General Relativity and Gravitation最新文献

In this work, we investigated an inhomogeneous spherically symmetric star consisting of dust fluid and dark energy components. We obtained similarity solutions for the energy density of the inhomogeneous dust fluid (rho (t,r)), dark energy (rho _{DE}(t,r)), and the mass function inside the star m(t, r). The symmetries of Einstein field equations for this model are derived using the symmetry group analysis method, where the Einstein field equations have been reduced into nonlinear ordinary differential equations (NODEs). Some interesting explicit analytical solutions are obtained for the reduced NODEs. Consequently, a new class of similarity solutions has been obtained for the energy density of the inhomogeneous dust fluid and dark energy as functions of coordinates t and r. These solutions are obtained when the star is composed of both dust fluid and dark energy components, dark energy components only, and dust fluid only. When the star is composed of dust fluid only, we discussed the possibility of black hole formation by assuming that the collapsing star is not initially trapped. Graphical representations of some solutions are given and discussed in the last section.

The geodesic motion in a Lorentzian spacetime can be described by trajectories in a 3-dimensional Riemannian metric. In this article we present a generalized Jacobi metric obtained from projecting a Lorentzian metric over the directions of its Killing vectors. The resulting Riemannian metric inherits the geodesics for asymptotically flat spacetimes including the stationary and axisymmetric ones. The method allows us to find Riemannian metrics in three and two dimensions plus the radial geodesic equation when we project over three different directions. The 3-dimensional Riemannian metric reduces to the Jacobi metric when static, spherically symmetric and asymptotically flat spacetimes are considered. However, it can be calculated for a larger variety of metrics in any number of dimensions. We show that the geodesics of the original spacetime metrics are inherited by the projected Riemannian metric. We calculate the Gaussian and geodesic curvatures of the resulting 2-dimensional metric, we study its near horizon and asymptotic limit. We also show that this technique can be used for studying the violation of the strong cosmic censorship conjecture in the context of general relativity.

This paper is the first in a sequence of three devoted to the formulation of a theory of self-gravitating anisotropic fluids in both Newtonian and relativistic gravity. In this first paper we set the stage, place our work in the context of a vast literature on anisotropic stars in general relativity, and provide an overview of the results obtained in the remaining two papers. In the second paper we develop the Newtonian theory, inspired by a familiar example of an anisotropic fluid, the (nematic) liquid crystal, and apply the theory to the construction of Newtonian stellar models. In the third paper we port the theory to general relativity, and exploit it to obtain relativistic stellar models. In both cases, Newtonian and relativistic, the state of the fluid is described by the familiar variables of an isotropic fluid (such as mass density and velocity field), to which we adjoin a director vector, which defines a locally preferred direction within the fluid. The director field contributes to the kinetic and potential energies of the fluid, and therefore to its dynamics. Both the Newtonian and relativistic theories are defined in terms of an action functional; variation of the action gives rise to dynamical equations for the fluid and gravitational field. While each theory is formulated in complete generality, in these papers we apply them to the construction of stellar models by restricting the fluid configurations to be static and spherically symmetric. We find that the equations of anisotropic stellar structure are generically singular at the stellar surface. To avoid a singularity, we postulate the existence of a phase transition at a critical value of the mass density; the fluid is anisotropic at high densities, and goes to an isotropic phase at low densities. In the case of Newtonian stars, we find that sequences of equilibrium configurations terminate at a maximum value of the central density; beyond this maximum the density profile becomes multi-valued within the star, and the model therefore becomes unphysical. In the case of relativistic stars, this phenomenon typically occurs beyond the point at which the stellar mass achieves a maximum, and we conjecture that this point marks the onset of a dynamical instability to radial perturbations (as it does for isotropic stars). Also in the case of relativistic stars, we find that for a given equation of state and a given assignment of central density, anisotropic stellar models are always less compact than isotropic models.

