An Exact solution of the Einstein-Maxwell field equations for a conformastationary metric with ma... more An Exact solution of the Einstein-Maxwell field equations for a conformastationary metric with magnetized disk-halos sources is worked out in full. The characterization of the nature of the energy momentum tensor of the source is discussed. All the expressions are presented in terms of a solution of the Laplace's equation. A ``generalization'' of the Kuzmin solution of the Laplace's equations is used as a particular example. The solution obtained is asymptotically flat in general and turns out to be free of singularities. All the relevant quantities show a reasonable physical behaviour.
We apply the Darmois and the C3 matching conditions to three different spherically symmetric spac... more We apply the Darmois and the C3 matching conditions to three different spherically symmetric spacetimes. The exterior spacetime is described by the Schwarzschild vacuum solution whereas for the interior counterpart we choose different perfect fluid solutions with the same symmetry. We show that Darmois matching conditions are satisfied in all the three cases whereas the C3 conditions are not fulfilled. We argue that this difference is due to a non-physical behavior of the pressure on the matching surface.
A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativi... more A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativistic thin disks constituted by two perfect charged fluids is presented. Describing the surface of the disk as a single charged fluid we find explicit expressions for the rest energies, the pressures and the electric charge densities of the two fluids. An explicit example is given. The particular case of the thin disks composed by two charged perfect fluids with barotropic equation of state is also presented.
Applying the Horsk\'y-Mitskievitch conjecture to the empty space solutions of Morgan and Mor... more Applying the Horsk\'y-Mitskievitch conjecture to the empty space solutions of Morgan and Morgan due to the gravitational field of a finite disk, we have obtained the corresponding solutions of the Einstein-Maxwell equations. These solutions represent fields due to magnetized static thin disk of finite extension. The resulting expressions are written simply, in terms of oblate spheroidal coordinates. The masses of the disks are finite and the energy-momentum tensor agrees with the energy conditions. The magnetic field and the ...
Abstract: An infinite family of relativistic finite thin disk model with magnetic field is presen... more Abstract: An infinite family of relativistic finite thin disk model with magnetic field is presented. The model is obtained for solving the Einstein-Maxwell equations for static spacetimes by means of the Horsk\'y-Mitskievitch generating conjecture. The vacuum limit of these obtained solutions is the well known Morgan and Morgan solution. The obtained expressions are simply written in terms of oblate spheroidal coordinates. The mass of the disks are finite and the energy-momentum tensor agrees with all the energy conditions. The magnetic field ...
The first fully integrated explicit exact solution of the Einstein field equations corresponding ... more The first fully integrated explicit exact solution of the Einstein field equations corresponding to the superposition of a counterrotating dust disk with a central black hole is presented. The obtained solution represents an infinite annular thin disk (a disk with an inner edge) around the Schwarszchild black hole. The mass of the disk is finite and the energy-momentum tensor agrees with all the energy conditions. Furthermore, the total mass of the disk when the black hole is present is less than the total mass of the disk alone. The solution can also be interpreted as describing a thin disk made of two counterrotanting dust fluids that are also in agreement with all the energy conditions. Additionally, as we will show shortly in a subsequent paper, the above solution is the first one of an infinite family of solutions.
We investigate the motion of test particles in the gravitational field of a static naked singular... more We investigate the motion of test particles in the gravitational field of a static naked singularity generated by a mass distribution with quadrupole moment. We use the quadrupole-metric (q−metric) which is the simplest generalization of the Schwarzschild metric with a quadrupole parameter. We study the influence of the quadrupole on the motion of massive test particles and photons and show that the behavior of the geodesics can drastically depend on the values of the quadrupole parameter. In particular, we prove explicitly that the perihelion distance depends on the value of the quadrupole. Moreover, we show that an accretion disk on the equatorial plane of the quadrupole source can be either continuous or discrete, depending on the value of the quadrupole. The inner radius of the disk can be used in certain cases to determine the value of the quadrupole parameter. The case of a discrete accretion is interpreted as due to the presence of repulsive gravity generated by the naked singularity. Radial geodesics are also investigated and compared with the Schwarzschild counterparts.
""We present an exact, axially symmetric, static, vacuum solution for f (R) gravity in Weyl’s can... more ""We present an exact, axially symmetric, static, vacuum solution for f (R) gravity in Weyl’s canonical coordinates. We obtain a
general explicit expression for the dependence of d f (R)/dR upon the r and z coordinates and then the corresponding explicit form
of f (R), which must be consistent with the field equations. We analyze in detail the modified Schwarzschild solution in prolate
spheroidal coordinates. Finally, we study the curvature invariants and show that, in the case of f (R)\neq R, this solution corresponds
to a naked singularity.
