Two-dimensional Dilaton Gravity 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.

From minimal strings towards Jackiw–Teitelboim gravity: on their resurgence, resonance, and black holes

Abstract Two remarkable facts about Jackiw–Teitelboim (JT) two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensembles are described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e. changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations—as derived from the Gel’fand–Dikii construction of the resolvent—are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed—in the string-equation context—and, in particular, the string equation for JT gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of JT gravity, is included—alongside a brief discussion of quasinormal modes.

Kink solutions in generalized 2D dilaton gravity

We study static kink solutions in a generalized two-dimensional dilaton gravity model, where the kinetic term of the dilaton is generalized to be an arbitrary function of the canonical one X=−12(∇φ)2, say F(X), and the kink is generated by a canonical scalar matter field ϕ. It is found that for arbitrary F(X), the background field equations have a simple first-order formalism, and the linear perturbation equation can always be written as a Schrödinger-like equation with factorizable Hamiltonian operator. After choosing appropriate F(X) and superpotential, we obtain a sine-Gordon type kink solution with pure AdS2 metric. The linear perturbation issue of this solution becomes an exactly solvable conformal quantum mechanics problem, if one of the model parameter takes a critical value.

Colliding fields in two-dimensional dilaton gravity background

The ([Formula: see text])-dimensional dilatonic background geometry of [C. Callan, S. Giddings, J. Harvey and A. Strominger, Phys. Rev. D 45 (1992) R1005] admits an infinite class of colliding wave solutions. We give examples from real and ghost fields with bounded/ unbounded profiles. In particular, colliding ghost fields in the “lineland” geometry create particle-like wormholes. Such wormholes, however, collapse to a black hole whenever the supporting ghosts turn off. Lastly, it is shown that the vacuum collision of null fields yields a ghost wormhole which is unstable.

Generalized black hole entropy in two dimensions

The Bekenstein–Hawking entropy of a black hole is proportional to its horizon area, hence in [Formula: see text] spacetime dimensions it is constant because the horizon degenerates into two points. This fact is consistent with Einstein’s gravity becoming topological in two dimensions. In [Formula: see text] gravity, which is non-trivial even in [Formula: see text], we find that the entropy is constant, as for Bekenstein–Hawking. As shown in Europhys. Lett. 139(6) (2022) 69001, arXiv: 2208.10146, two-dimensional [Formula: see text] gravity is equivalent to Jackiw–Teitelboim gravity, in turn, equivalent to the Sachdev–Ye–Kitaev model where the entropy becomes constant in the large [Formula: see text] limit. Several recently proposed entropies are functions of the Bekenstein–Hawking entropy and become constant in [Formula: see text], but in two-dimensional dilaton gravity entropies are not always constant. We study general dilaton gravity and obtain arbitrary static black hole solutions for which the non-constant entropies depend on the mass, horizon radius, or Hawking temperature, and constitute new proposals for a generalized entropy.

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.

Non-isometric quantum error correction in gravity

We construct and study an ensemble of non-isometric error correcting codes in a toy model of an evaporating black hole in two-dimensional dilaton gravity. In the preferred bases of Euclidean path integral states in the bulk and Hamiltonian eigenstates in the boundary, the encoding map is proportional to a linear transformation with independent complex Gaussian random entries of zero mean and unit variance. Using measure concentration, we show that the typical such code is very likely to preserve pairwise inner products in a set S of states that can be subexponentially large in the microcanonical Hilbert space dimension of the black hole. The size of this set also serves as an upper limit on the bulk effective field theory Hilbert space dimension. Similar techniques are used to demonstrate the existence of state-specific reconstructions of S-preserving code space unitary operators. State-specific reconstructions on subspaces exist when they are expected to by entanglement wedge reconstruction. We comment on relations to complexity theory and the breakdown of bulk effective field theory.

