333 research outputs found
The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited
We study the effect of the cosmological constant on the bending of
light by a concentrated spherically symmetric mass. Contrarily to previous
claims, we show that when the Schwarzschild-de Sitter geometry is taken into
account, does indeed contribute to the bending.Comment: 5 pages, 2 figure
Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes
We study the absorption and scattering of massless scalar waves propagating
in spherically symmetric spacetimes with dynamical cosmological constant both
in low-energy and high-energy zones. In the former low-energy regime, we solve
analytically the Regge-Wheeler wave equation and obtain an analytic absorption
probability expression which varies with , where is the
central mass and is cosmological constant. The low-energy absorption
probability, which is in the range of , increases monotonically
with increase in . In the latter high-energy regime, the scalar
particles adopt their geometric optics limit value. The trajectory equation
with effective potential emerges and the analytic high-energy greybody factor,
which is relevant with the area of classically accessible regime, also
increases monotonically with increase in , as long is less
than or of the order of . In this high-energy case, the null cosmological
constant result reduces to the Schwarzschild value .Comment: 12 pages, 6 figure
Light Deflection, Lensing, and Time Delays from Gravitational Potentials and Fermat's Principle in the Presence of a Cosmological Constant
The contribution of the cosmological constant to the deflection angle and the
time delays are derived from the integration of the gravitational potential as
well as from Fermat's Principle. The findings are in agreement with recent
results using exact solutions to Einstein's equations and reproduce precisely
the new -term in the bending angle and the lens equation. The
consequences on time delay expressions are explored. While it is known that
contributes to the gravitational time delay, it is shown here that a
new -term appears in the geometrical time delay as well. Although
these newly derived terms are perhaps small for current observations, they do
not cancel out as previously claimed. Moreover, as shown before, at galaxy
cluster scale, the contribution can be larger than the second-order
term in the Einstein deflection angle for several cluster lens systems.Comment: 6 pages, 1 figure, matches version published in PR
The Schwarzschild-de Sitter solution in five-dimensional general relativity briefly revisited
We briefly revisit the Schwarzschild-de Sitter solution in the context of
five-dimensional general relativity. We obtain a class of five-dimensional
solutions of Einstein vacuum field equations into which the four-dimensional
Schwarzschild-de Sitter space can be locally and isometrically embedded. We
show that this class of solutions is well-behaved in the limit of lambda
approaching zero. Applying the same procedure to the de Sitter cosmological
model in five dimensions we obtain a class of embedding spaces which are
similarly well-behaved in this limit. These examples demonstrate that the
presence of a non-zero cosmological constant does not in general impose a rigid
relation between the (3+1) and (4+1)-dimensional spacetimes, with degenerate
limiting behaviour.Comment: 7 page
Multi-Black-Holes in Three Dimensions
We construct time-dependent multi-centre solutions to three-dimensional
general relativity with zero or negative cosmological constant. These solutions
correspond to dynamical systems of freely falling black holes and conical
singularities, with a multiply connected spacetime topology. Stationary
multi-black-hole solutions are possible only in the extreme black hole case.Comment: 8 pages, \LaTex, 4 figures (available on request), GCR 94/02/0
Classical 5D fields generated by a uniformly accelerated point source
Gauge fields associated with the manifestly covariant dynamics of particles
in spacetime are five-dimensional. In this paper we explore the old
problem of fields generated by a source undergoing hyperbolic motion in this
framework. The 5D fields are computed numerically using absolute time
-retarded Green-functions, and qualitatively compared with Maxwell fields
generated by the same motion. We find that although the zero mode of all fields
coincides with the corresponding Maxwell problem, the non-zero mode should
affect, through the Lorentz force, the observed motion of test particles.Comment: 36 pages, 8 figure
Submanifolds in five-dimensional pseudo-Euclidean spaces and four-dimensional FRW universes
Equations for submanifolds, which correspond to embeddings of the
four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are
presented in convenient form in general case. Several specific examples are
considered.Comment: 7 pages, LaTeX, the mathematical part of this paper is based on the
withdrawn preprint arXiv:1012.0320 [gr-qc
Covariant Calculation of General Relativistic Effects in an Orbiting Gyroscope Experiment
We carry out a covariant calculation of the measurable relativistic effects
in an orbiting gyroscope experiment. The experiment, currently known as Gravity
Probe B, compares the spin directions of an array of spinning gyroscopes with
the optical axis of a telescope, all housed in a spacecraft that rolls about
the optical axis. The spacecraft is steered so that the telescope always points
toward a known guide star. We calculate the variation in the spin directions
relative to readout loops rigidly fixed in the spacecraft, and express the
variations in terms of quantities that can be measured, to sufficient accuracy,
using an Earth-centered coordinate system. The measurable effects include the
aberration of starlight, the geodetic precession caused by space curvature, the
frame-dragging effect caused by the rotation of the Earth and the deflection of
light by the Sun.Comment: 7 pages, 1 figure, to be submitted to Phys. Rev.
Gravitational waves in the presence of a cosmological constant
We derive the effects of a non-zero cosmological constant on
gravitational wave propagation in the linearized approximation of general
relativity. In this approximation we consider the situation where the metric
can be written as , , where is
the background perturbation and is a modification
interpretable as a gravitational wave. For this linearization
of Einstein equations is self-consistent only in certain coordinate systems.
The cosmological Friedmann-Robertson-Walker coordinates do not belong to this
class and the derived linearized solutions have to be reinterpreted in a
coordinate system that is homogeneous and isotropic to make contact with
observations. Plane waves in the linear theory acquire modifications of order
, both in the amplitude and the phase, when considered in FRW
coordinates. In the linearization process for , we have also
included terms of order . For the background
perturbation the difference is very small but when the
term is retained the equations of motion can be
interpreted as describing massive spin-2 particles. However, the extra degrees
of freedom can be approximately gauged away, coupling to matter sources with a
strength proportional to the cosmological constant itself. Finally we discuss
the viability of detecting the modifications caused by the cosmological
constant on the amplitude and phase of gravitational waves. In some cases the
distortion with respect to gravitational waves propagating in Minkowski
space-time is considerable. The effect of could have a detectable
impact on pulsar timing arrays.Comment: 20 pages, 1 figur
Deriving relativistic momentum and energy
We present a new derivation of the expressions for momentum and energy of a
relativistic particle. In contrast to the procedures commonly adopted in
textbooks, the one suggested here requires only the knowledge of the
composition law for velocities along one spatial dimension, and does not make
use of the concept of relativistic mass, or of the formalism of four-vectors.
The basic ideas are very general and can be applied also to kinematics
different from the Newtonian and Einstein ones, in order to construct the
corresponding dynamics.Comment: 15 pages, 2 figure
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