Static spherically symmetric perfect fluid solutions in f(R)f(R) theories of gravity

Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ ie. given a matter distribution and an equation state, one cannot determine the functional form of $f(R)$. However, we also show that matching the outside Schwarzschild-de Sitter-metric to the metric inside the mass distribution leads to additional constraints that severely limit the allowed fluid configurations.Comment: 5 page

Extraordinary vacuum black string solutions

In addition to the boosted static solution there are two other classes of stationary string-like solutions of the vacuum Einstein equation in (4+1)-dimensions. Each class is characterized by three parameters of mass, tension, and momentum flow along the fifth coordinate. We analyze the metric properties of one of the two classes, which was previously assumed to be naked singular, and show that the solution spectrum contains black string and wormhole in addition to the known naked singularity as the momentum flow to mass ratio increases. Interestingly, there does not exist new zero momentum solution in these cases.Comment: 20 pages, 4 figures, add 2 reference

Variational principle for the Wheeler-Feynman electrodynamics

We adapt the formally-defined Fokker action into a variational principle for the electromagnetic two-body problem. We introduce properly defined boundary conditions to construct a Poincare-invariant-action-functional of a finite orbital segment into the reals. The boundary conditions for the variational principle are an endpoint along each trajectory plus the respective segment of trajectory for the other particle inside the lightcone of each endpoint. We show that the conditions for an extremum of our functional are the mixed-type-neutral-equations with implicit state-dependent-delay of the electromagnetic-two-body problem. We put the functional on a natural Banach space and show that the functional is Frechet-differentiable. We develop a method to calculate the second variation for C2 orbital perturbations in general and in particular about circular orbits of large enough radii. We prove that our functional has a local minimum at circular orbits of large enough radii, at variance with the limiting Kepler action that has a minimum at circular orbits of arbitrary radii. Our results suggest a bifurcation at some radius below which the circular orbits become saddle-point extrema. We give a precise definition for the distributional-like integrals of the Fokker action and discuss a generalization to a Sobolev space of trajectories where the equations of motion are satisfied almost everywhere. Last, we discuss the existence of solutions for the state-dependent delay equations with slightly perturbated arcs of circle as the boundary conditions and the possibility of nontrivial solenoidal orbits

Covariant EBK quantization of the electromagnetic two-body problem

We discuss a method to transform the covariant Fokker action into an implicit two-degree-of-freedom Hamiltonian for the electromagnetic two-body problem with arbitrary masses. This dynamical system appeared 100 years ago and it was popularized in the 1940's by the still incomplete Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. The Hamiltonian formalism is then used to motivate an EBK quantization based on the classical trajectories with a non-perturbative formula that predicts energies free of infinities.Comment: 21 page

Comment on "Correlation between Compact Radio Lout Quasars and Ultrahigh Energy Cosmic Rays"

In a recent paper, Farrar and Biermann argue that there is a strong correlation between the direction of the five highest-energy cosmic-ray events and compact, radio-loud quasars. This Comment shows that this analysis contains several inconsistencies and errors so that the significance of any such correlation is certainly greatly overestimated and perhaps nonexistent.Comment: 2 pages, REVTE

Dynamics of the Fisher Information Metric

We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional $J[g^{\mu\nu}(\theta^i)]$, where $g^{\mu\nu}(\theta^i)$ is the Fisher metric. We postulate that this functional of the dynamical variable $g^{\mu\nu}(\theta^i)$ is stationary with respect to small variations of these variables. Our approach enables a dynamical approach to Fisher information metric. It allows to impose symmetries on a statistical system in a systematic way. This work is mainly motivated by the entropy approach to nonmonotonic reasoning.Comment: 11 page

Empirical constraints on vacuum decay in the stringy landscape

It is generally considered as self evident that the lifetime of our vacuum in the landscape of string theory cannot be much shorter than the current age of the universe. Here I show why this lower limit is invalid. A certain type of ``parallel universes'' is a necessary consequence of the string-landscape dynamics and might well allow us to ``survive'' vacuum decay. As a consequence our stringy vacuum's lifetime is empirically unconstrained and could be very short. Based on this counter-intuitive insight I propose a novel type of laboratory experiment that searches for an apparent violation of the quantum-mechanical Born rule by gravitational effects on vacuum decay. If the lifetime of our vacuum should turn out to be shorter than 6 x 10^{-13} seconds such an experiment is sufficiently sensitive to determine its value with state-of-the-art equipment.Comment: 13 pages, 2 figures, proposes a laboratory experimen

Alternative derivation of the relativistic contribution to perihelic precession

An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for approximately elliptical motion. The method of solution makes use of coordinate transformations and the correspondence principle, rather than the standard perturbative approach. The form of the resulting orbit equation is similar to that derived from Newtonian mechanics and includes first-order corrections to Kepler's orbits due to general relativity. The associated relativistic contribution to perihelic precession agrees with established first-order results. The reduced radius for the circular orbit is in agreement to first-order with that calculated from the Schwarzschild effective potential. The method of solution is understandable by undergraduate students.Comment: 12 pages, 2 figures. Accepted for publication in the American Journal of Physic