Two-dimensional Dilaton Gravity Theory Research Articles

Island formula from Wald-like entropy with backreaction

We propose a Lorentzian derivation of the generalized entropy associated with the island formula for black holes as a Wald-like entropy without reference to the exterior non-gravitating region or field-theoretic von Neumann entropy of Hawking radiation in a fixed curved spacetime background. We illustrate this idea by studying two-dimensional black holes in the Jackiw-Teitelboim gravity and the Russo-Susskind-Thorlacius model in which Hawking radiation is represented by conformal scalars. With some prescriptions assumed, we show that the generalized entropy for the island formula can be reproduced as the Wald-like entropy of the two-dimensional dilaton-gravity theories upon the inclusion of the backreaction from Hawking radiation described by conformal anomaly. We give a discussion on how a similar idea can be applied to higher-dimensional black holes. It is emphasized that the generalized entropy is obtained in a fully gravitational fashion, yet it yields the same Page curve as that of the half-gravitational set-up. We argue that the results in this paper exacerbate the issues raised in the work of massive islands and inconsistency of islands in theories of long-range gravity.

A Matrix Model for Flat Space Quantum Gravity

We take a step towards the non-perturbative description of a two-dimensional dilaton-gravity theory which has a vanishing cosmological constant and contains black holes. This is done in terms of a double-scaled Hermitian random matrix model which non-perturbatively computes the partition function for the asymptotic Bondi Hamiltonian. To arrive at this connection we first construct the gauge-invariant asymptotic phase space of the theory and determine the relevant asymptotic boundary conditions, compute the classical S-matrix and, finally, shed light on the interpretation of the Euclidean path integral defined in previous works. We then construct a matrix model that matches the topological expansion of the latter, to all orders. This allows us to compute the fine-grained Bondi spectrum and other late time observables and to construct asymptotic Hilbert spaces. We further study aspects of the semi-classical dynamics of the finite cut-off theory coupled to probe matter and find evidence of maximally chaotic behavior in out-of-time-order correlators. We conclude with a strategy for constructing the non-perturbative S-matrix for our model coupled to probe matter and comment on the treatment of black holes in celestial holography.

Entanglement islands in generalized two-dimensional dilaton black holes

The Fabbri--Russo model is a generalized model of a two-dimensional dilaton gravity theory with various parameters ``$n$'' describing various specific gravities. Particularly, the Russo--Susskind--Thorlacius gravity model fits the case $n=1$. In the Fabbri--Russo model, we investigate Page curves and the entanglement island. Islands are considered in eternal and evaporating black holes. Surprisingly, in any black hole, the emergence of islands causes the rise of the entanglement entropy of the radiation to decelerate after the Page time, satisfying the principle of unitarity. For eternal black holes, the fine-grained entropy reaches a saturation value that is twice the Bekenstein--Hawking entropy. For evaporating black holes, the fine-grained entropy finally reaches zero. At late times and large distance limit, the impact of the parameter ``$n$'' is a subleading term and is exponentially suppressed. As a result, the shape of Page curves is ``$n$'' independent in the leading order, which also indicates the universality of the Page curve in generalized two-dimensional models. Furthermore, we discuss the relationship between islands and firewalls. We show that the island is a better candidate than firewalls for encountering the quantum entanglement-monogamy problem. Finally, we briefly review the gravity/ensemble duality as a possible resolution to the state paradox resulting from the island formula.

Microcanonical action and the entropy of Hawking radiation

The island formula---an extremization prescription for generalized entropy---is known to result in a unitary Page curve for the entropy of Hawking radiation. This semiclassical entropy formula has been derived for Jackiw-Teitelboim (JT) gravity coupled to conformal matter using the ``replica trick'' to evaluate the Euclidean path integral. Alternatively, for eternal Anti--de Sitter black holes, we derive the extremization of generalized entropy from minimizing the microcanonical action of an entanglement wedge. The on-shell action is minus the entropy and arises in the saddle-point approximation of the (nonreplicated) microcanonical path integral. When the black hole is coupled to a bath, islands emerge from maximizing the entropy at fixed energy, consistent with the island formula. Our method applies to JT gravity as well as other two-dimensional dilaton gravity theories.

