725 research outputs found

### Static spherically symmetric perfect fluid solutions in $f(R)$ 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

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