Sitter Gravity Research Articles

De Sitter bounces

By analytically continuing with the recently found instantons, we construct time-dependent solutions of the Einstein–Maxwell de Sitter gravity which smoothly bounce between two de Sitter phases. These deformations of de Sitter space undergo several stages in their time evolution. Four- and five-dimensional de Sitter bounces can be lifted to non-singular time-dependent solutions of M-theory.

Four-dimensional Einstein Yang–Mills de Sitter gravity from eleven dimensions

We obtain D=4 de Sitter gravity coupled to SU(2) Yang–Mills gauge fields from an explicit and consistent truncation of D=11 supergravity via Kaluza–Klein dimensional reduction on a non-compact space. The “internal” space is a smooth hyperbolic 7-space (H7) written as a foliation of two 3-spheres, on which the SU(2) Yang–Mills fields reside. The positive cosmological constant is completely fixed by the SU(2) gauge coupling constant. The explicit reduction ansatz enables us to lift any of the D=4 solutions to D=11. In particular, we obtain dS2 in M-theory, where the nine-dimensional transverse space is an H7 bundle over S2. We also obtain a new smooth embedding of dS3 in D=6 supergravity.

Holography: 2D or not 2D?

As was recently pointed out by Cadoni, a certain class of two-dimensional gravitational theories will exhibit a (black hole) thermodynamic behavior that is reminiscent of a free field theory. In the current Rapid Communication, a direct correspondence is established between these two-dimensional models and the strongly curved regime of (arbitrary-dimensional) anti--de Sitter gravity. On this basis, we go on to speculatively argue that two-dimensional gravity may ultimately be utilized for identifying and perhaps even understanding holographic dualities.

Closed string tachyon condensation and worldsheet inflation

Closed string tachyon condensation in spacetime generates potentials on the worldsheet that model two-dimensional inflationary cosmology. These models illustrate and elucidate a variety of aspects of inflation, in particular the generation of quantum fluctuations and their back reaction on geometry. We exhibit a class of Liouville gravity models coupled to matter that can exhibit, for example, (a) pure de Sitter gravity, (b) slow-roll inflation, (c) topological inflation, and (d) graceful exit into a Friedmann-Robertson-Walker (FRW) phase. The models also provide a quantitative testing ground for ideas about the origin of inflation, such as the various ``no-boundary or tunnelling'' proposals, and the ``eternal or chaotic'' inflationary scenario. We suggest an alternative mechanism for quantum creation of cosmological spacetimes which, in the context of the model, provides a natural explanation for why the typical FRW cosmology at large scales underwent a period of inflation at small scale.

AdS 2 supergravity and superconformal quantum mechanics

We investigate the asymptotic dynamics of topological anti-de Sitter supergravity in two dimensions. Starting from the formulation as a BF theory, it is shown that the AdS 2 boundary conditions imply that the asymptotic symmetries form a super-Virasoro algebra. Using the central charge of this algebra in Cardy’s formula, we exactly reproduce the thermodynamical entropy of AdS 2 black holes. Furthermore, we show that the dynamics of the dilaton and its superpartner reduces to that of superconformal transformations that leave invariant one chiral component of the stress tensor supercurrent of a two-dimensional conformal field theory. This dynamics is governed by a supersymmetric extension of the de Alfaro–Fubini–Furlan model of conformal quantum mechanics. Finally, two-dimensional de Sitter gravity is also considered, and the dS 2 entropy is computed by counting CFT states.

Comments on Quantum Aspects of Three-Dimensional de Sitter Gravity(Quantum Field Theories: Fundamental Problems and Applications)

Comments on Quantum Aspects of Three-Dimensional de Sitter Gravity(Quantum Field Theories: Fundamental Problems and Applications)

Comments on quantum aspects of three-dimensional de Sitter gravity

We investigate the quantum aspects of three-dimensional gravity with a positive cosmological constant. The reduced phase space of the three-dimensional de Sitter gravity is obtained as the space which consists of the Kerr–de Sitter spacetimes and their Virasoro deformations. A quantization of the phase space is carried out by the geometric quantization of the coadjoint orbits of the asymptotic Virasoro symmetries. The Virasoro algebras with real central charges are obtained as the quantum asymptotic symmetries. The states of globally de Sitter and point particle solutions become the primary states of the unitary irreducible representations of the Virasoro algebras. It is shown that those states are perturbatively stable at the quantum level. The Virasoro deformations of these solutions correspond to the excited states in the unitary irreducible representations. In view of the dS/CFT correspondence, we also study the relationship between the Liouville field theory obtained by a reduction of the SL(2; C) Chern–Simons theory and the three-dimensional gravity both classically and quantum mechanically. In the analyses of the both theories, the Kerr–de Sitter geometries with non-zero angular momenta do not give the unitary representations of the Virasoro algebras.

