On gravitational fields of stars in f(R) gravity theories

Einstein's general relativity is a classical theory of gravitation: it is a postulate on the coupling between the four-dimensional, continuos spacetime and the matter fields in the universe, and it yields their dynamical evolution. It is believed that general relativity must be replaced by a quantum theory of gravity at least at extremely high energies of the early universe and at regions of strong curvature of spacetime, cf. black holes. Various attempts to quantize gravity, including conceptually new models such as string theory, have suggested that modification to general relativity might show up even at lower energy scales. On the other hand, also the late time acceleration of the expansion of the universe, known as the dark energy problem, might originate from new gravitational physics. Thus, although there has been no direct experimental evidence contradicting general relativity so far - on the contrary, it has passed a variety of observational tests - it is a question worth asking, why should the effective theory of gravity be of the exact form of general relativity? If general relativity is modified, how do the predictions of the theory change? Furthermore, how far can we go with the changes before we are face with contradictions with the experiments? Along with the changes, could there be new phenomena, which we could measure to find hints of the form of the quantum theory of gravity? This thesis is on a class of modified gravity theories called f(R) models, and in particular on the effects of changing the theory of gravity on stellar solutions. It is discussed how experimental constraints from the measurements in the Solar System restrict the form of f(R) theories. Moreover, it is shown that models, which do not differ from general relativity at the weak field scale of the Solar System, can produce very different predictions for dense stars like neutron stars. Due to the nature of f(R) models, the role of independent connection of the spacetime is emphasized throughout the thesis.

Anomalous transport at weak coupling

We evaluate the contribution of chiral fermions in d = 2, 4, 6, chiral bosons, a chiral gravitino like theory in d = 2 and chiral gravitinos in d = 6 to all the leading parity odd transport coefficients at one loop. This is done by using finite temperature field theory to evaluate the relevant Kubo formulae. For chiral fermions and chiral bosons the relation between the parity odd transport coefficient and the microscopic anomalies including gravitational anomalies agree with that found by using the general methods of hydrodynamics and the argument involving the consistency of the Euclidean vacuum. For the gravitino like theory in d = 2 and chiral gravitinos in d = 6, we show that relation between the pure gravitational anomaly and parity odd transport breaks down. From the perturbative calculation we clearly identify the terms that contribute to the anomaly polynomial, but not to the transport coefficient for gravitinos. We also develop a simple method for evaluating the angular integrals in the one loop diagrams involved in the Kubo formulae. Finally we show that charge diffusion mode of an ideal 2 dimensional Weyl gas in the presence of a finite chemical potential acquires a speed, which is equal to half the speed of light.

Nematic ordering pattern formation in the process of self-organization of microtubules in a gravitational field

Papaseit et al. (Proc. Nati. Acad. Sci. U.S.A. 97, 8364, 2000) showed the decisive role of gravity in the formation of patterns by assemblies of microtubules in vitro. By virtue of a functional scaling, the free energy for MT systems in a gravitational field was constructed. The influence of the gravitational field on MT's self-organization process, that can lead to the isotropic to nematic phase transition, is the focus of this paper. A coupling of a concentration gradient with orientational order characteristic of nernatic ordering pattern formation is the new feature emerging in the presence of gravity. The concentration range corresponding to a phase coexistence region increases with increasing g or NIT concentration. Gravity facilitates the isotropic to nernatic phase transition leading to a significantly broader transition region. The phase transition represents the interplay between the growth in the isotropic phase and the precipitation into the nematic phase. We also present and discuss the numerical results obtained for local NIT concentration change with the height of the vessel, order parameter and phase transition properties.

Thermodynamics/dynamics coupling in weakly compressible turbulent stratified fluids

In traditional and geophysical fluid dynamics, it is common to describe stratified turbulent fluid flows with low Mach number and small relative density variations by means of the incompressible Boussinesq approximation. Although such an approximation is often interpreted as decoupling the thermodynamics from the dynamics, this paper reviews recent results and derive new ones that show that the reality is actually more subtle and complex when diabatic effects and a nonlinear equation of state are retained. Such an analysis reveals indeed: (1) that the compressible work of expansion/contraction remains of comparable importance as the mechanical energy conversions in contrast to what is usually assumed; (2) in a Boussinesq fluid, compressible effects occur in the guise of changes in gravitational potential energy due to density changes. This makes it possible to construct a fully consistent description of the thermodynamics of incompressible fluids for an arbitrary nonlinear equation of state; (3) rigorous methods based on using the available potential energy and potential enthalpy budgets can be used to quantify the work of expansion/contraction B in steady and transient flows, which reveals that B is predominantly controlled by molecular diffusive effects, and act as a significant sink of kinetic energy.

