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

Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity

We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation, which leads to the exact Hamiltonian to infinite order of the gravitational coupling constant. In the equal mass case explicit expressions of the trajectories of the particles are given as the functions of the proper time, which show characteristic features of the motion depending on the strength of gravity (mass) and the magnitude and sign of the cosmological constant. As expected, we find that a positive cosmological constant has a repulsive effect on the motion, while a negative one has an attractive effect. However, some surprising features emerge that are absent for vanishing cosmological constant. For a certain range of the negative cosmological constant the motion shows a double maximum behavior as a combined result of an induced momentum-dependent cosmological potential and the gravitational attraction between the particles. For a positive cosmological constant, not only bounded motions but also unbounded ones are realized. The change of the metric along the movement of the particles is also exactly derived.Comment: 37 pages, Latex, 24 figure

Promoting Public Health In The Context Of The “Obesity Epidemic”: False Starts And Promising New Directions

In the battle to combat obesity rates in the United States, several misconceptions have dominated policy initiatives. We address those misconceptions, including the notion that restrictive diets lead to long-term weight loss, that stigmatizing obesity is an effective strategy for promoting weight reduction, and that weight and physical health should be considered synonymous with one another. In offering correctives to each of these points, we draw on psychological science to suggest new policies that could be enacted at both the local and national levels. Instead of policies that rely solely on individual willpower, which is susceptible to failure, we recommend those that make use of environmental changes to reduce the amount of willpower necessary to achieve healthy behavior. Ultimately, the most effective policies will promote health rather than any arbitrary level of weight

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

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

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

Symmetry Breaking Using Value Precedence

We present a comprehensive study of the use of value precedence constraints to break value symmetry. We first give a simple encoding of value precedence into ternary constraints that is both efficient and effective at breaking symmetry. We then extend value precedence to deal with a number of generalizations like wreath value and partial interchangeability. We also show that value precedence is closely related to lexicographical ordering. Finally, we consider the interaction between value precedence and symmetry breaking constraints for variable symmetries.Comment: 17th European Conference on Artificial Intelligenc

Sterile neutrinos, dark matter, and the pulsar velocities in models with a Higgs singlet

We identify the range of parameters for which the sterile neutrinos can simultaneously explain the cosmological dark matter and the observed velocities of pulsars. To satisfy all cosmological bounds, the relic sterile neutrinos must be produced sufficiently cold. This is possible in a class of models with a gauge-singlet Higgs boson coupled to the neutrinos. Sterile dark matter can be detected by the x-ray telescopes. The presence of the singlet in the Higgs sector can be tested at the Large Hadron Collider.Comment: 4 pages, one figur

The 1953 Cosmic Ray Conference at Bagneres de Bigorre

The cosmic ray conference at Bagn`eres de Bigorre in July, 1953 organized by Patrick Blackett and Louis Leprince-Ringuet was a seminal one. It marked the beginning of sub atomic physics and its shift from cosmic ray research to research at the new high energy accelerators. The knowledge of the heavy unstable particles found in the cosmic rays was essentially correct in fact and interpretation and defined the experiments that needed to be carried out with the new accelerators. A large fraction of the physicists who had been using cosmic rays for their research moved to the accelerators. This conference can be placed in importance in the same category as two other famous conferences, the Solvay congress of 1927 and the Shelter Island Conference of 1948

Hearing in the Juvenile Green Sea Turtle (Chelonia mydas): A Comparison of Underwater and Aerial Hearing Using Auditory Evoked Potentials

Sea turtles spend much of their life in aquatic environments, but critical portions of their life cycle, such as nesting and hatching, occur in terrestrial environments, suggesting that it may be important for them to detect sounds in both air and water. In this study we compared underwater and aerial hearing sensitivities in five juvenile green sea turtles (Chelonia mydas) by measuring auditory evoked potential responses to tone pip stimuli. Green sea turtles detected acoustic stimuli in both media, responding to underwater stimuli between 50 and 1600 Hz and aerial stimuli between 50 and 800 Hz, with maximum sensitivity between 200 and 400 Hz underwater and 300 and 400 Hz in air. When underwater and aerial hearing sensitivities were compared in terms of pressure, green sea turtle aerial sound pressure thresholds were lower than underwater thresholds, however they detected a wider range of frequencies underwater. When thresholds were compared in terms of sound intensity, green sea turtle sound intensity level thresholds were 2–39 dB lower underwater particularly at frequencies below 400 Hz. Acoustic stimuli may provide important environmental cues for sea turtles. Further research is needed to determine how sea turtles behaviorally and physiologically respond to sounds in their environment