5,139 research outputs found
Moving Observers in an Isotropic Universe
We show how the anisotropy resulting from the motion of an observer in an
isotropic universe may be determined by measurements. This provides a means to
identify inertial frames, yielding a simple resolution to the twins paradox of
relativity theory. We propose that isotropy is a requirement for a frame to be
inertial; this makes it possible to relate motion to the large scale structure
of the universe.Comment: 8 pages, 1 figure, with minor typographical correctio
The Maxwell Lagrangian in purely affine gravity
The purely affine Lagrangian for linear electrodynamics, that has the form of
the Maxwell Lagrangian in which the metric tensor is replaced by the
symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of
homothetic curvature, is dynamically equivalent to the Einstein-Maxwell
equations in the metric-affine and metric formulation. We show that this
equivalence is related to the invariance of the Maxwell Lagrangian under
conformal transformations of the metric tensor. We also apply to a purely
affine Lagrangian the Legendre transformation with respect to the tensor of
homothetic curvature to show that the corresponding Legendre term and the new
Hamiltonian density are related to the Maxwell-Palatini Lagrangian for the
electromagnetic field. Therefore the purely affine picture, in addition to
generating the gravitational Lagrangian that is linear in the curvature,
justifies why the electromagnetic Lagrangian is quadratic in the
electromagnetic field.Comment: 9 pages; published versio
Two-dimensional gravity with a dynamical aether
We investigate the two-dimensional behavior of gravity coupled to a dynamical
unit timelike vector field, i.e. "Einstein-aether theory". The classical
solutions of this theory in two dimensions depend on one coupling constant.
When this coupling is positive the only solutions are (i) flat spacetime with
constant aether, (ii) de Sitter or anti-de Sitter spacetimes with a uniformly
accelerated unit vector invariant under a two-dimensional subgroup of SO(2,1)
generated by a boost and a null rotation, and (iii) a non-constant curvature
spacetime that has no Killing symmetries and contains singularities. In this
case the sign of the curvature is determined by whether the coupling is less or
greater than one. When instead the coupling is negative only solutions (i) and
(iii) are present. This classical study of the behavior of Einstein-aether
theory in 1+1 dimensions may provide a starting point for further
investigations into semiclassical and fully quantum toy models of quantum
gravity with a dynamical preferred frame.Comment: 11 pages, 4 figure
On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity
The quantum field theoretic prediction for the vacuum energy density leads to
a value for the effective cosmological constant that is incorrect by between 60
to 120 orders of magnitude. We review an old proposal of replacing Einstein's
Field Equations by their trace-free part (the Trace-Free Einstein Equations),
together with an independent assumption of energy--momentum conservation by
matter fields. While this does not solve the fundamental issue of why the
cosmological constant has the value that is observed cosmologically, it is
indeed a viable theory that resolves the problem of the discrepancy between the
vacuum energy density and the observed value of the cosmological constant.
However, one has to check that, as well as preserving the standard cosmological
equations, this does not destroy other predictions, such as the junction
conditions that underlie the use of standard stellar models. We confirm that no
problems arise here: hence, the Trace-Free Einstein Equations are indeed viable
for cosmological and astrophysical applications.Comment: Substantial changes from v1 including added author, change of title
and emphasis of the paper although all original results of v1. remai
Vortices in fermion droplets with repulsive dipole-dipole interactions
Vortices are found in a fermion system with repulsive dipole-dipole
interactions, trapped by a rotating quasi-two-dimensional harmonic oscillator
potential. Such systems have much in common with electrons in quantum dots,
where rotation is induced via an external magnetic field. In contrast to the
Coulomb interactions between electrons, the (externally tunable) anisotropy of
the dipole-dipole interaction breaks the rotational symmetry of the
Hamiltonian. This may cause the otherwise rotationally symmetric exact
wavefunction to reveal its internal structure more directly.Comment: 5 pages, 5 figure
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
Thermodynamical Properties and Quasi-localized Energy of the Stringy Dyonic Black Hole Solution
In this article, we calculate the heat flux passing through the horizon and the difference of energy between the Einstein and
M{\o}ller prescription within the region , in which is the region
between outer horizon and inner horizon , for the
modified GHS solution, KLOPP solution and CLH solution. The formula . E_{\rm
Einstein}|_{\cal M} = . E_{\rm M{\o}ller}|_{\cal M} - \sum_{\partial {\cal M}}
{\bf TS}$ is obeyed for the mGHS solution and the KLOPP solution, but not for
the CLH solution. Also, we suggest a RN-like stringy dyonic black hole
solution, which comes from the KLOPP solution under a dual transformation, and
its thermodynamical properties are the same as the KLOPP solution
Action Principle for the Generalized Harmonic Formulation of General Relativity
An action principle for the generalized harmonic formulation of general
relativity is presented. The action is a functional of the spacetime metric and
the gauge source vector. An action principle for the Z4 formulation of general
relativity has been proposed recently by Bona, Bona--Casas and Palenzuela
(BBP). The relationship between the generalized harmonic action and the BBP
action is discussed in detail.Comment: This version is contains more thorough presentations and discussions
of the key results. To be published in PRD. (8 pages, no figures
Acceleration-Induced Nonlocality: Uniqueness of the Kernel
We consider the problem of uniqueness of the kernel in the nonlocal theory of
accelerated observers. In a recent work, we showed that the convolution kernel
is ruled out as it can lead to divergences for nonuniform accelerated motion.
Here we determine the general form of bounded continuous kernels and use
observational data regarding spin-rotation coupling to argue that the kinetic
kernel given by is the only physically acceptable
solution.Comment: LaTeX file, 2 figures, 14 page
Universality in the Gravitational Stretching of Clocks, Waves and Quantum States
There are discernible and fundamental differences between clocks, waves and
physical states in classical physics. These fundamental concepts find a common
expression in the context of quantum physics in gravitational fields; matter
and light waves, quantum states and oscillator clocks become quantum synonymous
through the Planck-Einstein-de Broglie relations and the equivalence principle.
With this insight, gravitational effects on quantum systems can be simply and
accurately analyzed. Apart from providing a transparent framework for
conceptual and quantitative thinking on matter waves and quantum states in a
gravitational field, we address and resolve with clarity the recent
controversial discussions on the important issue of the relation and the
crucial difference between gravimetery using atom interferometers and the
measurement of gravitational time dilation.Comment: Gravity Research Foundation honorable mention, 201
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