Conformal coupling and Foldy-Wouthuysen transformation

The propagation of a free scalar field phi with mass m in a curved background is generally described by the equation (g(munu) delmudelnu + m(2) + xiR)phi = 0. There exist some arguments in the literature that seem to favor the conformal coupling to the detriment of the minimal one. However, the majority of these claims axe inconclusive. Here we show that the exact Foldy Wouthuysen transformation for spin-0 particle coupled to a wide class of static spacetime metrics exists independently of the value of. Nevertheless, if the coupling is of the conformal type, the gravitational Darwin-like term has an uncomplicated structure and it is proportional to the corresponding term in the fermionic case. In addition, an independent computation of this term, which has its origin in the zitterbewegung fluctuation of the boson's position with the mean square <(deltar)(2)> approximate to 1/m(2), gives a result that coincides with that obtained using the aforementioned exact transformation with xi = 1/6.

Metric-scalar gravity with torsion and the measurability of the non-minimal coupling

The measurability of the non-minimal coupling is discussed by considering the correction to the Newtonian static potential in the semiclassical approach. The coefficient of the gravitational Darwin term (GDT) gets redefined by the non-minimal torsion scalar couplings. Based on a similar analysis of the GDT in the effective field theory approach to non-minimal scalar, we conclude that for reasonable values of the couplings the correction is very small.

Riemannian and teleparallel descriptions of the scalar field gravitational interaction

A comparative study between the metric and the teleparallel descriptions of gravitation is made for the case of a scalar field. In contrast to the current belief that only spin matter could detect the teleparallel geometry, scalar matter being able to feel the metric geometry only, we show that a scalar field is able not only to feel anyone of these geometries, but also to produce torsion. Furthermore, both descriptions are found to be completely equivalent, which means that in fact, besides coupling to curvature, a scalar field couples also to torsion.

Quaternionic coupling

Physics is in its development a major challenge to relate fields, this paper presents a proposal to relate classical fields of physics, ie the electric field, magnetic field and gravitational equations by time-dependent. The proposal begins with the work that determines the Cauchy-Riemann conditions for quaternions [1], and the determination of Laplace’s equation in four dimensions[3], it was possible to determine mathematical components important to make the couplings of classical fields discussed above.

Correction to Variations of Ice Bed Coupling Beneath and Beyond Ice Streams: The Force Balance

A geometrical force balance that links stresses to ice bed coupling along a flow band of an ice sheet was developed in 1988 for longitudinal tension in ice streams and published 4 years later. It remains a work in progress. Now gravitational forces balanced by forces producing tensile, compressive, basal shear, and side shear stresses are all linked to ice bed coupling by the floating fraction phi of ice that produces the concave surface of ice streams. These lead inexorably to a simple formula showing how phi varies along these flow bands where surface and bed topography are known: phi = h(O)/h(I) with h(O) being ice thickness h(I) at x = 0 for x horizontal and positive upslope from grounded ice margins. This captures the basic fact in glaciology: the height of ice depends on how strongly ice couples to the bed. It shows how far a high convex ice sheet (phi = 0) has gone in collapsing into a low flat ice shelf (phi = 1). Here phi captures ice bed coupling under an ice stream and h(O) captures ice bed coupling beyond ice streams.

Variations of Ice Bed Coupling Beneath and Beyond Ice Streams: The Force Balance

A geometrical force balance that links stresses to ice bed coupling along a flow band of an ice sheet was developed in 1988 for longitudinal tension in ice streams and published 4 years later. It remains a work in progress. Now gravitational forces balanced by forces producing tensile, compressive, basal shear, and side shear stresses are all linked to ice bed coupling by the floating fraction phi of ice that produces the concave surface of ice streams. These lead inexorably to a simple formula showing how phi varies along these flow bands where surface and bed topography are known: phi = h(O)/h(I) with h(O) being ice thickness h(I) at x = 0 for x horizontal and positive upslope from grounded ice margins. This captures the basic fact in glaciology: the height of ice depends on how strongly ice couples to the bed. It shows how far a high convex ice sheet (phi = 0) has gone in collapsing into a low flat ice shelf (phi = 1). Here phi captures ice bed coupling under an ice stream and h(O) captures ice bed coupling beyond ice streams.

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.

Distribution of respiratory droplets in enclosed environments under different air distribution methods

Dispersion characteristics of respiratory droplets in indoor environments are of special interest in controlling transmission of airborne diseases. This study adopts an Eulerian method to investigate the spatial concentration distribution and temporal evolution of exhaled and sneezed/coughed droplets within the range of 1.0~10.0μm in an office room with three air distribution methods, i.e. mixing ventilation (MV), displacement ventilation (DV), and under-floor air distribution (UFAD). The diffusion, gravitational settling, and deposition mechanism of particulate matters are well accounted in the one-way coupling Eulerian approach. The simulation results find that exhaled droplets with diameters up to 10.0μm from normal respiration process are uniformly distributed in MV, while they are trapped in the breathing height by thermal stratifications in DV and UFAD, resulting in a high droplet concentration and a high exposure risk to other occupants. Sneezed/coughed droplets are diluted much slower in DV/UFAD than in MV. Low air speed in the breathing zone in DV/UFAD can lead to prolonged residence of droplets in the breathing zone.