4,519 research outputs found
On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories
We generalize the notion of quasi-local charges, introduced by P. Tod for
Yang--Mills fields with unitary groups, to non-Abelian gauge theories with
arbitrary gauge group, and calculate its small sphere and large sphere limits
both at spatial and null infinity. We show that for semisimple gauge groups no
reasonable definition yield conserved total charges and Newman--Penrose (NP)
type quantities at null infinity in generic, radiative configurations. The
conditions of their conservation, both in terms of the field configurations and
the structure of the gauge group, are clarified. We also calculate the NP
quantities for stationary, asymptotic solutions of the field equations with
vanishing magnetic charges, and illustrate these by explicit solutions with
various gauge groups.Comment: 22 pages, typos corrected, appearing in Classical and Quantum Gravit
Schwarzschild Tests of the Wahlquist-Estabrook-Buchman-Bardeen Tetrad Formulation for Numerical Relativity
A first order symmetric hyperbolic tetrad formulation of the Einstein
equations developed by Estabrook and Wahlquist and put into a form suitable for
numerical relativity by Buchman and Bardeen (the WEBB formulation) is adapted
to explicit spherical symmetry and tested for accuracy and stability in the
evolution of spherically symmetric black holes (the Schwarzschild geometry).
The lapse and shift which specify the evolution of the coordinates relative to
the tetrad congruence are reset at frequent time intervals to keep the
constant-time hypersurfaces nearly orthogonal to the tetrad congruence and the
spatial coordinate satisfying a kind of minimal rate of strain condition. By
arranging through initial conditions that the constant-time hypersurfaces are
asymptotically hyperbolic, we simplify the boundary value problem and improve
stability of the evolution. Results are obtained for both tetrad gauges
(``Nester'' and ``Lorentz'') of the WEBB formalism using finite difference
numerical methods. We are able to obtain stable unconstrained evolution with
the Nester gauge for certain initial conditions, but not with the Lorentz
gauge.Comment: (accepted by Phys. Rev. D) minor changes; typos correcte
Accelerating relativistic reference frames in Minkowski space-time
We study accelerating relativistic reference frames in Minkowski space-time
under the harmonic gauge. It is well-known that the harmonic gauge imposes
constraints on the components of the metric tensor and also on the functional
form of admissible coordinate transformations. These two sets of constraints
are equivalent and represent the dual nature of the harmonic gauge. We explore
this duality and show that the harmonic gauge allows presenting an accelerated
metric in an elegant form that depends only on two harmonic potentials. It also
allows reconstruction of the spatial structure of the post-Galilean coordinate
transformation functions relating inertial and accelerating frames. The
remaining temporal dependence of these functions together with corresponding
equations of motion are determined from dynamical conditions, obtained by
constructing the relativistic proper reference frame of an accelerated test
particle. In this frame, the effect of external forces acting on the observer
is balanced by the fictitious frame-reaction force that is needed to keep the
test particle at rest with respect to the frame, conserving its relativistic
linear momentum. We find that this approach is sufficient to determine all the
terms of the coordinate transformation. The same method is then used to develop
the inverse transformations. The resulting post-Galilean coordinate
transformations extend the Poincar\'e group on the case of accelerating
observers. We present and discuss the resulting coordinate transformations,
relativistic equations of motion, and the structure of the metric tensors
corresponding to the relativistic reference frames involved.Comment: revtex4, 21 page
Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits
The Mathisson-Papapetrou equations in the Schwarzschild background both at
Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered.
The region of existence of highly relativistic circular orbits of a spinning
particle in this background and dependence of the particle's orbital velocity
on its spin and radial coordinate are investigated. It is shown that in
contrast to the highly relativistic circular orbits of a spinless particle,
which exist only for , , the corresponding
orbits of a spinning particle are allowed in a wider space region, and the
dimension of this region significantly depends on the supplementary condition.
At the Mathisson-Pirani condition new numerical results which describe some
typical cases of non-circular highly relativistic orbits of a spinning particle
starting from are presented.Comment: 10 pages, 11 figure
Spin precession in the Schwarzschild spacetime: circular orbits
We study the behavior of nonzero rest mass spinning test particles moving
along circular orbits in the Schwarzschild spacetime in the case in which the
components of the spin tensor are allowed to vary along the orbit, generalizing
some previous work.Comment: To appear on Classical and Quantum Gravity, 200
Association analysis identifies TLR7 and TLR8 as novel risk genes in asthma and related disorders
Space-time defects and teleparallelism
We consider the class of space-time defects investigated by Puntigam and
Soleng. These defects describe space-time dislocations and disclinations
(cosmic strings), and are in close correspondence to the actual defects that
arise in crystals and metals. It is known that in such materials dislocations
and disclinations require a small and large amount of energy, respectively, to
be created. The present analysis is carried out in the context of the
teleparallel equivalent of general relativity (TEGR). We evaluate the
gravitational energy of these space-time defects in the framework of the TEGR
and find that there is an analogy between defects in space-time and in
continuum material systems: the total gravitational energy of space-time
dislocations and disclinations (considered as idealized defects) is zero and
infinit, respectively.Comment: 22 pages, no figures, to appear in the Class. Quantum Gravit
New innovative Moving Bed Biofilm Reactor (MBBR) concept removes pharmaceutical from municipal wastewater using only biological polishing
Thomas rotation and Thomas precession
Exact and simple calculation of Thomas rotation and Thomas precessions along
a circular world line is presented in an absolute (coordinate-free) formulation
of special relativity. Besides the simplicity of calculations the absolute
treatment of spacetime allows us to gain a deeper insight into the phenomena of
Thomas rotation and Thomas precession.Comment: 20 pages, to appear in Int. J. Theo. Phy
- …