1,756 research outputs found
Effective stress-energy tensors, self-force, and broken symmetry
Deriving the motion of a compact mass or charge can be complicated by the
presence of large self-fields. Simplifications are known to arise when these
fields are split into two parts in the so-called Detweiler-Whiting
decomposition. One component satisfies vacuum field equations, while the other
does not. The force and torque exerted by the (often ignored) inhomogeneous
"S-type" portion is analyzed here for extended scalar charges in curved
spacetimes. If the geometry is sufficiently smooth, it is found to introduce
effective shifts in all multipole moments of the body's stress-energy tensor.
This greatly expands the validity of statements that the homogeneous R field
determines the self-force and self-torque up to renormalization effects. The
forces and torques exerted by the S field directly measure the degree to which
a spacetime fails to admit Killing vectors inside the body. A number of
mathematical results related to the use of generalized Killing fields are
therefore derived, and may be of wider interest. As an example of their
application, the effective shift in the quadrupole moment of a charge's
stress-energy tensor is explicitly computed to lowest nontrivial order.Comment: 22 pages, fixed typos and simplified discussio
Mechanics of extended masses in general relativity
The "external" or "bulk" motion of extended bodies is studied in general
relativity. Compact material objects of essentially arbitrary shape, spin,
internal composition, and velocity are allowed as long as there is no direct
(non-gravitational) contact with other sources of stress-energy. Physically
reasonable linear and angular momenta are proposed for such bodies and exact
equations describing their evolution are derived. Changes in the momenta depend
on a certain "effective metric" that is closely related to a non-perturbative
generalization of the Detweiler-Whiting R-field originally introduced in the
self-force literature. If the effective metric inside a self-gravitating body
can be adequately approximated by an appropriate power series, the
instantaneous gravitational force and torque exerted on it is shown to be
identical to the force and torque exerted on an appropriate test body moving in
the effective metric. This result holds to all multipole orders. The only
instantaneous effect of a body's self-field is to finitely renormalize the
"bare" multipole moments of its stress-energy tensor. The MiSaTaQuWa expression
for the gravitational self-force is recovered as a simple application. A
gravitational self-torque is obtained as well. Lastly, it is shown that the
effective metric in which objects appear to move is approximately a solution to
the vacuum Einstein equation if the physical metric is an approximate solution
to Einstein's equation linearized about a vacuum background.Comment: 39 pages, 2 figures; fixed equation satisfied by the Green function
used to construct the effective metri
Self-forces from generalized Killing fields
A non-perturbative formalism is developed that simplifies the understanding
of self-forces and self-torques acting on extended scalar charges in curved
spacetimes. Laws of motion are locally derived using momenta generated by a set
of generalized Killing fields. Self-interactions that may be interpreted as
arising from the details of a body's internal structure are shown to have very
simple geometric and physical interpretations. Certain modifications to the
usual definition for a center-of-mass are identified that significantly
simplify the motions of charges with strong self-fields. A derivation is also
provided for a generalized form of the Detweiler-Whiting axiom that pointlike
charges should react only to the so-called regular component of their
self-field. Standard results are shown to be recovered for sufficiently small
charge distributions.Comment: 21 page
Electromagnetic self-forces and generalized Killing fields
Building upon previous results in scalar field theory, a formalism is
developed that uses generalized Killing fields to understand the behavior of
extended charges interacting with their own electromagnetic fields. New notions
of effective linear and angular momenta are identified, and their evolution
equations are derived exactly in arbitrary (but fixed) curved spacetimes. A
slightly modified form of the Detweiler-Whiting axiom that a charge's motion
should only be influenced by the so-called "regular" component of its
self-field is shown to follow very easily. It is exact in some interesting
cases, and approximate in most others. Explicit equations describing the
center-of-mass motion, spin angular momentum, and changes in mass of a small
charge are also derived in a particular limit. The chosen approximations --
although standard -- incorporate dipole and spin forces that do not appear in
the traditional Abraham-Lorentz-Dirac or Dewitt-Brehme equations. They have,
however, been previously identified in the test body limit.Comment: 20 pages, minor typos correcte
Gravitational self-torque and spin precession in compact binaries
We calculate the effect of self-interaction on the "geodetic" spin precession
of a compact body in a strong-field orbit around a black hole. Specifically, we
consider the spin precession angle per radian of orbital revolution for
a particle carrying mass and spin in a circular orbit
around a Schwarzschild black hole of mass . We compute
through in perturbation theory, i.e, including the correction
(obtained numerically) due to the torque exerted by the
conservative piece of the gravitational self-field. Comparison with a
post-Newtonian (PN) expression for , derived here through 3PN
order, shows good agreement but also reveals strong-field features which are
not captured by the latter approximation. Our results can inform
semi-analytical models of the strong-field dynamics in astrophysical binaries,
important for ongoing and future gravitational-wave searches.Comment: 5 pages, 1 table, 1 figure. Minor changes to match published versio
Unreasonable Distinctions: A Comparative Analysis of the Definitional Framework of Koreas New Anti-Age Discrimination Law
Korea has recently enacted legislation that strengthens existing prohibitions on age discrimination by providing stiff penalties for violation. The core of any legislation lies in its definitional framework since it is through this framework that liability is ultimately established. This article examines and evaluates the scope and definitional language of the new Korean legislation through a comparative analysis of related provisions in the anti-age discrimination statutes of the US and UK. These jurisdictions are selected for comparison because they represent both a long-standing statutory regime and one that has been more recently established. The analysis reveals critical weaknesses in the structural and definitional aspects of the Korean legislation that may render determinations of liability ambiguous and therefore unreliable. Specifically, ambiguities in the scope of application due to faulty construction, reliance on a minimalist definition that appears to merely prohibit unreasonable distinctions, and a
confusion in the possible exceptions to discrimination raise concerns as to whether the new penalties will have any significant impact on reducing age discrimination in the Korean workplace since the prospects for ultimately reaching those penalties are doubtful
A Rigorous Derivation of Electromagnetic Self-force
During the past century, there has been considerable discussion and analysis
of the motion of a point charge, taking into account "self-force" effects due
to the particle's own electromagnetic field. We analyze the issue of "particle
motion" in classical electromagnetism in a rigorous and systematic way by
considering a one-parameter family of solutions to the coupled Maxwell and
matter equations corresponding to having a body whose charge-current density
and stress-energy tensor scale to zero size
in an asymptotically self-similar manner about a worldline as . In this limit, the charge, , and total mass, , of the body go to
zero, and goes to a well defined limit. The Maxwell field
is assumed to be the retarded solution associated with
plus a homogeneous solution (the "external field") that varies
smoothly with . We prove that the worldline must be a
solution to the Lorentz force equations of motion in the external field
. We then obtain self-force, dipole forces, and spin force
as first order perturbative corrections to the center of mass motion of the
body. We believe that this is the first rigorous derivation of the complete
first order correction to Lorentz force motion. We also address the issue of
obtaining a self-consistent perturbative equation of motion associated with our
perturbative result, and argue that the self-force equations of motion that
have previously been written down in conjunction with the "reduction of order"
procedure should provide accurate equations of motion for a sufficiently small
charged body with negligible dipole moments and spin. There is no corresponding
justification for the non-reduced-order equations.Comment: 52 pages, minor correction
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