2D Dilaton Gravity Models Research Articles

Gravitating kinks with asymptotically flat metrics

In this work, we consider a two-dimensional (2D) dilaton gravity model where the dilaton kinetic term is modified by an additional derivative coupling term . In the case with a canonical scalar matter field, the field equations of this model have a simple first-order formalism, from which exact static kink solutions can be constructed. The novelty of these solutions is that the corresponding metric can be asymptotically flat rather than asymptotically anti-de Sitter. The linear stability and the localization of scalar matter fields are also studied. It was found that the solutions are stable against small linear perturbations, and the localization of scalar matter fields can be realized by introducing scalar-kink interactions.

DS$\boldsymbol{_2}$ as excitation of AdS$\boldsymbol{_2}$

We introduce a family of 2D dilaton gravity models with state-dependent constant curvature so that dS_22 emerges as an excitation of AdS_22. Curiously, the strong coupling region corresponds to the asymptotic region geometrically. Apart from these key differences, many features resemble the Almheiri–Polchinski model. We discuss perturbative and non-perturbative thermodynamical stability, bubble nucleation through matter shockwaves, and semiclassical backreaction effects. In some of these models, we find that low temperatures are dominated by AdS_22 but high temperatures are dominated by dS_22, concurrent with a recent proposal by Susskind.

From quantum groups to Liouville and dilaton quantum gravity

We investigate the underlying quantum group symmetry of 2d Liouville and dilaton gravity models, both consolidating known results and extending them to the cases with mathcal{N} = 1 supersymmetry. We first calculate the mixed parabolic representation matrix element (or Whittaker function) of Uq( mathfrak{sl} (2, ℝ)) and review its applications to Liouville gravity. We then derive the corresponding matrix element for Uq( mathfrak{osp} (1|2, ℝ)) and apply it to explain structural features of mathcal{N} = 1 Liouville supergravity. We show that this matrix element has the following properties: (1) its q → 1 limit is the classical OSp+(1|2, ℝ) Whittaker function, (2) it yields the Plancherel measure as the density of black hole states in mathcal{N} = 1 Liouville supergravity, and (3) it leads to 3j-symbols that match with the coupling of boundary vertex operators to the gravitational states as appropriate for mathcal{N} = 1 Liouville supergravity. This object should likewise be of interest in the context of integrability of supersymmetric relativistic Toda chains. We furthermore relate Liouville (super)gravity to dilaton (super)gravity with a hyperbolic sine (pre)potential. We do so by showing that the quantization of the target space Poisson structure in the (graded) Poisson sigma model description leads directly to the quantum group Uq( mathfrak{sl} (2, ℝ)) or the quantum supergroup Uq( mathfrak{osp} (1|2, ℝ)).

Liouville quantum gravity \u2014 holography, JT and matrices

We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ℝ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.

Ghost-free modification of the Polyakov action and Hawking radiation

In this paper we discuss possible effects of non-locality in black hole spacetimes. We consider a two-dimensional theory in which the action describing matter is a ghost-free modification of the Polyakov action. For this purpose we write the Polyakov action in a local form by using an auxiliary scalar field and modify its kinetic term by including into it a non-local ghost-free form factor. We demonstrate that the effective stress-energy tensor is modified and we study its properties in a background of a two-dimensional black hole. We obtain the expression for the contribution of the ghost-free auxiliary field to the entropy of the black hole. We also demonstrate that if the back-reaction effects are not taken into account, such a ghost-free modification of the theory does not change the energy flux of the Hawking radiation measured at infinity. We illustrate the discussed properties for black hole solution of a 2D dilaton gravity model which admits a rather complete analytical study.

On the Liouville 2D dilaton gravity models with sinh-Gordon matter

We study 1 + 1 dimensional dilaton gravity models which take into account backreaction of the sinh-Gordon matter field. We found a wide class of exact solutions which generalizes black hole solutions of the Jackiw-Teitelboim gravity model and its hyperbolic deformation.