""
An Exact solution of the Einstein-Maxwell field equations for a conformastationary metric w... more An Exact solution of the Einstein-Maxwell field equations for a conformastationary metric with magnetized disk-halos sources is worked out in full. The characterization of the nature of the energy momentum tensor of the source is discussed. All the expressions are presented in terms of a solution of the Laplace's equation. A ``generalization'' of the Kuzmin solution of the Laplace's equations is used as a particular example. The solution obtained is asymptotically flat in general and turns out to be free of singularities. All the relevant quantities show a reasonable physical behaviour.
We present a relativistic model describing a thin disk system composed of two fluids. The system ... more We present a relativistic model describing a thin disk system composed of two fluids. The system is surrounded by a halo in the presence of a non-trivial electromagnetic field. We show that the model is compatible with the variational multi-fluid thermodynamics formalism, allowing us to determine all the thermodynamic variables associated with the matter content of the disk. The asymptotic behaviour of these quantities indicates that the single fluid interpretation should be abandoned in favour of a two-fluid model.
An Exact solution of the Einstein-Maxwell field equations for a conformastationary metric with ma... more An Exact solution of the Einstein-Maxwell field equations for a conformastationary metric with magnetized disk-halos sources is worked out in full. The characterization of the nature of the energy momentum tensor of the source is discussed. All the expressions are presented in terms of a solution of the Laplace's equation. A ``generalization'' of the Kuzmin solution of the Laplace's equations is used as a particular example. The solution obtained is asymptotically flat in general and turns out to be free of singularities. All the relevant quantities show a reasonable physical behaviour.
We apply the Darmois and the C3 matching conditions to three different spherically symmetric spac... more We apply the Darmois and the C3 matching conditions to three different spherically symmetric spacetimes. The exterior spacetime is described by the Schwarzschild vacuum solution whereas for the interior counterpart we choose different perfect fluid solutions with the same symmetry. We show that Darmois matching conditions are satisfied in all the three cases whereas the C3 conditions are not fulfilled. We argue that this difference is due to a non-physical behavior of the pressure on the matching surface.
A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativi... more A method to describe exact solutions of the Einstein-Maxwell field equations in terms of relativistic thin disks constituted by two perfect charged fluids is presented. Describing the surface of the disk as a single charged fluid we find explicit expressions for the rest energies, the pressures and the electric charge densities of the two fluids. An explicit example is given. The particular case of the thin disks composed by two charged perfect fluids with barotropic equation of state is also presented.
Applying the Horsk\'y-Mitskievitch conjecture to the empty space solutions of Morgan and Mor... more Applying the Horsk\'y-Mitskievitch conjecture to the empty space solutions of Morgan and Morgan due to the gravitational field of a finite disk, we have obtained the corresponding solutions of the Einstein-Maxwell equations. These solutions represent fields due to magnetized static thin disk of finite extension. The resulting expressions are written simply, in terms of oblate spheroidal coordinates. The masses of the disks are finite and the energy-momentum tensor agrees with the energy conditions. The magnetic field and the ...
Abstract: An infinite family of relativistic finite thin disk model with magnetic field is presen... more Abstract: An infinite family of relativistic finite thin disk model with magnetic field is presented. The model is obtained for solving the Einstein-Maxwell equations for static spacetimes by means of the Horsk\'y-Mitskievitch generating conjecture. The vacuum limit of these obtained solutions is the well known Morgan and Morgan solution. The obtained expressions are simply written in terms of oblate spheroidal coordinates. The mass of the disks are finite and the energy-momentum tensor agrees with all the energy conditions. The magnetic field ...
The first fully integrated explicit exact solution of the Einstein field equations corresponding ... more The first fully integrated explicit exact solution of the Einstein field equations corresponding to the superposition of a counterrotating dust disk with a central black hole is presented. The obtained solution represents an infinite annular thin disk (a disk with an inner edge) around the Schwarszchild black hole. The mass of the disk is finite and the energy-momentum tensor agrees with all the energy conditions. Furthermore, the total mass of the disk when the black hole is present is less than the total mass of the disk alone. The solution can also be interpreted as describing a thin disk made of two counterrotanting dust fluids that are also in agreement with all the energy conditions. Additionally, as we will show shortly in a subsequent paper, the above solution is the first one of an infinite family of solutions.
We investigate the motion of test particles in the gravitational field of a static naked singular... more We investigate the motion of test particles in the gravitational field of a static naked singularity generated by a mass distribution with quadrupole moment. We use the quadrupole-metric (q−metric) which is the simplest generalization of the Schwarzschild metric with a quadrupole parameter. We study the influence of the quadrupole on the motion of massive test particles and photons and show that the behavior of the geodesics can drastically depend on the values of the quadrupole parameter. In particular, we prove explicitly that the perihelion distance depends on the value of the quadrupole. Moreover, we show that an accretion disk on the equatorial plane of the quadrupole source can be either continuous or discrete, depending on the value of the quadrupole. The inner radius of the disk can be used in certain cases to determine the value of the quadrupole parameter. The case of a discrete accretion is interpreted as due to the presence of repulsive gravity generated by the naked singularity. Radial geodesics are also investigated and compared with the Schwarzschild counterparts.
