Some remarks on the coupling prescription of teleparallel gravity

By using a nonholonomic moving frame version of the general covariance principle, an active version of the equivalence principle, an analysis of the gravitational coupling prescription of teleparallel gravity is made. It is shown that the coupling prescription determined by this principle is always equivalent with the corresponding prescription of general relativity, even in the presence of fermions. An application to the case of a Dirac spinor is made.

Teleparallel spin connection

A new expression for the spin connection of teleparallel gravity is proposed, given by minus the contorsion tensor plus a zero connection. The corresponding minimal coupling is covariant under local Lorentz transformation, and equivalent to the minimal coupling prescription of general relativity. With this coupling prescription, therefore, teleparallel gravity turns out to be fully equivalent to general relativity, even in the presence of spinor fields.

Torsion and gravitation: A new view

According to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Though equivalent, they act differently: curvature yields a geometric description, in which the concept of gravitational force is absent whereas torsion acts as a true gravitational force, quite similar to the Lorentz force of electrodynamics. As a consequence, the right-hand side of a spinless-particle equation of motion (which would represent a gravitational force) is always zero in the geometric description, but not in the teleparallel case. This means that the gravitational coupling prescription can be minimal only in the geometric case. Relying on this property, a new gravitational coupling prescription in the presence of curvature and torsion is proposed. It is constructed in such a way to preserve the equivalence between curvature and torsion, and its basic property is to be equivalent to the usual coupling prescription of general relativity. According to this view, no new physics is connected with torsion, which is just an alternative to curvature in the description of gravitation. An application of this formulation to the equations of motion of both a spinless and a spinning particle is discussed.

Torsion and the gravitational interaction

By using a nonholonomous-frame formulation of the general covariance principle, seen as an active version of the strong equivalence principle, an analysis of the gravitational coupling prescription in the presence of curvature and torsion is made. The Coupling prescription implied by this principle is found to be always equivalent to that of general relativity, a result that reinforces the completeness of this theory, as well as the teleparallel point of view according to which torsion does not represent additional degrees of freedom for gravity, but simply an alternative way of representing the gravitational field.

Gravitation and the local symmetry group of space-time

According to general relativity, the interaction of a matter field with gravitation requires the simultaneous introduction of a tetrad field, which is a field related to translations, and a spin connection, which is a field assuming values in the Lie algebra of the Lorentz group. These two fields, however, are not independent. By analyzing the constraint between them, it is concluded that the relevant local symmetry group behind general relativity is provided by the Lorentz group. Furthermore, it is shown that the minimal coupling prescription obtained from the Lorentz covariant derivative coincides exactly with the usual coupling prescription of general relativity. Instead of the tetrad, therefore, the spin connection is to be considered as the fundamental field representing gravitation.

Torsion gravity: A reappraisal

The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Einstein-Cartan and gauge theories for the Poincare and the affine groups, consider curvature and torsion as representing independent degrees of freedom. By using an active version of the strong equivalence principle, a possible solution to this conceptual question is reviewed. This solution ultimately favors the teleparallel point of view, and consequently the completeness of general relativity. A discussion of the consequences for gravitation is presented.

An alternative approach for general covariant Horava-Lifshitz gravity and matter coupling

Recently, in [3] Horava and Melby-Thompson proposed a nonrelativistic gravity theory with extended gauge symmetry that is free of the spin-0 graviton. We propose a minimal substitution recipe to implement this extended gauge symmetry which reproduces the results obtained by them. Our prescription has the advantage of being manifestly gauge invariant and immediately generalizable to other fields, like matter. We briefly discuss the coupling of gravity with scalar and vector fields found by our method. We show also that the extended gauge invariance in gravity does not force the value of. to be lambda = 1 as claimed in [3]. However, the spin-0 graviton is eliminated even for general lambda.

An alternative prescription for gauging Floreanini-Jackiw chiral bosons

We seek new couplings of chiral bosons to U(1) gauge fields. Lorentz covariance of the resulting constrained lagrangian is checked with the help of a procedure based in the first-order formalism of Faddeev and Jackiw. We find Harada's constraint and another local one not previously considered. We analyze the constraint structure and part of the spectrum of this second solution and show that it is equivalent to an explicitly covariant coupling of Siegel's chiral boson to gauge fields, which preserves chirality under gauge transformations.

Information–movement coupling in developing cricketers under changing ecological practice constraints

Changing informational constraints of practice, such as when using ball projection machines, has been shown to significantly affect movement coordination of skilled cricketers. To date, there has been no similar research on movement responses of developing batters, an important issue since ball projection machines are used heavily in cricket development programmes. Timing and coordination of young cricketers (n = 12, age = 15.6 ± 0.7 years) were analyzed during the forward defensive and forward drive strokes when facing a bowling machine and bowler (both with a delivery velocity of 28.14 ± 0.56 m s−1). Significant group performance differences were observed between the practice task constraints, with earlier initiation of the backswing, front foot movement, downswing, and front foot placement when facing the bowler compared to the bowling machine. Peak height of the backswing was higher when facing the bowler, along with a significantly larger step length. Altering the informational constraints of practice caused major changes to the information–movement couplings of developing cricketers. Data from this study were interpreted to emanate from differences in available specifying variables under the distinct practice task constraints. Considered with previous findings, results confirmed the need to ensure representative batting task constraints in practice, cautioning against an over-reliance on ball projection machines in cricket development programmes.

Exercise-induced energy expenditure : implications for exercise prescription and obesity

Objective: Walking is commonly recommended to help with weight management. We measured total energy expenditure (TEE) and its components to quantify the impact of increasing exercise-induced energy expenditure (ExEE) on other components of TEE. Methods: Thirteen obese women underwent an 8-week walking group intervention. TEE was quantified using doubly labeled water, ExEE was quantified using heart rate monitors, daily movement was assessed by accelerometry and resting metabolic rate was measured using indirect calorimetry. Results: Four of the 13 participants achieved the target of 1500 kcal wk−1 of ExEE and all achieved 1000 kcal wk−1. The average ExEE achieved by the group across the 8 weeks was 1434 ± 237 kcal wk−1. Vigorous physical activity, as assessed by accelerometry, increased during the intervention by an average of 30 min per day. Non-exercise activity thermogenesis (NEAT) decreased, on average, by 175 kcal d−1 (−22%) from baseline to the intervention and baseline fitness was correlated with change in NEAT. Conclusions: Potential alterations in non-exercise activity should be considered when exercise is prescribed. The provision of appropriate education on how to self-monitor daily activity levels may improve intervention outcomes in groups who are new to exercise. Practice implications: Strategies to sustain incidental and light physical activity should be offered to help empower individuals as they develop and maintain healthy and long-lasting lifestyle habits.