Exactly solvable models of 2D dilaton gravity

We give the full list of types of static (homogeneous) solutions within a wide family of exactly solvable 2D dilaton gravities with the back-reaction of conformal fields. We discuss in detail the class of black hole solutions which includes the previously known ones as particular cases. For this class, the whole spacetime can be divided into dierent sheets with one horizon on each sheet between neighboring singularities with a finite value of dilaton field, the neighboring sheets being glued along the singularity. The position of singularities coincide with the values of dilaton in solutions with a constant dilaton field. Quantum corrections to the Hawking temperature vanish. We also consider a general approach to exactly solvable 2D dilaton cosmology. We find a rather rich class of everywhere regular solutions which exist practically in every type of the analyzed solutions. They exhibit dierent kinds of asymptotic behavior in the past and future, including inflation, superinflation, deflation, power expansion or contraction. In particular, for some models the dS spacetime with a time-dependent dilaton field is the exact solution of field equations. For some kinds of solutions the weak energy condition is violated independently of a specific model. We find also the solutions with a singularity which is situated in an infinite past (or future), so at any finite moment of a co-moving time the universe is singularity-free. It is pointed out that for some models the spacetime may be everywhere regular even in spite of infinitely large quantum back-reaction in an infinite past.

BOULWARE STATE IN EXACTLY SOLVABLE MODELS OF 2D DILATON GRAVITY

We discuss self-consistent geometries and behavior of dilaton in exactly solvable models of 2D dilaton gravity, with quantum fields in the Boulware state. If the coupling H(ϕ) between curvature and dilaton ϕ is non-monotonic, back-reaction can remove the classical singularity. As a result, an everywhere regular star-like configuration may appear, in which case the Boulware state, contrary to expectations, smooths out the system. For monotonic H(ϕ), exact solutions confirm the features found before with the help of numerical methods: the appearance of the bouncing point and the presence of isotropic singularity at the classically forbidden branch of the dilaton.

Quantum extreme black holes at finite temperature and exactly solvable models of 2d dilaton gravity

It is argued that in certain 2d dilaton gravity theories there exist self-consistent solutions of field equations with quantum terms which describe extreme black holes at nonzero temperature. The curvature remains finite on the horizon due to cancellation of thermal divergences in the stress-energy tensor against divergences in the classical part of field equations. The extreme black hole solutions under discussion are due to quantum effects only and do not have classical counterparts.

Dimensional reduction of 4D heterotic string black holes

We perform a spherical symmetric dimensional reduction $4\stackrel{\ensuremath{\rightarrow}}{d}2d$ of heterotic string theory. We find a class of two-dimensional (2D) dilaton gravity models that gives a general description of the near-horizon, near-extremal behavior of four-dimensional (4D) heterotic string black holes. We show that the duality group of the 4D theory is realized in two dimensions in terms of Weyl transformations of the metric. We use the 2D dilaton gravity theory to compute the statistical entropy of a near-extremal 4D, $a=1/\sqrt{3},$ black hole.

Semi-infinite throats at finite temperature and static solutions in exactly solvable models of 2d dilaton gravity

Found is a general form of static solutions in exactly solvable models of 2d dilaton gravity at finite temperature. We reveal a possibility for the existence of everywhere regular solutions including black holes, semi-infinite throats and star-like configurations. In particular, we consider the Bose-Parker-Peleg (BPP) model which possesses a semi-infinite throat and analyze it at finite temperature. We also suggest generalization of the BPP model in which the appearance of semi-infinite throat has a generic character and does not need special fine tuning between parameters of the solution.

2D extremal black holes as solitons

We discuss the relationship between two-dimensional (2D) dilaton gravity models and sine-Gordon-like field theories. We show that there is a one-to-one correspondence between the solutions of 2D dilaton gravity and the solutions of a (two fields) generalization of the sine-Gordon model. In particular, we find a connection between the soliton solutions of the generalized sine-Gordon model and extremal black hole solutions of 2D dilaton gravity. As a by-product of our calculations we find a easy way to generate cosmological solutions of 2D dilaton gravity.

Free fields for chiral 2D dilaton gravity

We give an explicit canonical transformation which transforms a generic chiral 2D dilaton gravity model into a free field theory.

Symmetries and solvable models for evaporating 2D black holes

We study the evaporation process of a 2D black hole in thermal equilibrium when the ingoing radiation is suddenly switched off. We also introduce global symmetries of generic 2D dilaton gravity models which generalize the extra symmetry of the CGHS model.

