25 research outputs found
Two-dimensional Einstein manifolds in geometrothermodynamics
We present a class of thermodynamic systems with constant thermodynamic
curvature which, within the context of geometric approaches of thermodynamics,
can be interpreted as constant thermodynamic interaction among their
components. In particular, for systems constrained by the vanishing of the
Hessian curvature we write down the systems of partial differential equations.
In such a case it is possible to find a subset of solutions lying on a
circumference in an abstract space constructed from the first derivatives of
the isothermal coordinates. We conjecture that solutions on the characteristic
circumference are of physical relevance, separating them from those of pure
mathematical interest. We present the case of a one-parameter family of
fundamental relations that -- when lying in the circumference -- describe a
polytropic fluid
Counterrotating Dust Disk Around a Schwarzschild Black Hole: New Fully Integrated Explicit Exact Solution
The first fully integrated explicit exact solution of Einstein's 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 Schwarsz-child black hole, and the corresponding to energy-momentum tensor agrees with all the energy conditions. The solution can also be interpreted as des-cribing a thin disk made of two counterrotating dust fluids that are also in agreement with all the energy conditions.
 
Exact relativistic models of thin disks around static black holes in a magnetic field
The exact superposition of a central static black hole with surrounding thin
disk in presence of a magnetic field is investigated. We consider two models of
disk, one of infinite extension based on a Kuzmin-Chazy-Curzon metric and other
finite based on the first Morgan-Morgan disk. We also analyze a simple model of
active galactic nuclei consisting of black hole, a Kuzmin-Chazy-Curzon disk and
two rods representing jets, in presence of magnetic field. To explain the
stability of the disks we consider the matter of the disk made of two
pressureless streams of counterrotating charged particles (counterrotating
model) moving along electrogeodesic. Using the Rayleigh criterion we derivate
for circular orbits the stability conditions of the particles of the streams.
The influence of the magnetic field on the matter properties of the disk and on
its stability are also analyzed.Comment: 17 pages, 14 figures. arXiv admin note: text overlap with
arXiv:gr-qc/0409109 by other author
A family of relativistic charged thin disks with an inner edge
A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.
A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.
 
A family of relativistic charged thin disks with an inner edge
A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.
A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.
 
Relativistic static thin dust disks with an inner edge: An infinite family of new exact solutions
An infinite family of new exact solutions of the Einstein vacuum equations
for static and axially symmetric spacetimes is presented. All the metric
functions of the solutions are explicitly computed and the obtained expressions
are simply written in terms of oblate spheroidal coordinates. Furthermore, the
solutions are asymptotically flat and regular everywhere, as it is shown by
computing all the curvature scalars. These solutions describe an infinite
family of thin dust disks with a central inner edge, whose energy densities are
everywhere positive and well behaved, in such a way that their energy-momentum
tensor are in fully agreement with all the energy conditions. Now, although the
disks are of infinite extension, all of them have finite mass. The
superposition of the first member of this family with a Schwarzschild black
hole was presented previously [G. A. Gonz\'alez and A. C.
Guti\'errez-Pi\~neres, arXiv: 0811.3002v1 (2008)], whereas that in a subsequent
paper a detailed analysis of the corresponding superposition for the full
family will be presented.Comment: 9 pages, 3 figure
Finite axisymmetric charged dust disks in conformastatic spacetimes
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 Gonz\'alez 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.Comment: Submitted to PR
Electromagnetic sources distributed on shells in a Schwarzschild background
In the Introduction we briefly recall our previous results on stationary
electromagnetic fields on black-hole backgrounds and the use of spin-weighted
spherical harmonics. We then discuss static electric and magnetic test fields
in a Schwarzschild background using some of these results. As sources we do not
consider point charges or current loops like in previous works, rather, we
analyze spherical shells with smooth electric or magnetic charge distributions
as well as electric or magnetic dipole distributions depending on both angular
coordinates. Particular attention is paid to the discontinuities of the field,
of the 4-potential, and their relation to the source.Comment: dedicated to Professor Goldberg's 86th birthday, accepted for
publication in Gen. Relat. Gravit., 12 page