Study the behaviour and the evolution of the cosmological field equations in an homogeneous and anisotropic spacetime with two scalar fields coupled in the kinetic term. Specifically, the kinetic energy for the scalar field Lagrangian is that of the
Chiral model and defines a two-dimensional maximally symmetric space with negative curvature. For the background space we assume the locally rotational spacetime which describes the Bianchi I, the Bianchi III and the Kantowski-Sachs anisotropic spaces. We work on the $H$% -normalization and we investigate the stationary points and their stability. For the exponential potential we find a new exact solution which describes an anisotropic inflationary solution. The anisotropic inflation is always unstable, while future attractors are the scaling inflationary solution or the hyperbolic inflation. For scalar field potential different from the exponential, the de Sitter universe exists.
In this paper a neutron star with an inner core which undergoes a phase transition, which is characterized by conformal degrees of freedom on the phase boundary, is considered. Typical cases of such a phase transition are e.g. quantum Hall effect, su
perconductivity and superfluidity. Assuming the mechanical stability of this system the effects induced by the conformal degrees of freedom on the phase boundary will be analyzed. We will see that the inclusion of conformal degrees of freedom is not always consistent with the staticity of the phase boundary. Indeed also in the case of mechanical equilibrium there may be the tendency of one phase to swallow the other. Such a shift of the phase boundary would not imply any compression or decompression of the core. By solving the Israel junction conditions for the conformal matter, we have found the range of physical parameters which can guarantee a stable equilibrium of the phase boundary of the neutron star. The relevant parameters turn out to be not only the density difference but also the difference of the slope of the density profiles of the two phases. The values of the parameters which guarantee the stability turn out to be in a phenomenologically reasonable range. For the parameter values where the the phase boundary tends to move, a possible astrophysical consequence related to sudden small changes of the moment of inertia of the star is briefly discussed.
Exact solutions with torsion in Einstein-Gauss-Bonnet gravity are derived. These solutions have a cross product structure of two constant curvature manifolds. The equations of motion give a relation for the coupling constants of the theory in order t
o have solutions with nontrivial torsion. This relation is not the Chern-Simons combination. One of the solutions has a $AdS_2times S^3$ structure and is so the purely gravitational analogue of the Bertotti-Robinson space-time where the torsion can be seen as the dual of the covariantly constant electromagnetic field.
We propose a discontinuous finite element approximation for a model of quasi-static growth of brittle fractures in linearly elastic bodies formulated by Francfort and Marigo, and based on the classical Griffiths criterion. We restrict our analysis to
the case of anti-planar shear and we consider discontinuous displacements which are piecewise affine with respect to a regular triangulation.
In this article we compute the black hole entropy by finding a classical central charge of the Virasoro algebra of a Liouville theory using the Cardy formula. This is done by performing a dimensional reduction of the Einstein Hilbert action with the
ansatz of spherical symmetry and writing the metric in conformally flat form. We obtain two coupled field equations. Using the near horizon approximation the field equation for the conformal factor decouples. The one concerning the conformal factor is a Liouville equation, it posses the symmetry induced by a Virasoro algebra. We argue that it describes the microstates of the black hole, namely the generators of this symmetry do not change the thermodynamical properties of the black hole.
We study the lower semicontinuity for functionals defined on compact sets in R^2 with a finite number of connected components and finite length which depend on their normal vector. We apply the result to the study of quasi-static growth of brittle fr
actures in linearly elastic inhomogeneous and anisotropic bodies.
