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

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

3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating System

The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of the system and discuss the numerical solution of the resulting equations of motion. This solution is compared to the corresponding non-relativistic and post-Newtonian approximation solutions so that the dynamics of the fully relativistic system can be interpretted as a correction to the one-dimensional Newtonian self-gravitating system. We find that the structure of the phase space of each of these systems yields a large variety of interesting dynamics that can be divided into three distinct regions: annulus, pretzel, and chaotic; the first two being regions of quasi-periodicity while the latter is a region of chaos. By changing the relative masses of the three particles we find that the relative sizes of these three phase space regions changes and that this deformation can be interpreted physically in terms of the gravitational interactions of the particles. Furthermore, we find that many of the interesting characteristics found in the case where all of the particles share the same mass also appears in our more general study. We find that there are additional regions of chaos in the unequal mass system which are not present in the equal mass case. We compare these results to those found in similar systems.Comment: latex, 26 pages, 17 figures, high quality figures available upon request; typos and grammar correcte

Chaos in an Exact Relativistic 3-body Self-Gravitating System

We consider the problem of three body motion for a relativistic one-dimensional self-gravitating system. After describing the canonical decomposition of the action, we find an exact expression for the 3-body Hamiltonian, implicitly determined in terms of the four coordinate and momentum degrees of freedom in the system. Non-relativistically these degrees of freedom can be rewritten in terms of a single particle moving in a two-dimensional hexagonal well. We find the exact relativistic generalization of this potential, along with its post-Newtonian approximation. We then specialize to the equal mass case and numerically solve the equations of motion that follow from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining orbits in both the hexagonal and 3-body representations of the system, and plot the Poincare sections as a function of the relativistic energy parameter $\eta$. We find two broad categories of periodic and quasi-periodic motions that we refer to as the annulus and pretzel patterns, as well as a set of chaotic motions that appear in the region of phase-space between these two types. Despite the high degree of non-linearity in the relativistic system, we find that the the global structure of its phase space remains qualitatively the same as its non-relativisitic counterpart for all values of $\eta$ that we could study. However the relativistic system has a weaker symmetry and so its Poincare section develops an asymmetric distortion that increases with increasing $\eta$. For the post-Newtonian system we find that it experiences a KAM breakdown for $\eta \simeq 0.26$: above which the near integrable regions degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon reques

Soliton Solutions to the Einstein Equations in Five Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with negative cosmological constant that asymptotically approach AdS$_{5}/\Gamma$, but have less energy than AdS$_{5}/\Gamma$. We present evidence that these solutions are the lowest-energy states within their asymptotic class.Comment: 9 pages, Latex; Final version that appeared in Phys. Rev. Lett; title changed by journal from original title "Eguchi-Hanson Solitons

Possible evidence of extended objects inside the proton

Recent experimental determinations of the Nachtmann moments of the inelastic structure function of the proton F2p(x, Q**2), obtained at Jefferson Lab, are analyzed for values of the squared four-momentum transfer Q**2 ranging from ~ 0.1 to ~ 2 (GeV/c)**2. It is shown that such inelastic proton data exhibit a new type of scaling behavior and that the resulting scaling function can be interpreted as a constituent form factor consistent with the elastic nucleon data. These findings suggest that at low momentum transfer the inclusive proton structure function originates mainly from the elastic coupling with extended objects inside the proton. We obtain a constituent size of ~ 0.2 - 0.3 fm.Comment: 1 reference adde

New Types of Thermodynamics from (1+1)(1+1)-Dimensional Black Holes

For normal thermodynamic systems superadditivity $\S$, homogeneity \H and concavity \C of the entropy hold, whereas for $(3+1)$-dimensional black holes the latter two properties are violated. We show that $(1+1)$-dimensional black holes exhibit qualitatively new types of thermodynamic behaviour, discussed here for the first time, in which \C always holds, \H is always violated and $\S$ may or may not be violated, depending of the magnitude of the black hole mass. Hence it is now seen that neither superadditivity nor concavity encapsulate the meaning of the second law in all situations.Comment: WATPHYS-TH93/05, Latex, 10 pgs. 1 figure (available on request), to appear in Class. Quant. Gra