Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems

We consider the statistical mechanics of a general relativistic one-dimensional self-gravitating system. The system consists of $N$-particles coupled to lineal gravity and can be considered as a model of $N$ relativistically interacting sheets of uniform mass. The partition function and one-particle distitrubion functions are computed to leading order in $1/c$ where $c$ is the speed of light; as $c\to\infty$ results for the non-relativistic one-dimensional self-gravitating system are recovered. We find that relativistic effects generally cause both position and momentum distribution functions to become more sharply peaked, and that the temperature of a relativistic gas is smaller than its non-relativistic counterpart at the same fixed energy. We consider the large-N limit of our results and compare this to the non-relativistic case.Comment: latex, 60 pages, 22 figure

Expanding the Area of Gravitational Entropy

I describe how gravitational entropy is intimately connected with the concept of gravitational heat, expressed as the difference between the total and free energies of a given gravitational system. From this perspective one can compute these thermodyanmic quantities in settings that go considerably beyond Bekenstein's original insight that the area of a black hole event horizon can be identified with thermodynamic entropy. The settings include the outsides of cosmological horizons and spacetimes with NUT charge. However the interpretation of gravitational entropy in these broader contexts remains to be understood.Comment: Latex, 19 pgs., To appear in "Bekenstein Issues" of Foundations of Physic

Dynamical N-body Equlibrium in Circular Dilaton Gravity

We obtain a new exact equilibrium solution to the N-body problem in a one-dimensional relativistic self-gravitating system. It corresponds to an expanding/contracting spacetime of a circle with N bodies at equal proper separations from one another around the circle. Our methods are straightforwardly generalizable to other dilatonic theories of gravity, and provide a new class of solutions to further the study of (relativistic) one-dimensional self-gravitating systems.Comment: 4 pages, latex, reference added, minor changes in wordin

Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity

We present the exact solution of two-body motion in (1+1) dimensional dilaton gravity by solving the constraint equations in the canonical formalism. The determining equation of the Hamiltonian is derived in a transcendental form and the Hamiltonian is expressed for the system of two identical particles in terms of the Lambert $W$ function. The $W$ function has two real branches which join smoothly onto each other and the Hamiltonian on the principal branch reduces to the Newtonian limit for small coupling constant. On the other branch the Hamiltonian yields a new set of motions which can not be understood as relativistically correcting the Newtonian motion. The explicit trajectory in the phase space $(r, p)$ is illustrated for various values of the energy. The analysis is extended to the case of unequal masses. The full expression of metric tensor is given and the consistency between the solution of the metric and the equations of motion is rigorously proved.Comment: 34 pages, LaTeX, 16 figure

The Equivalence Principle and Anomalous Magnetic Moment Experiments

We investigate the possibility of testing of the Einstein Equivalence Principle (EEP) using measurements of anomalous magnetic moments of elementary particles. We compute the one loop correction for the $g-2$ anomaly within the class of non metric theories of gravity described by the \tmu formalism. We find several novel mechanisms for breaking the EEP whose origin is due purely to radiative corrections. We discuss the possibilities of setting new empirical constraints on these effects.Comment: 26 pages, latex, epsf, 1 figure, final version which appears in Physical Review