Color decorations of Jackiw-Teitelboim gravity

We introduce the colored version of Jackiw-Teitelboim (JT) gravity which is the two-dimensional dilaton gravity model with matrix-valued fields. It is straightforwardly formulated in terms of BF action with su(N, N) gauge algebra so that the standard JT gravity is embedded as su(1, 1) ⊂ su(N, N) subsector. We also elaborate on the respective metric formulation which is shown to involve the JT fields plus su(N) non-Abelian fields as well as su(N)-matrix valued metric and dilaton fields. Their interactions are governed by minimal couplings and potential terms of cubic and quartic orders involving derivatives.

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.

Testing the quantum effects near the event horizon with respect to the black hole shadow * *Supported the Special Natural Science Fund of Guizhou University (X2020068) and the financial support from the China Postdoctoral Science Foundation Funded Project (2019M650846)

In recent years, the study of quantum effects near the event horizon of a black hole (BH) has attracted extensive attention. It has become one of the important methods to explore BH quantum properties using the related properties of a quantum deformed BH. In this work, we study the effect of a quantum deformed BH on the BH shadow in two-dimensional Dilaton gravity. In this model, quantum effects are reflected by the quantum correction parameter m. By calculation, we find that: (1) the shape of the shadow boundary of a rotating BH is determined by the BH spin a, the quantum correction parameter m, and the BH type parameter n; (2) when the spin , the shape of the BH shadow is a perfect circle; when , the shape is distorted; if the quantum correction parameter , their shapes reduce to the cases of a Schwarzschild BH and Kerr BH, respectively; (3) the degree of distortion of the BH shadow is different for various quantum correction parameters m; with an increase in the parameter m, the boundary of the BH shadow expands; (4) the size of the BH shadow varies greatly with respect to various quantum deformed BHs (n), and the change in BH shadow shape caused by parameter n is similar to that caused by parameter m, which indicates that there is a "degenerate phenomenon" between the two parameters. Because the value of m in actual physics should be very small, the current observations of the event horizon telescope (EHT) cannot distinguish quantum effects from the BH shadow. In future BH shadow measurements, it will be possible to distinguish quantum deformed BHs, which will help to better understand the quantum effects of BHs.

K-field kinks in two-dimensional dilaton gravity

In this work, kinks with non-canonical kinetic energy terms are studied in a type of two-dimensional dilaton gravity model. The linear stability issue is generally discussed for arbitrary static solutions, and the stability criteria are obtained. As an explicit example, a model with cuscuton term is studied. After rewriting the equations of motion into simpler first-order formalism and choosing a polynomial superpotential, an exact self-gravitating kink solution is obtained. The impacts of the cuscuton term are discussed.

Replica wormholes and capacity of entanglement

We consider the capacity of entanglement as a probe of the Hawking radiation in a two-dimensional dilaton gravity coupled with conformal matter of large degrees of freedom. A formula calculating the capacity is derived using the gravitational path integral, from which we speculate that the capacity has a discontinuity at the Page time in contrast to the continuous behavior of the generalized entropy. We apply the formula to a replica wormhole solution in an eternal AdS black hole coupled to a flat non-gravitating bath and show that the capacity of entanglement is saturated by the thermal capacity of the black hole in the high temperature limit.

Nonsingular black hole in two-dimensional asymptotically flat spacetime

We study a special two-dimensional dilaton gravity with Lagrangian $\mathcal{L}=\frac{1}{2}\sqrt{-g}(\phi R+{\lambda^2}{\rm sech}^2\phi)$ where $\lambda$ is a parameter of dimension mass. This theory describes two-dimensional spacetimes that are asymptotically flat. Very interestingly, it has an exact solution for the metric, $\d s^2=-(c+\tanh \lambda x)\d t^2+ \d x^2/(c+\tanh {\lambda} x)$, parametrized by $c$. For $c\in(-1,1)$, the solution presents an event horizon but no singularity. Because of the kink profile for the metric components appearing in the solution, we refer to the spacetime described by the metric as a {\it gravitational domain wall} with the wall simply being the event horizon and separating two asymptotically Minkowskian spacetimes. The global causal structure for such an object is studied via coordinate extension and the thermodynamical quantities are computed. Only when $c\in(-1,0]$ are the entropy and energy non-negative.

