Multipole moments in Kaluza-Klein theories

This paper contains discussion of the problem of motion of extended i.e. non point test bodies in multidimensional space. Extended bodies are described in terms of so called multipole moments. Using approximated form of equations of motion for extended bodies deviation from geodesic motion is derived. Results are applied to special form of space-time.Comment: 11 pages, AMS-TeX, few misprints corrected, to appear in Classical and Quantum Gravit

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

General relativistic spinning fluids with a modified projection tensor

An energy-momentum tensor for general relativistic spinning fluids compatible with Tulczyjew-type supplementary condition is derived from the variation of a general Lagrangian with unspecified explicit form. This tensor is the sum of a term containing the Belinfante-Rosenfeld tensor and a modified perfect-fluid energy-momentum tensor in which the four-velocity is replaced by a unit four-vector in the direction of fluid momentum. The equations of motion are obtained and it is shown that they admit a Friedmann-Robertson-Walker space-time as a solution.Comment: Submitted to General Relativity and Gravitatio

A Generalization of the Goldberg-Sachs Theorem and its Consequences

The Goldberg-Sachs theorem is generalized for all four-dimensional manifolds endowed with torsion-free connection compatible with the metric, the treatment includes all signatures as well as complex manifolds. It is shown that when the Weyl tensor is algebraically special severe geometric restrictions are imposed. In particular it is demonstrated that the simple self-dual eigenbivectors of the Weyl tensor generate integrable isotropic planes. Another result obtained here is that if the self-dual part of the Weyl tensor vanishes in a Ricci-flat manifold of (2,2) signature the manifold must be Calabi-Yau or symplectic and admits a solution for the source-free Einstein-Maxwell equations.Comment: 14 pages. This version matches the published on

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

Cosmological model with macroscopic spin fluid

We consider a Friedmann-Robertson-Walker cosmological model with some exotic perfect fluid with spin known as the Weyssenhoff fluid. The possibility that the dark energy may be described in part by the Weyssenhoff fluid is discussed. The observational constraint coming from supernovae type Ia observations is established. This result indicates that, whereas the cosmological constant is still needed to explain current observations, the model with spin fluid is admissible. For high redshifts $z > 1$ the differences between the model with spin fluid and the cold dark matter model with a cosmological constant become detectable observationally for the flat case with $\Omega_{\text{m},0}=0.3$. From the maximum likelihood method we obtain the value of $\Omega_{\text{s},0} = 0.004 \pm 0.016$. This gives us the limit $\Omega_{\text{s},0} > -0.012$ at the $1\sigma$ level. While the model with ``brane effects'' is preferred by the supernovae Ia data, the model with spin fluid is statistically admissible. For comparison, the limit on the spin fluid coming from cosmic microwave background anisotropies is also obtained. The uncertainties in the location of a first peak give the interval $-1.4 \times 10^{-10} < \Omega_{\text{s},0} < -10^{-10}$. From big bang nucleosynthesis we obtain the strongest limit $\Omega_{\text{s},0} \gtrsim -10^{-20}$. The interconnection between the model considered and brane models is also pointed out.Comment: RevTeX4, 15 pages, 10 figures; some minor change

Correlation between depression and burden observed in informal caregivers of people suffering from dementia with time spent on caregiving and dementia severity

[Abstract] OBJECTIVE: The aim of the study is to compare data on the examined population of informal caregivers of people suffering from dementia with previous studies, as well as to assess the correlation between (i) depression determined on the basis of the Center for Epidemiologic Studies Depression Scale and (ii) caregiver burden measured by means of the Zarit Caregiver Burden Scale and some chosen parameters, such as total time devoted to caregiving, time of caregiving in hours per week and level of dementia severity measured by Global Deterioration Scale. PATIENTS AND METHODS: 41 informal caregivers of people suffering from dementia from different backgrounds were evaluated using the Zarit Caregiver Burden Scale and the Center for Epidemiologic Studies Depression Scale. Demographic data about the time devoted to caregiving and the number of hours spend on caregiving weekly were gathered. The type of dementia and its stage were registered using the Global Deterioration Scale (GDS). With the aid of the Statistica StatSoft program, mutual correlations between the parameters were measured. The study was conducted within the framework of AAL UnderstAID – a platform that supports and helps to understand and assist caregivers in the care of a relative with dementia. The international project is co-founded by the Joint Programme Ambient Assisted Living (Grant code: ESR-aal 2012 5 107). RESULTS: No significant correlations between the level of depression severity evaluated in caregivers and the total time of taking care of a demented person or time of caregiving in hours per week were observed. Similarly, no significant correlation between depression severity level and dementia severity level measured on the GDS scale were noted. There was also no significant correlation between Zarit Caregiver Burden Scale scores and the above-mentioned parameters. CONCLUSIONS: The level of depression among caregivers do not depend on socio-demographic factors

Eutectic Colony Formation: A Stability Analysis

Experiments have widely shown that a steady-state lamellar eutectic solidification front is destabilized on a scale much larger than the lamellar spacing by the rejection of a dilute ternary impurity and forms two-phase cells commonly referred to as `eutectic colonies'. We extend the stability analysis of Datye and Langer for a binary eutectic to include the effect of a ternary impurity. We find that the expressions for the critical onset velocity and morphological instability wavelength are analogous to those for the classic Mullins-Sekerka instability of a monophase planar interface, albeit with an effective surface tension that depends on the geometry of the lamellar interface and, non-trivially, on interlamellar diffusion. A qualitatively new aspect of this instability is the occurence of oscillatory modes due to the interplay between the destabilizing effect of the ternary impurity and the dynamical feedback of the local change in lamellar spacing on the front motion. In a transient regime, these modes lead to the formation of large scale oscillatory microstructures for which there is recent experimental evidence in a transparent organic system. Moreover, it is shown that the eutectic front dynamics on a scale larger than the lamellar spacing can be formulated as an effective monophase interface free boundary problem with a modified Gibbs-Thomson condition that is coupled to a slow evolution equation for the lamellar spacing. This formulation provides additional physical insights into the nature of the instability and a simple means to calculate an approximate stability spectrum. Finally, we investigate the influence of the ternary impurity on a short wavelength oscillatory instability that is already present at off-eutectic compositions in binary eutectics.Comment: 26 pages RevTex, 14 figures (28 EPS files); some minor changes; references adde

Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid

A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1+3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular form for the space-time metric. The spin contributions to the field equations produce a bounce that averts an initial singularity, provided that the spin density exceeds the rate of shear. At later times, when the spin contribution can be neglected, a Weyssenhoff fluid reduces to a standard cosmological fluid in general relativity. Numerical solutions for the time evolution of the generalised scale factor in spatially-curved models are presented, some of which exhibit eternal oscillatory behaviour without any singularities. In spatially-flat models, analytical solutions for particular values of the equation-of-state parameter are derived. Although the scale factor of a Weyssenhoff fluid generically has a positive temporal curvature near a bounce, it requires unreasonable fine tuning of the equation-of-state parameter to produce a sufficiently extended period of inflation to fit the current observational data.Comment: 34 pages, 18 figure

Torsion-induced spin precession

We investigate the motion of a spinning test particle in a spatially-flat FRW-type space-time in the framework of the Einstein-Cartan theory. The space-time has a torsion arising from a spinning fluid filling the space-time. We show that for spinning particles with nonzero transverse spin components, the torsion induces a precession of particle spin around the direction of the fluid spin. We also show that a charged spinning particle moving in a torsion-less spatially-flat FRW space-time in the presence of a uniform magnetic field undergoes a precession of a different character.Comment: latex, 4 eps figure