Dynamics of black hole formation in an exactly solvable model

We consider the process of black hole formation in particle collisions in the exactly solvable framework of 2+1 dimensional Anti de Sitter gravity. An effective Hamiltonian describing the near horizon dynamics of a head on collision is given. The Hamiltonian exhibits a universal structure, with a formation of a horizon at a critical distance. Based on it we evaluate the action for the process and discuss the semiclassical amplitude for black hole formation. The derived amplitude is seen to contain no exponential suppression or enhancement. Coments on the CFT description of the process are made.

De Sitter spacetimes from warped compactifications of IIB string theory

We continue our study of codimension two solutions of warped spacetime varying compactifications of string theory. In this Letter we discuss a non-supersymmetric solution of the classical type IIB string theory with de Sitter gravity on a codimension two uncompactified part of spacetime. A non-zero positive value of the cosmological constant is induced by the presence of non-trivial stringy moduli, such as the axion–dilaton system for the type IIB string theory. Furthermore, the naked singularity of the codimension two solution is resolved by the presence of a small but non-zero cosmological constant.

De Sitter Gravity and Liouville Theory

We show that the spectrum of conical defects in three-dimensional de Sitter space is in one-to-one correspondence with the spectrum of vertex operators in Liouville conformal field theory. The classical conformal dimensions of vertex operators are equal to the masses of the classical point particles in dS_3 that cause the conical defect. The quantum dimensions instead are shown to coincide with the mass of the Kerr-dS_3 solution computed with the Brown-York stress tensor. Therefore classical de Sitter gravity encodes the quantum properties of Liouville theory. The equality of the gravitational and the Liouville stress tensor provides a further check of this correspondence. The Seiberg bound for vertex operators translates on the bulk side into an upper mass bound for classical point particles. Bulk solutions with cosmological event horizons correspond to microscopic Liouville states, whereas those without horizons correspond to macroscopic (normalizable) states. We also comment on recent criticism by Dyson, Lindesay and Susskind, and point out that the contradictions found by these authors may be resolved if the dual CFT is not able to capture the thermal nature of de Sitter space. Indeed we find that on the CFT side, de Sitter entropy is merely Liouville momentum, and thus has no statistical interpretation in this approach.

The asymptotic dynamics of de Sitter gravity in three dimensions

We show that the asymptotic dynamics of three-dimensional gravity with a positive cosmological constant is described by Euclidean Liouville theory. This provides an explicit example of a correspondence between de Sitter (dS) gravity and conformal field theories. In the case at hand, this correspondence is established by formulating Einstein gravity with positive cosmological constant in three dimensions as an SL(2, ℂ) Chern–Simons (CS) theory. The de Sitter boundary conditions on the connection are divided into two parts. The first part reduces the CS action to a nonchiral SL(2, ℂ) WZNW model, whereas the second provides the constraints for a further reduction to Liouville theory, which resides on the past boundary of dS3.

Conservative Currents of Boundary Charges in AdS2+1 Gravity**The project supported by National Natural Science Foundation of China under Grant No. 19805004

The boundary charge which constitutes the Virasoro algebra in (2+1)-dimensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.

2D anti–de Sitter gravity as a conformally invariant mechanical system

We show that two-dimensional (2D) AdS gravity induces on the spacetime boundary a conformally invariant dynamics that can be described in terms of a de Alfaro--Fubini--Furlan model coupled to an external source with conformal dimension 2. The external source encodes information about the gauge symmetries of the 2D gravity system. Alternatively, there exists a description in terms of a mechanical system with anholonomic constraints. The considered systems are invariant under the action of the conformal group generated by a Virasoro algebra, which occurs also as an asymptotic symmetry algebra of two-dimensional anti--de Sitter space. We calculate the central charge of the algebra and find perfect agreement between the statistical and thermodynamical entropies of ${\mathrm{AdS}}_{2}$ black holes.

A Stress Tensor for Anti-de Sitter Gravity

We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central charge. We also find a nonzero ground state energy for global AdS_5, and show that it exactly matches the Casimir energy of the dual N=4 super Yang-Mills theory on S^3 x R.

