2+1 Gravity and Closed Time-Like Curves

In this paper we report some results obtained by applying the radial gauge to 2+1 dimensional gravity. The general features of this gauge are reviewed and it is shown how they allow the general solution of the problem in terms of simple quadratures. Then we concentrate on the general stationary problem providing the explicit solving formulas for the metric and the explicit support conditions for the energy momentum tensor. The chosen gauge allows, due to its physical nature, to exploit the weak energy condition and in this connection it is proved that for an open universe conical at space infinity the weak energy condition and the absence of closed time like curves (CTC) at space infinity imply the total absence of CTC. It is pointed out how the approach can be used to examine cosmological solution in 2+1 dimensions.Comment: Talk given at the Workshop on ``Constraint Theory and Quantization Methods'',10 pages, Latex, IFUP-TH-43/9

The radial gauge propagators in quantum gravity

We give a general procedure for extracting the propagators in gauge theories in presence of a sharp gauge fixing and we apply it to derive the propagators in quantum gravity in the radial gauge, both in the first and in the second order formalism in any space-time dimension. In the three dimensional case such propagators vanish except for singular collinear contributions, in agreement with the absence of propagating gravitons.Comment: 38 pages, 1 fig. not available, LATEX, IFUP-TH-30/9

Stationary Solutions in 2+1 Dimensional Gravity and Closed Time-Like Curves

We apply the reduced radial gauge to give the general solution of the metric in 2+1 dimensions in term of quadratures. It allows a complete controll on the support of the source. We use the result to prove that for a general stationary universe, conical at infinity, the weak energy condition and the absence of CTC at space infinity prevent the occurrrence of any CTC.Comment: Talk presented at Europhysics Conference on High Energy Physics, Marseille, France, July 22-28 1993, 5 pages, Latex, IFUP-49/9

Closed time like curve and the energy condition in 2+1 dimensional gravity

We consider gravity in 2+1 dimensions in presence of extended stationary sources with rotational symmetry. We prove by direct use of Einstein's equations that if i) the energy momentum tensor satisfies the weak energy condition, ii) the universe is open (conical at space infinity), iii) there are no CTC at space infinity, then there are no CTC at all.Comment: 10 pages (REVTEX 3.0), IFUP-60/9

Polyakov conjecture and 2+1 dimensional gravity coupled to particles

A proof is given of Polyakov conjecture about the auxiliary parameters of the SU(1,1) Riemann-Hilbert problem for general elliptic singularities. Such a result is related to the uniformization of the the sphere punctured by n conical defects. Its relevance to the hamiltonian structure of 2+1 dimensional gravity in the maximally slicing gauge is stressed.Comment: Talk by P. Menotti at Int. Europhysics Conference on High Energy Physics, Budapest 12-18 July 2001, 5 pages late

Beyond the Landau Criterion for Superfluidity

According to the Landau criterion for superfluidity, a Bose-Einstein condensate flowing with a group velocity smaller than the sound velocity is energetically stable to the presence of perturbing potentials. We found that this is strictly correct only for vanishingly small perturbations. The superfluid critical velocity strongly depends on the strength and shape of the defect. We quantitatively study, both numerically and with an approximate analytical model, the dynamical response of a one-dimensional condensate flowing against an istantaneously raised spatially periodic defect. We found that the critical velocity $v_c$ decreases by incresing the strength of the defect $V_0$, up to to a critical value of the defect intensity where the critical velocity vanishes

Supersolid phase with cold polar molecules on a triangular lattice

We study a system of heteronuclear molecules on a triangular lattice and analyze the potential of this system for the experimental realization of a supersolid phase. The ground state phase diagram contains superfluid, solid and supersolid phases. At finite temperatures and strong interactions there is an additional emulsion region, in contrast to similar models with short-range interactions. We derive the maximal critical temperature $T_c$ and the corresponding entropy $S/N = 0.04(1)$ for supersolidity and find feasible experimental conditions for its realization.Comment: 4 pages, 4 figure