1,134 research outputs found
Coframe teleparallel models of gravity. Exact solutions
The superstring and superbrane theories which include gravity as a necessary
and fundamental part renew an interest to alternative representations of
general relativity as well as the alternative models of gravity. We study the
coframe teleparallel theory of gravity with a most general quadratic
Lagrangian. The coframe field on a differentiable manifold is a basic dynamical
variable. A metric tensor as well as a metric compatible connection is
generated by a coframe in a unique manner. The Lagrangian is a general linear
combination of Weitzenb\"{o}ck's quadratic invariants with free dimensionless
parameters \r_1,\r_2,\r_3.
Every independent term of the Lagrangian is a global SO(1,3)-invariant
4-form. For a special choice of parameters which confirms with the local
SO(1,3) invariance this theory gives an alternative description of Einsteinian
gravity - teleparallel equivalent of GR.
We prove that the sign of the scalar curvature of a metric generated by a
static spherical-symmetric solution depends only on a relation between the free
parameters. The scalar curvature vanishes only for a subclass of models with
\r_1=0. This subclass includes the teleparallel equivalent of GR. We obtain
the explicit form of all spherically symmetric static solutions of the
``diagonal'' type to the field equations for an arbitrary choice of free
parameters. We prove that the unique asymptotic-flat solution with Newtonian
limit is the Schwarzschild solution that holds for a subclass of teleparallel
models with \r_1=0. Thus the Yang-Mills-type term of the general quadratic
coframe Lagrangian should be rejected.Comment: 28 pages, Latex error is fixe
Lower limb stiffness and maximal sprint speed in 11-16-year-old boys
The purpose of the study was to examine the relationship between vertical stiffness, leg stiffness and maximal sprint speed in a large cohort of 11-16-year-old boys. Three-hundred and thirty-six boys undertook a 30 m sprint test using a floor-level optical measurement system, positioned in the final 15 m section. Measures of speed, step length, step frequency, contact time and flight time were directly measured whilst force, displacement, vertical stiffness and leg stiffness, were modeled from contact and flight times, from the two fastest consecutive steps for each participant over two trials. All force, displacement and stiffness variables were significantly correlated with maximal sprint speed (p 0.7) relationship with sprint speed, while vertical center of mass displacement, absolute vertical stiffness, relative peak force, and maximal leg spring displacement had large (r > 0.5) relationships. Relative vertical stiffness and relative peak force did not significantly change with advancing age (p > 0.05), but together with maximal leg spring displacement accounted for 96% of the variance in maximal speed. It appears that relative vertical stiffness and relative peak force are important determinants of sprint speed in boys aged 11-16 years, but are qualities that may need to be trained due to no apparent increases from natural development. Practitioners may wish to utilize training modalities such as plyometrics and resistance training to enable adaptation to these qualities due to their importance as predictors of speed in youth
Axial Torsion-Dirac spin Effect in Rotating Frame with Relativistic Factor
In the framework of spacetime with torsion and without curvature, the Dirac
particle spin precession in the rotational system is studied. We write out the
equivalent tetrad of rotating frame, in the polar coordinate system, through
considering the relativistic factor, and the resultant equivalent metric is a
flat Minkowski one. The obtained rotation-spin coupling formula can be applied
to the high speed rotating case, which is consistent with the expectation.Comment: 6 page
On a class of invariant coframe operators with application to gravity
Let a differential 4D-manifold with a smooth coframe field be given. Consider
the operators on it that are linear in the second order derivatives or
quadratic in the first order derivatives of the coframe, both with coefficients
that depend on the coframe variables. The paper exhibits the class of operators
that are invariant under a general change of coordinates, and, also, invariant
under the global SO(1,3)-transformation of the coframe. A general class of
field equations is constructed. We display two subclasses in it. The subclass
of field equations that are derivable from action principles by free variations
and the subclass of field equations for which spherical-symmetric solutions,
Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the
resulting metric is computed. Invoking the Geodesic Postulate, we find all the
equations that are experimentally (by the 3 classical tests) indistinguishable
from Einstein field equations. This family includes, of course, also Einstein
equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool
employed in the paper is an invariant formulation reminiscent of Cartan's
structural equations. The article sheds light on the possibilities and
limitations of the coframe gravity. It may also serve as a general procedure to
derive covariant field equations
Stochastic Gravity
Gravity is treated as a stochastic phenomenon based on fluctuations of the
metric tensor of general relativity. By using a (3+1) slicing of spacetime, a
Langevin equation for the dynamical conjugate momentum and a Fokker-Planck
equation for its probability distribution are derived. The Raychaudhuri
equation for a congruence of timelike or null geodesics leads to a stochastic
differential equation for the expansion parameter in terms of the
proper time . For sufficiently strong metric fluctuations, it is shown that
caustic singularities in spacetime can be avoided for converging geodesics. The
formalism is applied to the gravitational collapse of a star and the
Friedmann-Robertson-Walker cosmological model. It is found that owing to the
stochastic behavior of the geometry, the singularity in gravitational collapse
and the big-bang have a zero probability of occurring. Moreover, as a star
collapses the probability of a distant observer seeing an infinite red shift at
the Schwarzschild radius of the star is zero. Therefore, there is a vanishing
probability of a Schwarzschild black hole event horizon forming during
gravitational collapse.Comment: Revised version. Eq. (108) has been modified. Additional comments
have been added to text. Revtex 39 page
Axial-Vector Torsion and the Teleparallel Kerr Spacetime
In the context of the teleparallel equivalent of general relativity, we
obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr
spacetime. It is shown that, in the slow rotation and weak field
approximations, the axial-vector torsion plays the role of the gravitomagnetic
component of the gravitational field, and is thus the responsible for the
Lense-Thirring effect.Comment: 9 pages, no figures, to appear in Class. Quant. Gra
Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation
We present a simple method to derive the semiclassical equations of motion
for a spinning particle in a gravitational field. We investigate the cases of
classical, rotating particles (pole-dipole particles), as well as particles
with intrinsic spin. We show that, starting with a simple Lagrangian, one can
derive equations for the spin evolution and momentum propagation in the
framework of metric theories of gravity and in theories based on a
Riemann-Cartan geometry (Poincare gauge theory), without explicitly referring
to matter current densities (spin and energy-momentum). Our results agree with
those derived from the multipole expansion of the current densities by the
conventional Papapetrou method and from the WKB analysis for elementary
particles.Comment: 28 page
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