New gauge supergravity in seven and eleven dimensions

Locally supersymmetric systems in odd dimensions whose Lagrangians are Chern-Simons forms for supersymmetric extensions of anti--de Sitter gravity are discussed. The construction is illustrated for $D=7$ and 11. In seven dimensions the theory is an $N=2$ supergravity whose fields are the vielbein ${(e}_{\ensuremath{\mu}}^{a}),$ the spin connection $({\ensuremath{\omega}}_{\ensuremath{\mu}}^{\mathrm{ab}}),$ two gravitini $({\ensuremath{\psi}}_{\ensuremath{\mu}}^{i})$ and an sp(2) gauge connection ${(a}_{\ensuremath{\mu}j}^{i}).$ These fields form a connection for $o\mathrm{sp}(2|8).$ In eleven dimensions the theory is an $N=1$ supergravity containing, apart from ${e}_{\ensuremath{\mu}}^{a}$ and ${\ensuremath{\omega}}_{\ensuremath{\mu}}^{\mathrm{ab}},$ one gravitino ${\ensuremath{\psi}}_{\ensuremath{\mu}}$ and a totally antisymmetric fifth rank Lorentz tensor one-form, ${b}_{\ensuremath{\mu}}^{\mathrm{abcde}}.$ These fields form a connection for $o\mathrm{sp}(32|1).$ The actions are by construction invariant under local supersymmetry and the algebra closes off shell without requiring auxiliary fields. The ${N=2}^{[D/2]}$ theory can be shown to have non-negative energy around an AdS background, which is a classical solution that saturates the Bogomol'nyi bound obtained from the superalgebra.

Gravitatingσmodel solitons

We study the axially symmetric static solitons of the O(3) nonlinear $\ensuremath{\sigma}$ model coupled to (2+1)-dimensional anti--de Sitter gravity. The obtained solutions are not self-dual under a static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged $\mathrm{Ba}\mathrm{n}\ifmmode \tilde{}\else \~{}\fi{}\mathrm{ados}$-Teitelboim-Zanelli black holes without non-Abelian scalar hair.

Topological black holes in Weyl conformal gravity

We present a class of exact solutions of Weyl conformal gravity, which have an interpretation as topological black holes. Solutions with negative, zero or positive scalar curvature at infinity are found, the former generalizing the well known topological black holes in anti-de Sitter gravity. The rather delicate question of thermodynamic properties of such objects in Weyl conformal gravity is discussed; suggesting that the thermodynamics of the solutions found should be treated within the framework of gravity as an induced phenomenon, in the spirit of Sakharov's work.

Edge states and entropy of two-dimensional black holes

In several recent publications Carlip, as well as Balachandran, Chandar, and Momen, has proposed a statistical-mechanical interpretation for black hole entropy in terms of ``would-be gauge'' degrees of freedom that become dynamical on the boundary to spacetime. After critically discussing several routes for deriving a boundary action, we examine their hypothesis in the context of generic 2D dilaton gravity. We first calculate the corresponding statistical-mechanical entropy of black holes in $1+1$ de Sitter gravity, which has a gauge theory formulation as a BF theory. Then we generalize the method to dilaton gravity theories that do not have a (standard) gauge theory formulation. This is facilitated greatly by the Poisson \ensuremath{\sigma}-model formulation of these theories. It turns out that the phase space of the boundary particles coincides precisely with a symplectic leaf of the Poisson manifold that enters as target space of the \ensuremath{\sigma} model. Despite this qualitatively appealing picture, the quantitative results are discouraging: In most of the cases, the symplectic leaves are noncompact and the number of microstates yields a meaningless infinity. In those cases where the particle phase space is compact---such as, e.g., in the Euclidean de Sitter theory---the edge state degeneracy is finite, but generically it is far too small to account for the semiclassical Bekenstein-Hawking entropy.

Thermodynamics and evaporation of the (2+1)-dimensional black hole.

The properties of canonical and microcanonical ensembles of a black hole with thermal radiation and the problem of black hole evaporation in 3-D are studied. In 3-D Einstein-anti-de Sitter gravity we have two relevant mass scales, $m_c=1/G$, and $m_p=(\hbar^2\Lambda/G)^{1/3}$, which are particularly relevant for the evaporation problem. It is argued that in the `weak coupling' regime $\Lambda<(\hbar G)^{-2}$, the end point of an evaporating black hole formed with an initial mass $m_0>m_p$, is likely to be a stable remnant in equilibrium with thermal radiation. The relevance of these results for the information problem and for the issue of back reaction is discussed. In the `strong coupling' regime, $\Lambda>(\hbar G)^{-2}$ a full fledged quantum gravity treatment is required. Since the total energy of thermal states in anti-de Sitter space with reflective boundary conditions at spatial infinity is bounded and conserved, the canonical and microcanonical ensembles are well defined. For a given temperature or energy black hole states are locally stable. In the weak coupling regime black hole states are more probable then pure radiation states.

Chern-Simons quantization of (2+1)-anti-de Sitter gravity on a torus

The Chern-Simons formulation of (2+1)-dimensional Einstein gravity with a negative cosmological constant is investigated when the spacetime has the topology . The physical phase space is shown to be a direct product of two sub-phase spaces each of which is a non-Hausdorff manifold plus a set with non-zero co-dimensions. The spacetime geometrical interpretation of each point in the phase space is also given and we explain the 1 to 2 correspondence with the ADM formalism from the geometrical viewpoint. In quantizing this theory, we construct a `modified phase space' which is a cotangent bundle on a torus. We also provide a modular invariant inner product and investigate the relation to the quantum theory which is directly related to the spinor representation of the ADM formalism.