Thermodynamics of the two-dimensional black hole in the Teitelboim-Jackiw theory

The two-dimensional theory of Teitelboim and Jackiw has constant and negative curvature. In spite of this, the theory admits a black hole solution with no singularities. In this work we study the thermodynamics of this black hole using York's formalism.Comment: 16 pages, Late

Hawking Radiation and Unitary evolution

We find a family of exact solutions to the semi-classical equations (including back-reaction) of two-dimensional dilaton gravity, describing infalling null matter that becomes outgoing and returns to infinity without forming a black hole. When a black hole almost forms, the radiation reaching infinity in advance of the original outgoing null matter has the properties of Hawking radiation. The radiation reaching infinity after the null matter consists of a brief burst of negative energy that preserves unitarity and transfers information faster than the theoretical bound for positive energy.Comment: LaTex file + uuencoded ps version including 4 figure

Entropy in the RST Model

The RST Model is given boundary term and Z-field so that it is well-posed and local. The Euclidean method is described for general theory and used to calculate the RST intrinsic entropy. The evolution of this entropy for the shockwave solutions is found and obeys a second law.Comment: 10 pages, minor revisions, published version in Late

Soliton Induced Singularities in 2 d Gravity and their Evaporation

Positive energy singularities induced by Sine-Gordon solitons in 1+1 dimensional dilaton gravity with positive and negative cosmological constant are considered. When the cosmological constant is positive, the singularities combine a white hole, a timelike singularity and a black hole joined smoothly near the soliton center. When the cosmological constant is negative, the solutions describe two timelike singularities joined smoothly near the soliton center. We describe these spacetimes and examine their evaporation in the one loop approximation.Comment: 15 pages (37.7 kb), PHYZZX. Figures available from authors

Geometric Entropy of Nonrelativistic Fermions and Two Dimensional Strings

We consider the geometric entropy of free nonrelativistic fermions in two dimensions and show that it is ultraviolet finite for finite fermi energies, but divergent in the infrared. In terms of the corresponding collective field theory this is a {\em nonperturbative} effect and is related to the soft behaviour of the usual thermodynamic entropy at high temperatures. We then show that thermodynamic entropy of the singlet sector of the one dimensional matrix model at high temperatures is governed by nonperturbative effects of the underlying string theory. In the high temperature limit the ``exact'' expression for the entropy is regular but leads to a negative specific heat, thus implying an instability. We speculate that in a properly defined two dimensional string theory, the thermodynamic entropy could approach a constant at high temperatures and lead to a geometric entropy which is finite in the ultraviolet.Comment: LaTex, 19 pages, no figures. Some references adde

Unruh Radiation, Holography and Boundary Cosmology

A uniformly acclerated observer in anti-deSitter space-time is known to detect thermal radiation when the acceleration exceeds a critical value. We investigate the holographic interpretation of this phenomenon. For uniformly accelerated trajectories transverse to the boundary of the AdS space, the hologram is a blob which expands along the boundary. Observers on the boundary co-moving with the hologram become observers in cosmological space-times. For supercritical accelerations one gets a Milne universe when the holographic screen is the boundary in Poincare coordinates, while for the boundary in hyperspherical coordinates one gets deSitter spacetimes. The presence or absence of thermality is then interpreted in terms of specific classes of observers in these cosmologies.Comment: LaTeX, 35 pages, 3 figures. A reference is added and typos are correcte

Does the generalized second law hold in the form of time derivative expression?

We investigate whether the generalized second law is valid, using two dimensional black hole spacetime, irrespective of models. A time derivative form of the generalized second law is formulated and it is shown that the law might become invalid. The way to resolve this difficulty is also presented and discussed.Comment: 12 pages, 3 figures, revte

Solving the Simplest Theory of Quantum Gravity

We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. We illustrate this by constructing its exact factorizable S-matrix. Despite its simplicity, the theory exhibits many of the salient features expected from more mature quantum gravity models, including the absence of local off-shell observables, a minimal length, a maximum achievable (Hagedorn) temperature, as well as (integrable relatives of) black holes. All these properties follow from the exact S-matrix. We show that the complete finite volume spectrum can be reconstructed analytically from this S-matrix with the help of the thermodynamic Bethe Ansatz. We argue that considered as a UV complete relativistic two-dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, "asymptotic fragility". Asymptotically fragile flows do not originate from a UV fixed point.Comment: 32+4 pages, 1 figure, v2: typos fixed, published versio

Predictability and Semiclassical Approximation at the onset of Black Hole formation

We combine analytical and numerical techniques to study the collapse of conformally coupled massless scalar fields in semiclassical 2D dilaton gravity, with emphasis on solutions just below criticality when a black hole almost forms. We study classical information and quantum correlations. We show explicitly how recovery of information encoded in the classical initial data from the outgoing classical radiation becomes more difficult as criticality is approached. The outgoing quantum radiation consists of a positive-energy flux, which is essentially the standard Hawking radiation, followed by a negative-energy flux which ensures energy conservation and guarantees unitary evolution through strong correlations with the positive-energy Hawking radiation. As one reaches the critical solution there is a breakdown of unitarity. We show that this breakdown of predictability is intimately related to a breakdown of the semiclassical approximation.Comment: 26 pages RevTex + 8 figures in a separate postscript fil

Hamiltonian thermodynamics of two-dimensional vacuum dilatonic black holes

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 of the dilaton field and the temperature at the boundary, and the heat capacity is always positive. For temperatures higher than $\beta_c^{-1} = \hbar\lambda/(2\pi)$, the partition function is dominated by a classical black hole solution, and the dominant contribution to the entropy is the two-dimensional Bekenstein-Hawking entropy. For temperatures lower than~$\beta_c^{-1}$, the partition function remains well-behaved and the heat capacity is positive in the asymptotically flat space limit, in contrast to the corresponding limit in four-dimensional spherically symmetric Einstein gravity; however, in this limit, the partition function is not dominated by a classical black hole solution.Comment: 20 pages, REVTEX. Added a discussion on the boundary action and boundary terms in Sec. IIIA. Minor changes in Acknowledgements and Reference