arXiv subjects

Nicola Tamanini

Publications and source records attributed to Nicola Tamanini.

82 records · Page 5Linked to original sources

arXiv2013

Rotational elasticity and couplings to linear elasticity

It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of static linear elasticity. An appropriate kinetic energy is identified and we present a dynamical model of rotational elasticity. The propagation of elastic waves in such a medium is studied and we find two classes of waves, transversal rotational waves and longitudinal rotational waves, both of which are solutions of the nonlinear partial differential equations. For certain parameter choices, the transversal wave velocity can be greater than the longitudinal wave velocity. Moreover, parameter ranges are identified where the model describes an auxetic material. However, in all cases the potential energy functional is positive definite. Finally, we couple the rotational waves to linear elastic waves to study the behaviour of the coupled system. We find wave like solutions to the coupled equations and can visualise our results with the help of suitable figures.

math-ph↗

arXiv2013

On the consistency of non-minimally coupled f(R) gravity

Theories with a non-minimal coupling between the space-time curvature and matter fields introduce an extra force due to the non-conservation of the matter energy momentum. In the present work the theoretical consistency of such couplings is studied using a scalar field Lagrangian to model the matter content. The conditions that the coupling does not introduce ghosts, classical instabilities or superluminal propagation of perturbations are derived. These consistency conditions are then employed to rule out or severely restrict the forms of the non-minimal coupling functions considered in the previous literature. For example, a power-law coupling is viable only for sublinear positive power of the curvature scalar.

gr-qc↗

arXiv2013

Ghosts in pure and hybrid formalisms of gravity theories: a unified analysis

In the first order formalism of gravitational theories, the spacetime connection is considered as an independent variable to vary together with the metric. However, the metric still generates its Levi-Civita connection that turns out to determine the geodesics of matter. Recently, "hybrid" gravity theories have been introduced by constructing actions involving both the independent Palatini connection and the metric Levi-Civita connection. In this study a method is developed to analyse the field content of such theories, in particular to determine whether the propagating degrees of freedom are ghosts or tachyons. New types of second, fourth and sixth order derivative gravity theories are investigated and the so called f(X) theories are singled out as a viable class of "hybrid" extensions of General Relativity.

gr-qc↗

arXiv2013

Definition of Good Tetrads for f(T) Gravity

The importance of choosing suitable tetrads for the study of exact solutions in f(T) gravity is discussed. For any given metric, we define the concept of good tetrads as the tetrads satisfying the field equations without constrainig the function f(T). Employing local Lorentz transformations, good tetrads in the context of spherical symmetry are found for Schwarzschild-de Sitter solutions.

gr-qc↗

arXiv2013

The Biconnection Variational Principle for General Relativity

A recently proposed variational approach for general relativity where, in addition to the metric tensor, two independent affine connections enter the action as dynamical variables, is revised. Field equations always reduce to the Einstein field equations for any dependence of the matter action upon an independent connection.

gr-qc↗

arXiv2013

Generalized hybrid metric-Palatini gravity

We introduce a new approach to modified gravity which generalizes the recently proposed hybrid metric-Palatini gravity. The gravitational action is taken to depend on a general function of both the metric and Palatini curvature scalars. The dynamical equivalence with a non-minimally coupled bi-scalar field gravitational theory is proved. The evolution of cosmological solutions is studied using dynamical systems techniques.

gr-qc↗

arXiv2012

Variational approach to gravitational theories with two independent connections

A new variational approach for general relativity and modified theories of gravity is presented. In addition to the metric tensor, two independent affine connections enter the action as dynamical variables. In the matter action the dependence upon one of the connections is left completely unspecified. When the variation is applied to the Einstein-Hilbert action the Einstein field equations are recovered. However when applied to $f(R)$ and Scalar-Tensor theories, it yields gravitational field equations which differ from their equivalents obtained with a metric or Palatini variation and reduce to the former ones only when no connections appear in the matter action.

gr-qc↗

arXiv2012

Good and bad tetrads in f(T) gravity

We investigate the importance of choosing good tetrads for the study of the field equations of $f(T)$ gravity. It is well known that this theory is not invariant under local Lorentz transformations, and therefore the choice of tetrad plays a crucial role in such models. Different tetrads will lead to different field equations which in turn have different solutions. We suggest to speak of a good tetrad if it imposes no restrictions on the form of $f(T)$. Employing local rotations, we construct good tetrads in the context of homogeneity and isotropy, and spherical symmetry, where we show how to find Schwarzschild-de Sitter solutions in vacuum. Our principal approach should be applicable to other symmetries as well.

gr-qc↗

arXiv2011

Existence of relativistic stars in f(T) gravity

We examine the existence of relativistic stars in f(T) modified gravity and explicitly construct several classes of static perfect fluid solutions. We derive the conservation equation from the complete f(T) gravity field equations and present the differences with its teleparallel counterpart. Firstly, we choose the tetrad field in the diagonal gauge and study the resulting field equations. Some exact solutions are explicitly constructed and it is noted that these solutions have to give a constant torsion scalar. Next, we choose a non diagonal tetrad field which results in field equations similar to those of general relativity. For specific models we are able to construct exact solutions of these field equations. Among those new classes of solutions, we find negative pressure solutions, and an interesting class of polynomial solutions.

gr-qc↗

arXiv2010

Inflationary Perturbations in Palatini Generalised Gravity

We examine the generation of primordial perturbations during an inflationary epoch in generalised theories of gravity when the equations of motion are derived using the Palatini variational principle. Both f(R) and Scalar-Tensor theories are considered and we compare our results with those obtained under the conventional metric formalism. Non-linear generalisations of the action lead to different theories under the two variational choices and we obtain distinct results for scalar and tensor spectral indices and their ratio. We find the following general result; inflation driven solely by f(R) modifications alone do not result in suitable curvature perturbations whilst Scalar-Tensor theories generate nearly scalar invariant curvature perturbations but no tensor modes.

gr-qc↗