125 research outputs found
Radiation reaction and the self-force for a point mass in general relativity
A point particle of mass m moving on a geodesic creates a perturbation h, of
the spacetime metric g, that diverges at the particle. Simple expressions are
given for the singular m/r part of h and its quadrupole distortion caused by
the spacetime. Subtracting these from h leaves a remainder h^R that is C^1. The
self-force on the particle from its own gravitational field corrects the
worldline at O(m) to be a geodesic of g+h^R. For the case that the particle is
a small non-rotating black hole, an approximate solution to the Einstein
equations is given with error of O(m^2) as m approaches 0.Comment: 4 pages, RevTe
An approximate binary-black-hole metric
An approximate solution to Einstein's equations representing two
widely-separated non-rotating black holes in a circular orbit is constructed by
matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The
spacetime metric is presented in a single coordinate system valid up to the
apparent horizons of the black holes. This metric could be useful in numerical
simulations of binary black holes. Initial data extracted from this metric have
the advantages of being linked to the early inspiral phase of the binary
system, and of not containing spurious gravitational waves.Comment: 20 pages, 1 figure; some changes in Sec. IV B,C and Sec.
Retarded coordinates based at a world line, and the motion of a small black hole in an external universe
In the first part of this article I present a system of retarded coordinates
based at an arbitrary world line of an arbitrary curved spacetime. The
retarded-time coordinate labels forward light cones that are centered on the
world line, the radial coordinate is an affine parameter on the null generators
of these light cones, and the angular coordinates are constant on each of these
generators. The spacetime metric in the retarded coordinates is displayed as an
expansion in powers of the radial coordinate and expressed in terms of the
world line's acceleration vector and the spacetime's Riemann tensor evaluated
at the world line. The formalism is illustrated in two examples, the first
involving a comoving world line of a spatially-flat cosmology, the other
featuring an observer in circular motion in the Schwarzschild spacetime. The
main application of the formalism is presented in the second part of the
article, in which I consider the motion of a small black hole in an empty
external universe. I use the retarded coordinates to construct the metric of
the small black hole perturbed by the tidal field of the external universe, and
the metric of the external universe perturbed by the presence of the black
hole. Matching these metrics produces the MiSaTaQuWa equations of motion for
the small black hole.Comment: 20 pages, revtex4, 2 figure
Fermi Coordinates for Weak Gravitational Fields
A Reference is corrected. (We derive the Fermi coordinate system of an
observer in arbitrary motion in an arbitrary weak gravitational field valid to
all orders in the geodesic distance from the worldline of the observer. In flat
space-time this leads to a generalization of Rindler space for arbitrary
acceleration and rotation. The general approach is applied to the special case
of an observer resting with respect to the weak gravitational field of a static
mass distribution. This allows to make the correspondence between general
relativity and Newtonian gravity more precise.)Comment: 7 Pages, Preprint KONS-RGKU-94-04, LaTe
Absorption of mass and angular momentum by a black hole: Time-domain formalisms for gravitational perturbations, and the small-hole/slow-motion approximation
The first objective of this work is to obtain practical prescriptions to
calculate the absorption of mass and angular momentum by a black hole when
external processes produce gravitational radiation. These prescriptions are
formulated in the time domain within the framework of black-hole perturbation
theory. Two such prescriptions are presented. The first is based on the
Teukolsky equation and it applies to general (rotating) black holes. The second
is based on the Regge-Wheeler and Zerilli equations and it applies to
nonrotating black holes. The second objective of this work is to apply the
time-domain absorption formalisms to situations in which the black hole is
either small or slowly moving. In the context of this small-hole/slow-motion
approximation, the equations of black-hole perturbation theory can be solved
analytically, and explicit expressions can be obtained for the absorption of
mass and angular momentum. The changes in the black-hole parameters can then be
understood in terms of an interaction between the tidal gravitational fields
supplied by the external universe and the hole's tidally-induced mass and
current quadrupole moments. For a nonrotating black hole the quadrupole moments
are proportional to the rate of change of the tidal fields on the hole's world
line. For a rotating black hole they are proportional to the tidal fields
themselves.Comment: 36 pages, revtex4, no figures, final published versio
The influence of the cosmological expansion on local systems
Following renewed interest, the problem of whether the cosmological expansion
affects the dynamics of local systems is reconsidered. The cosmological
correction to the equations of motion in the locally inertial Fermi normal
frame (the relevant frame for astronomical observations) is computed. The
evolution equations for the cosmological perturbation of the two--body problem
are solved in this frame. The effect on the orbit is insignificant as are the
effects on the galactic and galactic--cluster scales.Comment: To appear in the Astrophysical Journal, Late
On the physical meaning of Fermi coordinates
(Some Latex problems should be removed in this version) Fermi coordinates
(FC) are supposed to be the natural extension of Cartesian coordinates for an
arbitrary moving observer in curved space-time. Since their construction cannot
be done on the whole space and even not in the whole past of the observer we
examine which construction principles are responsible for this effect and how
they may be modified. One proposal for a modification is made and applied to
the observer with constant acceleration in the two and four dimensional
Minkowski space. The two dimensional case has some surprising similarities to
Kruskal space which generalize those found by Rindler for the outer region of
Kruskal space and the Rindler wedge. In perturbational approaches the
modification leads also to different predictions for certain physical systems.
As an example we consider atomic interferometry and derive the deviation of the
acceleration-induced phase shift from the standard result in Fermi coordinates.Comment: 11 pages, KONS-RGKU-94/02 (Latex
Weighing the Milky Way
We describe an experiment to measure the mass of the Milky Way galaxy. The
experiment is based on calculated light travel times along orthogonal
directions in the Schwarzschild metric of the Galactic center. We show that the
difference is proportional to the Galactic mass. We apply the result to light
travel times in a 10cm Michelson type interferometer located on Earth. The mass
of the Galactic center is shown to contribute 10^-6 to the flat space component
of the metric. An experiment is proposed to measure the effect.Comment: 10 pages, 1 figur
The Dipole Coupling of Atoms and Light in Gravitational Fields
The dipole coupling term between a system of N particles with total charge
zero and the electromagnetic field is derived in the presence of a weak
gravitational field. It is shown that the form of the coupling remains the same
as in flat space-time if it is written with respect to the proper time of the
observer and to the measurable field components. Some remarks concerning the
connection between the minimal and the dipole coupling are given.Comment: 10 pages, LaTe
The Gravitational Demise of Cold Degenerate Stars
We consider the long term fate and evolution of cold degenerate stars under
the action of gravity alone. Although such stars cannot emit radiation through
the Hawking mechanism, the wave function of the star will contain a small
admixture of black hole states. These black hole states will emit radiation and
hence the star can lose its mass energy in the long term. We discuss the
allowed range of possible degenerate stellar evolution within this framework.Comment: LaTeX, 18 pages, one figure, accepted to Physical Review
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