2D dilaton-gravity, deformations of the minimal string, and matrix models

A large class of two-dimensional dilaton-gravity theories in asymptotically AdS2 spacetimes are holographically dual to a matrix integral, interpreted as an ensemble average over Hamiltonians. Viewing these theories as Jackiw–Teitelboim gravity with a gas of defects, we extend this duality to a broader class of dilaton potentials compared to previous work by including conical defects with small deficit angles. In order to do this we show that these theories are equal to the large p limit of a natural deformation of the (2, p) minimal string theory.

Two-dimensional black holes in the limiting curvature theory of gravity

In this paper we discuss modified gravity models in which growth of the curvature is dynamically restricted. To illustrate interesting features of such models we consider a modification of two-dimensional dilaton gravity theory which satisfies the limiting curvature condition. We show that such a model describes two-dimensional black holes which contain the de Sitter-like core instead of the singularity of the original non-modified theory. In the second part of the paper we study Vaidya type solutions of the model of the limiting curvature theory of gravity and used them to analyse properties of black holes which are created by the collapse of null fluid. We also apply these solutions to study interesting features of a black hole evaporation.

Page curve for an evaporating black hole

A Page curve for an evaporating black hole in asymptotically flat spacetime is computed by adapting the Quantum Ryu-Takayanagi (QRT) proposal to an analytically solvable semi-classical two-dimensional dilaton gravity theory. The Page time is found to be one third of the black hole lifetime, at leading order in semi-classical corrections. A Page curve is also obtained for a semi-classical eternal black hole, where energy loss due to Hawking evaporation is balanced by an incoming energy flux.

Two-dimensional dilaton gravity theory and lattice Schwarzian theory

We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of nonvanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of nonvanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term [Formula: see text], where [Formula: see text] is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cutoff [Formula: see text] under a constant boundary dilaton field and the nonvanishing cosmological constant by identifying the lattice spacing [Formula: see text] of a lattice Schwarzian theory with the boundary cutoff [Formula: see text] of the two-dimensional dilaton gravity theory.

The probe of curvature in the Lorentzian AdS2/CFT1 correspondence

We establish the Lorentzian AdS2/CFT1 correspondence from a reconstruction of all bulk points through the kinematic-space approach. The OPE block is exactly a bulk local operator. We formulate the correspondence between the bulk propagator in the non-interacting scalar field theory and the conformal block in CFT1. When we consider the stress tensor, the variation probes the variation of AdS2 metric. The reparameterization provides the asymptotic boundary of the bulk spacetime as in the derivation of the Schwarzian theory from two-dimensional dilaton gravity theory. Finally, we find the AdS2 Riemann curvature tensor based on the above consistent check.

De Sitter horizons & holographic liquids

We explore asymptotically AdS2 solutions of a particular two-dimensional dilaton-gravity theory. In the deep interior, these solutions flow to the cosmological horizon of dS2. We calculate various matter perturbations at the linearised and non-linear level. We consider both Euclidean and Lorentzian perturbations. The results can be used to characterise the features of a putative dual quantum mechanics. The chaotic nature of the de Sitter horizon is assessed through the soft mode action at the AdS2 boundary, as well as the behaviour of shockwave type solutions.

Tunnelling Phenomenon near an Apparent Horizon in Two-Dimensional Dilaton Gravity**Supported by the National Natural Science Foundation of China under Grant Nos. 11622543 and 11235010, and by the Open Project Program of Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (No. Y5KF161CJ1)

Based on the definition of the apparent horizon in a general two-dimensional dilaton gravity theory, we analyze the tunnelling phenomenon near the apparent horizon. In this theory the definition of the horizon is very different from those in higher-dimensional gravity theories. By using the Hamilton–Jacobi method, the spectrum of the radiation is obtained and the temperature of the radiation is read out from this spectrum. The temperature is proportional to the surface gravity of the apparent horizon as usual. Besides, in stationary cases we calculate the spectrum by using Parikh and Wilczek’s null geodesic method and the result conforms to that obtained by using the Hamilton–Jacobi method. This is expected since the Hamilton–Jacobi method applies to generic spacetimes, including stationary ones.

Multiexponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models

The general properties of a class of two-dimensional dilaton gravity (DG) theories with multi-exponential potentials are studied and a subclass of these theories, in which the equations of motion reduce to Toda and Liouville equations, is treated in detail. A combination of parameters of the equations should satisfy a certain constraint that is identified and solved for the general model. It follows that in DG the integrable Toda equations, generally, cannot appear without accompanying Liouville equations. The most difficult problem in the two-dimensional Toda-Liouville DG is to solve the energy-momentum constraints. We discuss this problem using the simplest examples and identify the main obstacles to finding its analytic solution. Then we consider a subclass of integrable two-dimensional theories, in which scalar matter satisfy the Toda equations while the two-dimensional metric is trivial. We also show how the wave-like solutions of the general Toda-Liouville systems can be simply derived. In DG, these solutions describe nonlinear waves coupled to gravity as well as static states and cosmologies. For the static states and cosmologies we propose and study a more general one-dimensional Toda-Liouville model typically emerging in one-dimensional reductions of higher-dimensional gravity and supergravity theories. A special attention is paid to making the analytic structure of the solutions of the Toda equations as simple and transparent as possible, with the aim to gain a better understanding of realistic theories reduced to dimensions 1+1 and 1+0 or 0+1.

On black-hole solutions in two-dimensional dilaton gravity theories

On black-hole solutions in two-dimensional dilaton gravity theories

Two-dimensional static black holes with pointlike sources

We study the static black hole solutions of generalized two-dimensional dilaton-gravity theories generated by pointlike mass sources, in the hypothesis that the matter is conformally coupled. We also discuss the motion of test particles. Due to conformal coupling, these follow the geodesics of a metric obtained by rescaling the canonical metric with the dilaton.

THE AdS/CFT CORRESPONDENCE IN TWO DIMENSIONS

We review recent progress in understanding the anti-de Sitter/conformal field theory correspondence in the context of two-dimensional (2D) dilaton gravity theory.

Free-field realization of D-dimensional cylindricalgravitational waves

We find two-dimensional free-field variables for D-dimensionalgeneral relativity on spacetimes with D-2 commutingspacelike Killing vector fields and non-compact spatial sections for D>4.We show that there is a canonical transformation which mapsthe corresponding two-dimensional dilaton gravity theory into atwo-dimensional diffeomorphism-invariant theory of the free-fieldvariables.We also show that the spacetime metric components can be expressed asasymptotic series in negative powers of the dilaton, with coefficientswhichcan be determined in terms of the free fields.

Gauge Symmetry of the Two-dimensional Dilaton Gravity Theory

Gauge Symmetry of the Two-dimensional Dilaton Gravity Theory

Black hole thermodynamics and two-dimensional dilaton gravity theory

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 the thermodynamics of black holes in $D>~4$ can be effectively described by the 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 two-dimensional dilaton gravity model. We comment that the thermodynamics of a nonextreme stringy four-dimensional black hole with four charges and a five-dimensional black hole with three charges may be effectively described by the thermodynamics of black hole solutions with a constant dilaton field in two-dimensional dilaton gravity theories.

Normalization of Killing vectors and energy conservation in two-dimensional gravity

We explicitly show that, in the context of a recently proposed two-dimensional dilaton gravity theory, energy conservation requires the ``natural'' Killing vector to have, asymptotically, an unusual normalization. The Hawking temperature ${T}_{H}$ is then calculated according to this prescription.

One-loop corrections for a Schwarzschild black hole via 2D dilaton gravity

We study quantum corrections for the Schwarzshild black hole by considering it as a vacuum solution of a two-dimensional (2D) dilaton gravity theory obtained by spherical reduction of 4D gravity coupled with matter. We find perturbatively the vacuum solution for the standard one-loop effective action in the case of null-dust matter and in the case of minimally coupled scalar field. The corresponding state is in both cases a 2D Hartle-Hawking vacuum, and we evaluate the corresponding quantum corrections for the thermodynamic parameters of the black hole. We also find that the standard effective action does not allow boundary conditions corresponding to a 4D Hartle-Hawking vacuum state.