3D charged Banados-Teitelboim-Zanelli black hole interpolates between these two versions of AdS_2 QG. Applications to the computation of the microscopic entropy of black holes are…
We present a formalism for studying the thermodynamics of black holes in dilaton gravity. The thermodynamic variables are defined on a quasilocal surface surrounding the black hole system and are obtained from a general class of Lagrangians involving a dilaton. The formalism thus accommodates a large number of possible theories and black hole spacetimes. Many of the thermodynamic quantities are identified from the contribution of the action on the quasilocal boundary. The entropy is found using path integral techniques, and a first law of thermodynamics is obtained. As an illustration, we calc…
It is shown that all generalized two--dimensional dilaton theories with arbitrary matter content (with a curvature independent coupling to gravity) do not only obey a first law of black hole mechanics (which follows from Wald's general considerations, if the entropy S is defined appropriately), but also a second law: δS \ge 0 provided only that the null energy condition holds and that, loosely speaking, for late times a stationary state is assumed. Also any two-dimensional f(R)--theory is covered. This generalizes a previous proof of Frolov [1] to a much wider class of theories.
We study holographic entanglement entropy in four-dimensional quantum gravity with negative cosmological constant. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the Wheeler-DeWitt equation, we compute quantum corrections to the holographic entanglement entropy for a circular entangling surface on the boundary three sphere. Similarly to our previous work on the sphere partition function, the path integrals are dominated by a replica version of asymptotically AdS conic geometries at saddle points. As expected from a general CFT …
We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as $n$ approaches $1$ a contact term can emerge when the OPE contains defect operators of twist $d-2$. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the $n\to 1$ limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in a large class of…
