arXiv subjects
Publications and source records attributed to Guillermo A. Gonzalez.
The innermost stable circular orbits (ISCOs) around rapidly rotating neutron stars are studied in dilatonic Einstein-Gauss-Bonnet theory. Universal relations for properly scaled ISCO properties are extended from General Relativity to dilatonic Einstein-Gauss-Bonnet theory and additional relations are obtained.
We present the first family of magnetically polarized equilibrium tori around a Kerr black hole. The models were obtained in the test fluid approximation by assuming that the tori is a linear media, making it is possible to characterize the magnetic polarization of the fluid through the magnetic susceptibility $χ_{m}$. The magnetohydrodynamic (MHD) structure of the models was solved by following the Komissarov approach, but with the aim of including the magnetic polarization of the fluid, the integrability condition for the magnetic counterpart was modified. We build two kinds of magnetized tori depending on whether the magnetic susceptibility is constant in space or not. In the models with constant $χ_{m}$, we find that the paramagnetic tori ($χ_{m}>0$) are more dense and less magnetized than the diamagnetic ones ($χ_{m}<0$) in the region between the inner edge, $r_{in}$, and the center of the disk, $r_{c}$; however, we find the opposite behavior for $r>r_{c}$. Now, in the models with non-constant $χ_{m}$, the tori become more magnetized than the Komissarov solution in the region where $\partialχ_{m}/\partial r<0$, and less magnetized when $\partialχ_{m}/\partial r>0$. Nevertheless, it is worth mentioning that in all solutions presented in this paper the magnetic pressure is greater than the hydrodynamic pressure. These new equilibrium tori can be useful for studying the accretion of a magnetic media onto a rotating black hole.
We explore the influence of density fluctuations on isotropic and anisotropic configurations, extending the concept of cracking for general relativistic fluid spheres. This concept, conceived to describe the behaviour of anisotropic matter distributions just after its departure from equilibrium, could provide some insight on potential instabilities and future evolution of relativistic fluids. We have refined the idea of cracking, considering local fluctuations --represented by any function of compact support defined in a closed interval-- and their effect on the state variables and their gradients through "barotropic" equations of state, $P = P(ρ)$ and $P_{\perp}= P_{\perp}(ρ)$. Under this approach it is found that both isotropic and anisotropic models could exhibit cracking (or overturning), and that previously crackable anisotropic models become uncrackable.
We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.
Rotating disks with nonzero radial pressure and finite radius are studied. The models are based in the Taub-NUT metric and constructed using the well-known ``displace, cut and reflect'' method. We find that the disks are made of perfect fluids with constant energy density and pressure. The energy density is negative, but the effective Newotnian density is possitive as the strong energy condition requires. We also find that the disks are not stable under radial perturbations and that there are regions of the disks where the particles move with superluminal velocities.
A detailed study is presented of the counterrotating model (CRM) for generic electrovacuum static axially symmetric relativistic thin disks without radial pressure. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We also find explicit expressions for the energy densities, charge densities and velocities of the counterrotating fluids. We then show that this constraint can be satisfied if we take the two counterrotating streams as circulating along electro-geodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electro-geodesics nor take the two counterrotating tangential velocities as equal and opposite. Four simple families of models of counterrotating charged disks based on Chazy-Curzon-like, Zipoy-Voorhees-like, Bonnor-Sackfield-like and Kerr-like electrovacuum solutions are considered where we obtain some disks with a CRM well behaved. The models are constructed using the well-known ``displace, cut and reflect'' method extended to solutions of vacuum Einstein-Maxwell equations.
A new formalism is presented for finding equilibrium distribution functions for axisymmetric systems. The formalism, obtainded by using the concept of fractional derivatives, generalizes the methods of Fricke (1952), Kalnajs (1972) and Jiang & Ossipkov (2007), and has the advantage that can be applied to a wider variety of models. We found that this approach can be applied both to tridimensional systems and to flat systems, without the necessity of dealing with a pseudo-volume mass density. As an application, we obtain the distribution functions of the Binney's logarithmic model and of the Mestel disc.
Regular and chaotic test particle motion in gravitational fields due to stellar bodies with quadrupolar and octupolar deformation are studied using Poincare surfaces of section. In first instance, we analyze the purely Newtonian case and we find that the octupolar term induces a distortion in the KAM curves corresponding to regular trajectories as well as an increase in chaoticity, even in the case corresponding to oblate deformation. Then we examine the effect of the first general relativistic corrections, provided by the post Newtonian approach. For typical values of the post Newtonian multipoles we find that the phase-space structure practically remains the same as in the classical case, whereas that for certain larger values of these multipoles the chaoticity vanishes. This important fact provides an interesting example of a situation where a non-integrable dynamical system becomes integrable through the introduction of a large perturbation.
We present two formulations of Fokker-Planck-Rosenbluth-type (FPR) equations for many-particle self-gravitating systems, with first order relativistic corrections in the post-Newtonian approach (1PN). The first starts from a covariant Fokker-Planck equation for a simple gas, introduced recently by G. Chacon-Acosta and G. Kremer (Phys. Rev. E 76, 021201, 2007). The second derivation is based on the establishment of an 1PN-BBGKY hierarchy, developed systematically from the 1PN microscopic law of force and using the Klimontovich-Dupree (KD) method. We close the hierarchy by the introduction of a two-point correlation function that describes adequately the relaxation process. This picture reveals an aspect that is not considered in the first formulation: the contribution of ternary correlation patterns to the diffusion coefficients, as a consequence of the nature of 1PN interaction. Both formulations can be considered as a generalization of the equation derived by Rezania and Sobouti (Astron. Astrophys. 54, 1110-1114, 2000), to stellar systems where the relativistic effects of gravitation play a significant role.
