128 research outputs found
A note on Dolby and Gull on radar time and the twin "paradox"
Recently a suggestion has been made that standard textbook representations of
hypersurfaces of simultaneity for the travelling twin in the twin "paradox" are
incorrect. This suggestion is false: the standard textbooks are in agreement
with a proper understanding of the relativity of simultaneity.Comment: LaTeX, 3 pages, 2 figures. Update: added new section V and updated
reference
Spherically symmetric spacetimes in f(R) gravity theories
We study both analytically and numerically the gravitational fields of stars
in f(R) gravity theories. We derive the generalized Tolman-Oppenheimer-Volkov
equations for these theories and show that in metric f(R) models the
Parameterized Post-Newtonian parameter is a robust
outcome for a large class of boundary conditions set at the center of the star.
This result is also unchanged by introduction of dark matter in the Solar
System. We find also a class of solutions with in
the metric model, but these solutions turn out to be unstable
and decay in time. On the other hand, the Palatini version of the theory is
found to satisfy the Solar System constraints. We also consider compact stars
in the Palatini formalism, and show that these models are not inconsistent with
polytropic equations of state. Finally, we comment on the equivalence between
f(R) gravity and scalar-tensor theories and show that many interesting Palatini
f(R) gravity models can not be understood as a limiting case of a
Jordan-Brans-Dicke theory with .Comment: Published version, 12 pages, 7 figure
Birkhoff Theorem and Matter
Birkhoff's theorem for spherically symmetric vacuum spacetimes is a key
theorem in studying local systems in general relativity theory. However
realistic local systems are only approximately spherically symmetric and only
approximately vacuum. In a previous paper, we showed the theorem remains
approximately true in an approximately spherically symmetric vacuum space time.
In this paper we prove the converse case: the theorem remains approximately
true in a spherically symmetric, approximately vacuum space time.Comment: 7 pages, Revtex
Pound-Rebka experiment and torsion in the Schwarzschild spacetime
We develop some ideas discussed by E. Schucking [arXiv:0803.4128] concerning
the geometry of the gravitational field. First, we address the concept
according to which the gravitational acceleration is a manifestation of the
spacetime torsion, not of the curvature tensor. It is possible to show that
there are situations in which the geodesic acceleration of a particle may
acquire arbitrary values, whereas the curvature tensor approaches zero. We
conclude that the spacetime curvature does not affect the geodesic
acceleration. Then we consider the the Pound-Rebka experiment, which relates
the time interval of two light signals emitted at a position
, to the time interval of the signals received at a
position , in a Schwarzschild type gravitational field. The experiment is
determined by four spacetime events. The infinitesimal vectors formed by these
events do not form a parallelogram in the (t,r) plane. The failure in the
closure of the parallelogram implies that the spacetime has torsion. We find
the explicit form of the torsion tensor that explains the nonclosure of the
parallelogram.Comment: 16 pages, two figures, one typo fixed, one paragraph added in section
Redshifts and Killing Vectors
Courses in introductory special and general relativity have increasingly
become part of the curriculum for upper-level undergraduate physics majors and
master's degree candidates. One of the topics rarely discussed is symmetry,
particularly in the theory of general relativity. The principal tool for its
study is the Killing vector. We provide an elementary introduction to the
concept of a Killing vector field, its properties, and as an example of its
utility apply these ideas to the rigorous determination of gravitational and
cosmological redshifts.Comment: 16 Latex pages, 6 postscript figures, submitted to Am. J. Phy
A Radiation Scalar for Numerical Relativity
This letter describes a scalar curvature invariant for general relativity
with a certain, distinctive feature. While many such invariants exist, this one
vanishes in regions of space-time which can be said unambiguously to contain no
gravitational radiation. In more general regions which incontrovertibly support
non-trivial radiation fields, it can be used to extract local,
coordinate-independent information partially characterizing that radiation.
While a clear, physical interpretation is possible only in such radiation
zones, a simple algorithm can be given to extend the definition smoothly to
generic regions of space-time.Comment: 4 pages, 1 EPS figur
Metric of a tidally perturbed spinning black hole
We explicitly construct the metric of a Kerr black hole that is tidally
perturbed by the external universe in the slow-motion approximation. This
approximation assumes that the external universe changes slowly relative to the
rotation rate of the hole, thus allowing the parameterization of the
Newman-Penrose scalar by time-dependent electric and magnetic tidal
tensors. This approximation, however, does not constrain how big the spin of
the background hole can be and, in principle, the perturbed metric can model
rapidly spinning holes. We first generate a potential by acting with a
differential operator on . From this potential we arrive at the metric
perturbation by use of the Chrzanowski procedure in the ingoing radiation
gauge. We provide explicit analytic formulae for this metric perturbation in
spherical Kerr-Schild coordinates, where the perturbation is finite at the
horizon. This perturbation is parametrized by the mass and Kerr spin parameter
of the background hole together with the electric and magnetic tidal tensors
that describe the time evolution of the perturbation produced by the external
universe. In order to take the metric accurate far away from the hole, these
tidal tensors should be determined by asymptotically matching this metric to
another one valid far from the hole. The tidally perturbed metric constructed
here could be useful in initial data constructions to describe the metric near
the horizons of a binary system of spinning holes. This perturbed metric could
also be used to construct waveforms and study the absorption of mass and
angular momentum by a Kerr black hole when external processes generate
gravitational radiation.Comment: 17 pages, 3 figures. Final PRD version, minor typos, etc corrected.
v3: corrected typo in Eq. (35) and (57
Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations
This is the first in a series of articles on the numerical solution of
Friedrich's conformal field equations for Einstein's theory of gravity. We will
discuss in this paper why one should be interested in applying the conformal
method to physical problems and why there is good hope that this might even be
a good idea from the numerical point of view. We describe in detail the
derivation of the conformal field equations in the spinor formalism which we
use for the implementation of the equations, and present all the equations as a
reference for future work. Finally, we discuss the implications of the
assumptions of a continuous symmetry.Comment: 19 pages, LaTeX2
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