34 research outputs found
Equation of Motion of Small Bodies in Relativity
There is proven a theorem, to the effect that a material body in general
relativity, in a certain limit of sufficiently small size and mass, moves along
a geodesic.Comment: 7 page
Faster Than Light?
It is argued that special relativity remains a viable physical theory even
when there is permitted signals traveling faster than light.Comment: 13 pages; submitted to J. Lorentz Geometr
Total Mass-Momentum of Arbitrary Initial-Data Sets in General Relativity
For an asymptotically flat initial-data set in general relativity, the total
mass-momentum may be interpreted as a Hermitian quadratic form on the complex,
two-dimensional vector space of ``asymptotic spinors''. We obtain a
generalization to an arbitrary initial-data set. The mass-momentum is retained
as a Hermitian quadratic form, but the space of ``asymptotic spinors'' on which
it is a function is modified. Indeed, the dimension of this space may range
from zero to infinity, depending on the initial data. There is given a variety
of examples and general properties of this generalized mass-momentum.Comment: 25 pages, LaTe
The Motion of Small Bodies in Space-time
We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship between approaches that model such bodies as distributions supported on a curve, and those that employ smooth fields supported in small neighborhoods of a curve. This result also applies to "bodies" constructed from wave packets of Maxwell or Klein-Gordon fields. There follows a simple and precise formulation of the optical limit for Maxwell fields
Relativistic Lagrange Formulation
It is well-known that the equations for a simple fluid can be cast into what
is called their Lagrange formulation. We introduce a notion of a generalized
Lagrange formulation, which is applicable to a wide variety of systems of
partial differential equations. These include numerous systems of physical
interest, in particular, those for various material media in general
relativity. There is proved a key theorem, to the effect that, if the original
(Euler) system admits an initial-value formulation, then so does its
generalized Lagrange formulation.Comment: 34 pages, no figures, accepted in J. Math. Phy
An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
The problem of determining the electromagnetic and gravitational
``self-force'' on a particle in a curved spacetime is investigated using an
axiomatic approach. In the electromagnetic case, our key postulate is a
``comparison axiom'', which states that whenever two particles of the same
charge have the same magnitude of acceleration, the difference in their
self-force is given by the ordinary Lorentz force of the difference in their
(suitably compared) electromagnetic fields. We thereby derive an expression for
the electromagnetic self-force which agrees with that of DeWitt and Brehme as
corrected by Hobbs. Despite several important differences, our analysis of the
gravitational self-force proceeds in close parallel with the electromagnetic
case. In the gravitational case, our final expression for the (reduced order)
equations of motion shows that the deviation from geodesic motion arises
entirely from a ``tail term'', in agreement with recent results of Mino et al.
Throughout the paper, we take the view that ``point particles'' do not make
sense as fundamental objects, but that ``point particle equations of motion''
do make sense as means of encoding information about the motion of an extended
body in the limit where not only the size but also the charge and mass of the
body go to zero at a suitable rate. Plausibility arguments for the validity of
our comparison axiom are given by considering the limiting behavior of the
self-force on extended bodies.Comment: 37 pages, LaTeX with style package RevTeX 3.
Formation of Black Holes from Collapsed Cosmic String Loops
The fraction of cosmic string loops which collapse to form black holes is
estimated using a set of realistic loops generated by loop fragmentation. The
smallest radius sphere into which each cosmic string loop may fit is obtained
by monitoring the loop through one period of oscillation. For a loop with
invariant length which contracts to within a sphere of radius , the
minimum mass-per-unit length necessary for the cosmic string
loop to form a black hole according to the hoop conjecture is . Analyzing loops, we obtain the empirical estimate for the fraction of cosmic string
loops which collapse to form black holes as a function of the mass-per-unit
length in the range . We
use this power law to extrapolate to , obtaining the
fraction of physically interesting cosmic string loops which
collapse to form black holes within one oscillation period of formation.
Comparing this fraction with the observational bounds on a population of
evaporating black holes, we obtain the limit on the cosmic string mass-per-unit-length. This limit is consistent
with all other observational bounds.Comment: uuencoded, compressed postscript; 20 pages including 7 figure