This paper is the second in a sequence of three devoted to the formulation of a theory of self-gravitating anisotropic fluids in both Newtonian gravity and general relativity. In the first paper we set the stage, placed our work in context, and provided an overview of the results obtained in this paper and the next. In this second paper we develop the Newtonian theory, inspired by a real-life example of an anisotropic fluid, the (nematic) liquid crystal. We apply the theory to the construction of static and spherical stellar models. In the third paper we port the theory to general relativity, and exploit it to build relativistic stellar models. In addition to the usual fluid variables (mass density, velocity field), the Newtonian theory features a director vector field (varvec{c}(t,varvec{x})), whose length provides a local measure of the size of the anisotropy, and whose direction gives the local direction of anisotropy. The theory is defined in terms of a Lagrangian which implicates all the relevant forms of energy: kinetic energy (with contributions from the velocity field and the time derivative of the director vector), internal energy (with isotropic and anisotropic contributions), gravitational interaction energy, and gravitational-field energy. This Lagrangian is easy to motivate, and it provides an excellent starting point for a relativistic generalization in the third paper. The equations of motion for the fluid, and Poisson’s equation for the gravitational potential, follow from a variation of the action functional, given by the time integral of the Lagrangian. Because our stellar models feature a transition from an anisotropic phase at high density to an isotropic phase at low density, a substantial part of the paper is devoted to the development of a mechanics for the interface fluid, which mediates the phase transition.

This is the third and final entry in a sequence of papers devoted to the formulation of a theory of self-gravitating anisotropic fluids in Newtonian gravity and general relativity. In the first paper we placed our work in context and provided an overview of the results obtained in the second and third papers. In the second paper we took the necessary step of elaborating a Newtonian theory, and exploited it to build anisotropic stellar models. In this third paper we elevate the theory to general relativity, and apply it to the construction of relativistic stellar models. The relativistic theory is crafted by promoting the fluid variables to a curved spacetime, and promoting the gravitational potential to the spacetime metric. Thus, the director vector, which measures the local magnitude and direction of the anisotropy, is now a four-dimensional vector, and to keep the number of independent degrees of freedom at three, it is required to be orthogonal to the fluid’s velocity vector. The Newtonian action is then generalized in a direct and natural way, and dynamical equations for all the relevant variables are once more obtained through a variational principle. We specialize our relativistic theory of a self-gravitating anisotropic fluid to static and spherically symmetric configurations, and thus obtain models of anisotropic stars in general relativity. As in the Newtonian setting, the models feature a transition from an anisotropic phase at high density to an isotropic phase at low density. Our survey of stellar models reveals that for the same equations of state and the same central density, anisotropic stars are always less compact than isotropic stars.

The gauge formalism in telepalallel gravity provides an interesting viewpoint to describe interactions according to an anholonomic observer’s tetrad basis. Without going into assessing the complete viability of quantization in an early stage, this paper explores classical gravity within the framework of a classical-to-quantum bridge between the SU(1, 3) Yang–Mills gauge formalism and the gauge-like treatment of teleparallel gravity. Specifically, the perturbed spacetime algebra with Weitzenböck connection can be assimilated to a local complexification based on the SU(1, 3) Yang–Mills theory, what we call hypercolor or, simply, color. The formulation of the hypercolor dynamics is build by a translational gauge, as in the teleparallel gravities. In particular, this work analyses small perturbations of a metric decomposition related to the Wilson line and the Kaluza–Klein metric, but obtaining electrodynamics in four dimensions. The spacetime coordinates are now matrices that represent elements of the (mathfrak {su}(1,3)) algebra. To make compatible the formulation of a colored gravity with the Lorentz force and the Maxwell equations, it is enough to define every energy potential origin as 0 in the event horizon instead of the classic zero potential at infinity. Under the colored gravity framework, standard electromagnetism can be obtained as a particular abelian case.