""We present an exact, axially symmetric, static, vacuum solution for f (R) gravity in Weyl’s can... more ""We present an exact, axially symmetric, static, vacuum solution for f (R) gravity in Weyl’s canonical coordinates. We obtain a
general explicit expression for the dependence of d f (R)/dR upon the r and z coordinates and then the corresponding explicit form
of f (R), which must be consistent with the field equations. We analyze in detail the modified Schwarzschild solution in prolate
spheroidal coordinates. Finally, we study the curvature invariants and show that, in the case of f (R)\neq R, this solution corresponds
to a naked singularity.
""
An Exact solution of the Einstein-Maxwell field equations for a conformastationary metric w... more An Exact solution of the Einstein-Maxwell field equations for a conformastationary metric with magnetized disk-halos sources is worked out in full. The characterization of the nature of the energy momentum tensor of the source is discussed. All the expressions are presented in terms of a solution of the Laplace's equation. A ``generalization'' of the Kuzmin solution of the Laplace's equations is used as a particular example. The solution obtained is asymptotically flat in general and turns out to be free of singularities. All the relevant quantities show a reasonable physical behaviour.
We present a relativistic model describing a thin disk system composed of two fluids. The system ... more We present a relativistic model describing a thin disk system composed of two fluids. The system is surrounded by a halo in the presence of a non-trivial electromagnetic field. We show that the model is compatible with the variational multi-fluid thermodynamics formalism, allowing us to determine all the thermodynamic variables associated with the matter content of the disk. The asymptotic behaviour of these quantities indicates that the single fluid interpretation should be abandoned in favour of a two-fluid model.
An Exact solution of the Einstein-Maxwell field equations for a conformastatic metric with magnet... more An Exact solution of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources is study. In this context, effective potential are studied in order to understand the dynamics of the magnetic field in galaxies. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. In this particular case, we investigate the main physical properties of equatorial circular orbits and related effective potentials. In addition, we obtain an effective analytic expression for the perihelion advance of test particles. Our theoretical predictions are compared with the observational data calibrated with the ephemerides of the planets of the Solar system and the Moon (EPM2011). We show that, in general, the magnetic punctual mass predicts values that are in better agreement with observations than the values predicted in Einstein gravity alone.
The Newman-Janis Ansatz was used first to obtain the stationary Kerr metric from the static Schwa... more The Newman-Janis Ansatz was used first to obtain the stationary Kerr metric from the static Schwarzschild metric. Many works have been devoted to investigate the physical significance of this Ansatz, but no definite answer has been given so far. We show that this Ansatz can be applied in general to conformastatic vacuum metrics, and leads to stationary generalizations which, however, do not preserve the conformal symmetry. We investigate also the particular case when the seed solution is given by the Schwarzschild spacetime and show that the resulting rotating configuration does not correspond to a vacuum solution, even in the limiting case of slow rotation. In fact, it describes in general a relativistic fluid with anisotropic pressure and heat flux. This implies that the Newman-Janis Ansatz strongly depends on the choice of representation for the seed solution. We interpret this result as as a further indication of its applicability limitations.
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Papers by Antonio C. Gutierrez-Pineres
general explicit expression for the dependence of d f (R)/dR upon the r and z coordinates and then the corresponding explicit form
of f (R), which must be consistent with the field equations. We analyze in detail the modified Schwarzschild solution in prolate
spheroidal coordinates. Finally, we study the curvature invariants and show that, in the case of f (R)\neq R, this solution corresponds
to a naked singularity.
""
disk-halos sources is worked out in full. The characterization of the nature of the energy momentum tensor of the
source is discussed. All the expressions are presented in terms of a solution of the Laplace's equation. A
``generalization'' of the Kuzmin solution of the Laplace's equations is used as a particular example. The
solution obtained is asymptotically flat in general and turns out to be free of singularities. All the relevant
quantities show a reasonable physical behaviour.
general explicit expression for the dependence of d f (R)/dR upon the r and z coordinates and then the corresponding explicit form
of f (R), which must be consistent with the field equations. We analyze in detail the modified Schwarzschild solution in prolate
spheroidal coordinates. Finally, we study the curvature invariants and show that, in the case of f (R)\neq R, this solution corresponds
to a naked singularity.
""
disk-halos sources is worked out in full. The characterization of the nature of the energy momentum tensor of the
source is discussed. All the expressions are presented in terms of a solution of the Laplace's equation. A
``generalization'' of the Kuzmin solution of the Laplace's equations is used as a particular example. The
solution obtained is asymptotically flat in general and turns out to be free of singularities. All the relevant
quantities show a reasonable physical behaviour.