1,721,133 research outputs found
A new approach to the analysis of the phase space of f(R)-gravity
No full textWe propose a new dynamical system formalism for the analysis of f(R) cosmologies. The new approach eliminates the need for cumbersome inversions to close the dynamical system and allows the analysis of the phase space of f(R)-gravity models which cannot be investigated using the standard technique. Differently form previously proposed similar techniques, the new method is constructed in such a way to associate to the fixed points scale factors, which contain four integration constants (i.e. solutions of fourth order differential equations). In this way a new light is shed on the physical meaning of the fixed points. We apply this technique to some f(R) Lagrangians relevant for inflationary and dark energy models
Reconstructing static spherically symmetric metrics in general relativity
No full textWe present a general method to reconstruct static spherically symmetric metrics in general relativity based on the 1+1+2 covariant approach. This method allows a more complete exploration of the properties of these metrics in the case of a generic fluid and in the presence of a scalar field. A number of new exact solutions are reconstructed in these cases
Generalising the coupling between spacetime and matter
No full textWe explore the idea that the coupling between matter and spacetime is more complex than the one originally envisioned by Einstein. We propose that such coupling takes the form of a new fundamental tensor in the Einstein field equations. We then show that the introduction of this tensor can account for dark phenomenology in General Relativity, maintaining a weak field limit compatible with standard Newtonian gravitation. The same paradigm can be applied any other theory of gravitation. We show, as an example, that in the context of conformal gravity a generalised coupling is able to solve compatibility issues between the matter and the gravitational sector
Covariant Tolman-Oppenheimer-Volkoff equations. II. The anisotropic case
No full textWe generalize the covariant Tolman-Oppenheimer-Volkoff equations proposed in Carloni and Vernieri [Phys. Rev. D 97, 124056 (2018).PRVDAQ0556-282110.1103/PhysRevD.97.124056]. to the case of static and spherically symmetric spacetimes with anisotropic sources. The extended equations allow a detailed analysis of the role of the anisotropic terms in the interior solution of relativistic stars and lead to the generalization of some well-known solutions of this type. We show that, like in the isotropic case, one can define generating theorems for the anisotropic Tolman-Oppenheimer-Volkoff equations. We also find that it is possible to define a reconstruction algorithm able to generate a double infinity of interior solutions. Among these, we derive a class of solutions that can represent "quasi-isotropic" stars
On the anisotropic interior solutions in Hořava gravity and Einstein-æther theory
No full textWe find a reconstruction algorithm able to generate all the static spherically symmetric interior solutions in the framework of Hořava gravity and Einstein-æther theory in the presence of anisotropic fluids. We focus for simplicity on the case of a static æther finding a large class of possible viable interior star solutions which present a very rich phenomenology. We study one illustrative example in more detail
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No full textCovariant Tolman-Oppenheimer-Volkoff equations. I. The isotropic case
No full textWe construct a covariant version of the Tolman-Oppenheimer-Volkoff equations in the case of isotropic sources. The new equations make evident the mathematical problems in the determination of interior solutions of relativistic stellar objects. Using a reconstruction algorithm, we find two physically interesting generalizations of previously known stellar interior solutions. The variables that we use also allow an easier formulation of known generating theorems for solutions associated to relativistic stellar objects
Bounce cosmologies in generalized coupling theories
No full textWe describe an exact solution representing a bouncing cosmology in the Minimal Exponential Measure (MEMe) model. Such a solution, obtained by means of the linearization around small values of the characteristic energy scale q of the theory, has the peculiarity of representing a complete bounce model that can be used to explore quantitative processes in non-singular cosmologies
On the anisotropic interior solutions in Hořava gravity and Einstein-æther theory
No full textWe find a reconstruction algorithm able to generate all the static spherically symmetric interior solutions in the framework of Hořava gravity and Einstein-æther theory in the presence of anisotropic fluids. We focus for simplicity on the case of a static æther finding a large class of possible viable interior star solutions which present a very rich phenomenology. We study one illustrative example in more detail
Gauge invariant perturbations of static spatially compact LRS II spacetimes
No full textWe present a framework to describe completely general first-order perturbations of static, spatially compact, and locally rotationally symmetric class II spacetimes within the theory of general relativity. The perturbation variables are by construction covariant and identification gauge invariant and encompass the geometry and the thermodynamics of the fluid sources. The new equations are then applied to the study of isotropic, adiabatic perturbations. We discuss how the choice of frame in which perturbations are described can significantly simplify the mathematical analysis of the problem and show that it is possible to change frames directly from the linear level equations. We find explicitly that the case of isotropic, adiabatic perturbations can be reduced to a singular Sturm-Liouville eigenvalue problem, and lower bounds for the values of the eigenfrequencies can be derived. These results lay the theoretical groundwork to analytically describe linear, isotropic, and adiabatic perturbations of static, spherically symmetric spacetimes
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