Solutions of arbitrary topology in 1+1 gravity

We present a classification of all global solutions for generalized 2D dilaton gravity models (with Lorentzian signature). While for some of the popular choices of potential-like terms in the Lagrangian, describing, e.g., string inspired dilaton gravity or spherically reduced gravity, the possible topologies of the resulting spacetimes are severely restricted, we find that for generic choices of these ‘potentials’ there exist maximally extended solutions to the field equations on all non-compact two-surfaces.

Conformal and non-conformal symmetries in 2D dilaton gravity

We study finite-dimensional extra symmetries of generic 2D dilaton gravity models. Using a non-linear sigma model formulation we show that the unique theories admitting an extra (conformal) symmetry are the models with an exponential potential $V \propto e^{\beta\phi}$ ($ S ={1\over2\pi} \int d^2 x \sqrt{-g} [ R \phi + 4 \lambda^2 e^{\beta\phi} ]$), which include the CGHS model as a particular though limiting ($\beta=0$) case. These models give rise to black hole solutions with a mass-dependent temperature. The underlying extra symmetry can be maintained in a natural way in the one-loop effective action, thus implying the exact solubility of the semiclassical theory including back-reaction. Moreover, we also introduce three different classes of (non-conformal) transformations which are extra symmetries for generic 2D dilaton gravity models. Special linear combinations of these transformations turn out to be the (conformal) symmetries of the CGHS and $V \propto e^{\beta\phi}$ models. We show that one of the non-conformal extra symmetries can be converted into a conformal one by means of adequate field redefinitions involving the metric and the derivatives of the dilaton. Finally, by expressing the Polyakov-Liouville effective action in terms of an invariant metric, we are able to provide semiclassical models which are also invariant. This generalizes the solvable semiclassical model of Bose, Parker and Peleg (BPP) for a generic 2D dilaton gravity model.

Conformal equivalence of 2D dilaton gravity models

We investigate the behaviour of generic, matter-coupled, 2D dilaton gravity theories under dilaton-dependent Weyl rescalings of the metric. We show that physical observables associated with 2D black holes, such as the mass, the temperature and the flux of Hawking radiation are invariant under the action of both Weyl transformations and dilaton reparametrizations. The field theoretical and geometrical meaning of these invariances is discussed.

Black hole evaporation by thermal bath removal

We study the evaporation process of 2D black holes in thermal equilibrium when the incoming radiation is turned off. Our analysis is based on two different classes of 2D dilaton gravity models which are exactly solvable in the semiclassical approximation including back-reaction. We consider a one parameter family of models interpolating between the Russo-Susskind-Thorlacius and Bose-Parker-Peleg models. We find that the end-state geometry is the same as the one coming from an evaporating black hole formed by gravitational collapse. We also study the quantum evolution of black holes arising in a model with classical action S = 1 2π ∫ d 2x −g (Rφ + 4λ 2e βφ) . The black hole temperature is proportional to the mass and the exact semiclassical solution indicates that these black holes never disappear completely.

Solvable models for radiating black holes and area-preserving diffeomorphisms

Solvable theories of 2D dilaton gravity can be obtained from a Liouville theory by suitable field redefinitions. In this paper we propose a new framework to generate 2D dilaton gravity models which can also be exactly solved in the semiclassical approximation. Our approach is based on the recently introduced scheme to quantize massless scalar fields coupled to 2D gravity maintaining invariance under area-preserving diffeomorphisms and Weyl transformations. Starting from the CGHS model with the new effective action we reestablish the full diffeomorphism invariance by means of an adequate family of field redefinitions. The original theory is therefore mapped into a large family of solvable models. We focus our analysis on the one-parameter class of models interpolating between the Russo-Susskind-Thorlacius model and the Bose-Parker-Peleg model. Finally we shall briefly indicate how we can extend our approach to spherically symmetric Einstein gravity coupled to 2D conformal matter.

Exactly solvable models of 2D dilaton quantum gravity

We study canonical quantization of a class of 2D dilaton gravity models, which contains the model proposed by Callan, Giddings, Harvey and Strominger. A set of non-canonical phase space variables is found, forming an SL(2, R )×U(1) current algebra, such that the constraints become quadratic in these new variables. In the case when the spatial manifold is compact, the corresponding quantum theory can be solved exactly, since it reduces to a problem of finding the cohomology of a free-field Virasoro algebra. In the non-compact case, which is relevant for 2D black holes, this construction is likely to break down, since the most general field configuration cannot be expanded into Fourier modes. Strategy for circumventing this problem is discussed.