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.

Aspects of two-dimensional dilaton gravity, dimensional reduction, and holography

We discuss aspects of generic 2-dimensional dilaton gravity theories. The 2-dim geometry is in general conformal to $AdS_2$ and has IR curvature singularities at zero temperature: this can be regulated by a black hole. The on-shell action is divergent: we discuss the holographic energy-momentum tensor by adding appropriate counterterms. For theories obtained by dimensional reduction of the gravitational sector of higher dimensional theories, for instance higher dimensional $AdS$ gravity as a concrete example, the 2-dimensional description dovetails with the higher dimensional one. We also discuss more general theories containing an extra scalar field which now drives nontrivial dynamics. Finally we discuss aspects of the 2-dimensional cosmological singularities discussed in earlier work. These studies suggest that generic 2-dim dilaton gravity theories are somewhat distinct from JT gravity and theories "near JT".

Flat space holography in spin-2 extended dilaton-gravity

We present an interacting spin-2 gauge theory coupled to the two-dimensional dilaton-gravity in flat spacetime. The asymptotic symmetry group is enhanced to the central extension of Diff(S1)⋉C∞(S1)⋉Vec(S1) when the central element of the Heisenberg subgroup is zero (vanishing U(1) level). Using the BF-formulation of the model we derive the corresponding boundary coadjoint action which is the spin-2 extension of the warped Schwarzian theory at vanishing U(1) level. We also discuss the thermodynamics of black holes in this model.

Revisit on two-dimensional self-gravitating kinks: superpotential formalism and linear stability

Self-gravitating kink solutions of a two-dimensional dilaton gravity are revisited in this work. Analytical kink solutions are derived from a concise superpotential formalism of the dynamical equations. A general analysis on the linear stability is conducted for an arbitrary static solution of the model. After gauge fixing, a Schrödinger-like equation with factorizable Hamiltonian operator is obtained, which ensures the linear stability of the solution.

Quantum fields, geometric fluctuations, and the structure of spacetime

Quantum fluctuations of the vacuum stress-energy tensor are highly non-Gaussian, and can have unexpectedly large effects on spacetime geometry. In this paper, we study a two-dimensional dilaton gravity model coupled to a conformal field, in which the distribution of vacuum fluctuations is well understood. In this model, the fluctuations of the matter field are responsible for the fluctuations of the geometry itself. By analyzing the geodesic deviation in this model, we show that a pencil of massive particles propagating on this fuzzy spacetime eventually converges and collapses. This is consistent with our earlier analysis of null geodesics in [Phys. Rev. Lett.\ 107, 021303 (2011)].

Holographic renormalization group flows in two-dimensional gravity and AdS black holes

We look into the AdS black holes from two-dimensional gravity perspective. In this work, we extend the previous results of holographic renormalization group flows to dimensions two. By introducing a superpotential, we derive the flow equations in two-dimensional dilaton gravity. We also find a quantity which monotonically decreases along flows and give some comments on holographic c-theorem. As examples, we show that recently studied supersymmetric AdS black hole solutions generically dimensionally reduce to two-dimensional dilaton gravity, and obtain the flow equations for black hole solutions.

A one-loop test of the near-AdS2/near-CFT1 correspondence

We analyze quantum fluctuations around black hole solutions to the Jackiw-Teitelboim model. We use harmonic analysis on Euclidean AdS2 to show that the logarithmic corrections to the partition function are determined entirely by quadratic holomorphic differentials, even when conformal symmetry is broken and harmonic modes are no longer true zero modes. Our quantum-corrected partition function agrees precisely with the SYK result. We argue that our effective quantum field theory methods and results generalize to other theories of two-dimensional dilaton gravity.