In a work by Visser, Bassett and Liberati (VBL) (Nucl Phys B Proc Suppl 88:267, 2000) a relation was suggested between a null energy condition and the censorship of superluminal behaviour. Their result was soon challenged by Gao and Wald (Class Quantum Grav 17:4999, 2000) who argued that this relation is gauge dependent and therefore not appropriate to find such connections. In this paper, we clear up this controversy by showing that both papers are correct but need to be interpreted in distinct paradigms. In this context, we introduce a new paradigm to interpret gravitational phenomena, which we call the Harmonic Background Paradigm. This harmonic background paradigm starts from the idea that there exists a more fundamental background causality provided by a flat spacetime geometry. One of the consequences of this paradigm is that the VBL relation can provide an explanation of why gravity is attractive in all standard weak-field situations.

The Israel–Carter theorem (also known as the “no-hair theorem”) puts a restriction on the existence of parameters other than mass, electric charge, and angular momentum of a black hole. In this context, Bekenstein proposed no-hair theorems in various black hole models with neutral and electrically charged scalar fields. In this paper, we take the Einstein–Maxwell-charged scalar model with an electrically charged scalar field gauge-coupled to the Maxwell field surrounding a charged black hole with a static spherically symmetric metric. In particular, we consider a quadratic scalar potential without any higher order terms and we do not impose any restriction on the magnitude of the scalar charge with respect to the black hole charge. With this setting, we ascertain the validity of all energy conditions coupled with the causality condition, suggesting the possibility of existence of charged hairy solutions. Consequently, we obtain, by exact numerical integration, detailed solutions of the field equations that incorporate backreaction on the spacetime due to the presence of the charged scalar field. The solutions exhibit damped oscillatory behaviours for the charged scalar hair. We also find that the electric potential is a monotonic function of the radial coordinate, as required by electrodynamics. In order to ascertain the existence of our charged hairy solutions, we carry out dynamic stability analyses against time-dependant perturbations about the static solutions. For a definite conclusion, we employ two different methodologies. The first methodology involves a Sturm–Liouville equation, whereas the second methodology employs a Schrödinger-like equation, for the dynamic perturbations. We find that our solutions are stable against time-dependant perturbations by both methodologies, confirming the existence of the charged hairy solutions.

In the era of gravitational waves physics, when detections of wave fronts are increasing in number, sensitivity, frequencies and distances, gravitational physics has entered a period of maximum activity and brilliance. This has open a new window where General Relativity can be challenged in both weak as strong-field regimes. In this paper, we focus on the analysis of gravitational waves propagation and emission in the weak-field regime for gravitational theories within the Palatini formalism. Our results show that gravitational waves propagation in vacuum matches General Relativity predictions as well as the functional form of the multipolar expansion when considering weak sources. However, a rescaling of the gravitational constant arises, which affects the energy radiated by the gravitational waves emission.

Neutron stars (NSs) provide a unique laboratory to study matter under extreme densities. Recent observations from gravitational and electromagnetic waves have enabled constraints on NS properties, such as tidal deformability (related to the tidal Love number) and stellar compactness. Although each of these two NS observables depends strongly on the stellar internal structure, the relation between them (called the Love–C relation) is known to be equation-of-state insensitive. In this study, we investigate the effects of a possible crystalline phase in the core of hybrid stars (HSs) on the mass–radius and Love–C relations, where HSs are a subclass of NS models with a quark matter core and a nuclear matter envelope with a sharp phase transition in between. We find that both the maximum mass and the corresponding radius increase as one increases the stiffness of the quark matter core controlled by the speed of sound, while the density discontinuity at the nuclear-quark matter transition effectively softens the equations of state. Deviations of the Love–C relation for elastic HSs from that of fluid NSs become more pronounced with a larger shear modulus, lower transition pressure, and larger density gap and can be as large as 60%. These findings suggest a potential method for testing the existence of distinct phases within HSs, though deviations are not large enough to be detected with current measurements of the tidal deformability and compactness.