An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, it is assumed that the metric function and the electric potential are functionally related and that the metric function is functionally dependent of another auxiliary function, which is taken as a solution of Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by González and Reina (MNRAS 371, 1873, 2006), which is expressed in terms of the oblate spheroidal coordinates and represents a well behaved family of finite axisymmetric flat galaxy models. The so obtained relativistic thin disks have then a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor it agrees with all the energy conditions.
An infinite family of axially symmetric thin disks of finite radius is presented. The family of disks is obtained by means of a method developed by Hunter and contains, as its first member, the Kalnajs disk. The surface densities of the disks present a maximum at the center of the disk and then decrease smoothly to zero at the edge, in such a way that the mass distribution of the higher members of the family is more concentrated at the center. The first member of the family have a circular velocity proportional to the radius, representing thus a uniformly rotating disk. On the other hand, the circular velocities of the other members of the family increases from a value of zero at the center of the disks until a maximum and then decreases smoothly until a finite value at the edge of the disks, in such a way that for the higher members of the family the maximum value of the circular velocity is attained nearest the center of the disks.
The motion of test particles in the gravitational fields generated by the first four members of the infinite family of generalized Kalnajs discs, is studied. In first instance, we analyze the stability of circular orbits under radial and vertical perturbations and describe the behavior of general equatorial orbits and so we find that radial stability and vertical instability dominate such disc models. Then we study bounded axially symmetric orbits by using the Poincare surfaces of section and Lyapunov characteristic numbers and find chaos in the case of disc-crossing orbits and completely regular motion in other cases.
We present the formulation of a new infinite family of self-consistent stellar models, designed to describe axisymmetric flat galaxies. The corresponding density-potential pair is obtained as a superposition of members belonging to the generalized Kalnajs family, by imposing the condition that the density can be expressed as a regular function of the gravitational potential, in order to derive analytically the corresponding equilibrium distribution functions (DF). The resulting models are characterized by a well-behaved surface density, as in the case of generalized Kalnajs discs. Then, we present a study of the kinematical behavior which reveals, in some particular cases, a very satisfactory behavior of the rotational curves (without the assumption of a dark matter halo). We also analyze the equatorial orbit's stability and Poincare surfaces of section are performed for the 3-dimensional orbits. Finally, we obtain the corresponding equilibrium DFs, using the approaches introduced by Kalnajs (Ap. J., 205, 751, 1976) and Dejonghe (Phys. Rep., 133 (3-4), 217, 1986).
Two families of exact simple solutions of Einstein field equations for inhomogeneous stiff cosmologies are presented. The method to obtain the solutions is based on the introduction of auxiliary functions in order to cast the Einstein equations in such a way that can be explicitly integrated. Now, despite of the equations are mathematically equivalent to the equations obtained when the source of matter is a scalar field, is worth to mention that the source that we consider is not a scalar field but a perfect fluid with the stiff equation of state. The obtained solutions are expressed in terms of simple functions of the used coordinates and two families of particular solutions are considered. The geometrical and kinematical properties of the solutions are then analyzed and the parameters are restricted in order to have a physically acceptable behavior. The two particular solutions are of the Petrov type I, the first one being regular everywhere whereas the second one presents a big-bang singularity. Now, for a particular value of one of the parameters, the second particular solution is a vacuum solution of the Bianchi I type that reduces to the Kasner solution.
A method to construct exact general relativistic thick disks that is a simple generalization of the ``displace, cut and reflect'' method commonly used in Newtonian, as well as, in Einstein theory of gravitation is presented. This generalization consists in the addition of a new step in the above mentioned method. The new method can be pictured as a ``displace, cut, {\it fill} and reflect'' method. In the Newtonian case, the method is illustrated in some detail with the Kuzmin-Toomre disk. We obtain a thick disk with acceptable physical properties. In the relativistic case two solutions of the Weyl equations, the Weyl gamma metric (also known as Zipoy-Voorhees metric) and the Chazy-Curzon metric are used to construct thick disks. Also the Schwarzschild metric in isotropic coordinates is employed to construct another family of thick disks. In all the considered cases we have non trivial ranges of the involved parameter that yield thick disks in which all the energy conditions are satisfied.
A detailed study of the Counter-Rotating Model (CRM) for generic finite static axially symmetric thin disks with nonzero radial pressure is presented. We find a general constraint over the counter-rotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counter-rotating perfect fluids. We also found expressions for the energy density and pressure of the counter-rotating fluids. Then we shown that, in general, there is not possible to take the two counter-rotating fluids as circulating along geodesics neither take the two counter-rotating tangential velocities as equal and opposite. An specific example is studied where we obtain some CRM with well defined counter-rotating tangential velocities and stable against radial perturbations. The CRM obtained are in agree with the strong energy condition, but there are regions of the disks with negative energy density, in violation of the weak energy condition.