L. Herrera

Some models of anisotropic spheres in general relativity

A heuristic procedure is developed to obtain interior solutions of Einstein’s equations for anisotropic matter from known solutions for isotropic matter. Five known solutions are generalized to give solutions with anisotropic sources.

Isotropic and anisotropic charged spheres admitting a one‐parameter group of conformal motions

Some exact analytical solutions of the static Einstein–Maxwell equations for perfect and anisotropic fluids were found under the assumption of spherical symmetry and the existence of a one‐parameter group of conformal motions. All solutions are matched to the Reissner‘xnNordstrom metric and possess positive energy density larger than the stresses, everywhere within the sphere.

Anisotropic fluids and conformal motions in general relativity

We study the consequences of the existence of a one‐parameter group of conformal motions for anisotropic matter, in the context of general relativity. It is shown that for a class of conformal motions (special conformal motions), the equation of state is uniquely determined by the Einstein equations. For spherically symmetric and static distributions of matter we found two analytical solutions of the Einstein equations which correspond to isotropic and anisotropic matter, respectively. Both solutions can be matched to the Schwarzschild exterior metric and possesses positive energy density larger than the stresses, everywhere within the sphere.

Anisotropic spheres admitting a one‐parameter group of conformal motions

The Einstein equations for spherically symmetric distributions of anisotropic matter (principal stresses unequal), are solved, assuming the existence of a one‐parameter group of conformal motions. All solutions can be matched with the Schwarzschild exterior metric on the boundary of matter. Two families of solutions represent, respectively, expanding and contracting spheres which asymptotically tend to a static sphere with a surface potential equal to (1)/(3) . A third family of solutions describes ‘‘oscillating black holes.’’ All solutions possess a positive energy density larger than the stresses everywhere.

Perfect fluid spheres admitting a one-parameter group of conformal motions

Some exact analytical solutions of the Einstein equations for perfect fluids were found under the assumption of spherical symmetry and the existence of a one‐parameter group of conformal motions. The first solution exhibited represents a nonstatic homogeneous spherically symmetric distribution of matter which is singular at t=0. Two other solutions represent contracting and expanding fluids, respectively, whose evolution tends asymptotically to a static sphere with a surface gravitational potential equal to (1)/(3) . These two solutions possess vanishing pressure surfaces which are not the boundary of matter except in the static limit. Finally an oscillating distribution of matter is presented.

The complexification of a nonrotating sphere: An extension of the Newman–Janis algorithm

A procedure given by Newman and Janis, to obtain the exterior Kerr metric from the exterior Schwarzschild metric by performing a complex coordinate transformation, is applied to an interior spherically symmetric metric. The resulting metric can be matched to the exterior Kerr metric on the boundary of the source which is chosen to be an oblate spheroid. A specific example of an interior solution for which the energy density is positive is given in detail.

Confined gravitational fields produced by anisotropic fluids

A family of solutions of the Einstein equations for a spherically symmetric distribution of anisotropic matter is presented, which can be matched with the flat (Minkowskian) space‐time on the boundary of the matter, although the energy density and stresses are nonvanishing within the sphere.

Einstein–Cartan theory in the spin coefficient formalism

The field equations of the Einstein–Cartan theory are written down using the spin coefficient formalism developed by Newman and Penrose for the Einstein theory. The irreducible spinor decomposition of the Riemann tensor in a U4 space is obtained.

Conformally symmetric radiating spheres in general relativity

A method used to study the evolution of radiating anisotropic (principal stresses unequal) spheres is applied to the case in which the space‐time (within the sphere) admits a one‐parameter group of conformal motions. Two different kind of models are obtained, depending on the equation of state for the stresses. In one case the energy flux density at the boundary of the sphere (the luminosity) should be given as a function of the timelike coordinate in order to integrate the system of equations. In the other case the luminosity is inferred from the equation of state for the stresses. Both models are integrated numerically and their eventual applications to some astrophysical problems are discussed.

Neutrino fields in axially and reflection symmetric space–times

It is shown that there exist no physically significant (i.e., nonsingular) solutions to the Einstein‐neutrino field equations in an axially and reflection symmetric space–time.