The Inner Structure of Black Holes

We study the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a final central singularity. We find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor of a strong, spacelike singularity along the r = 0 hypersurface. The inner black hole region is bounded (in the future) by singularities. This resembles the classical inner structure of a Schwarzschild black hole and it is remarkably different from the inner structure of a charged static Reissner-Nordström or a stationary rotating Kerr black holes.     

On Lynden-Bell and Katz's definition of gravitational field energy

The covariant definition of gravitational field energy given by Lynden-Bell and Katz is expressed in terms of Israel's theory of surface layers in general relativity. In this way an expression, valid for arbitrary radial coordinates, of the gravitational field energy in a static, spherically symmetric space-time, is deduced. This expression is applied to the Schwarschild and Reissner-Nordström space-times, and leads here to the same results as those given by Einstein's pseudotensor expression in isotropic coordinates.     

On spherically symmetric fields with dynamic torsion in gauge theories of gravitation

Within the framework of the Poincaré gauge field theory of gravity, the general gravitational Lagrangian coupled to the electromagnetic field is investigated. We treat the case of a static, spherically symmetric field with space reflection invariance. The exact solutions presented will be generated by a double-duality ansatz for the curvature. The Reissner-Nordström metric is singled out within a class of Lagrangians admitting an asymptotically flat metric.     

Herlt metrics and gravitational-electrostatic balance in general relativity

The balance problem in general relativity is reviewed. The transformation connecting the Herlt equations for electrovacuum and the Weyl equations for axially symmetric vacuum is given. This yields a new exact solution for the superposition of two separated Reissner-Nordström sources with a balance condition which depends upon their separation distance. This result has potential implications for averting gravitational collapse. Details of the singularity structure are also presented.     

Charged gravastars admitting conformal motion

We propose a new model of a gravastar admitting conformal motion. While retaining the framework of the Mazur-Mottola model, the gravastar is assumed to be internally charged, with an exterior defined by a Reissner-Nordström instead of a Schwarzschild line element. The solutions, obtained by exploiting an assumed conformal Killing vector, involve (i) the interior region, (ii) the shell, and (iii) the exterior region of the sphere. Of these three cases the first one is of primary interest since the total gravitational mass here turns out to be an electromagnetic mass under some specific conditions. This suggests that the interior de Sitter vacuum of a charged gravastar is essentially an electromagnetic mass model that must generate gravitational mass which provides a stable configuration by balancing the repulsive pressure arising from charge with its attractive gravity to avert a singularity. Therefore the present model, like the Mazur-Mottola model, results in the construction of a compact astrophysical object, as an alternative to a black hole. We have also analyzed various other aspects such as the stress energy tensor in the thin shell and the entropy of the system.     

Energy, momentum and angular momentum in the dyadosphere of a charged spacetime in teleparallel equivalent of general relativity

We apply the energy momentum and angular momentum tensor to a tetrad field, with two unknown functions of radial coordinate, in the framework of a teleparallel equivalent of general relativity (TEGR). The definition of the gravitational energy is used to investigate the energy within the external event horizon of the dyadosphere region for the Reissner-Nordström black hole. We also calculate the spatial momentum and angular momentum.     

Einstein-Proca Model, Micro Black Holes, and Naked Singularities

The Einstein-Proca equations, describing a spin-1 massive vector field in general relativity, are studied in the static spherically-symmetric case. The Proca field equation is a highly nonlinear wave equation, but can be solved to good accuracy in perturbation theory, which should be very accurate for a wide range of mass scales. The resulting first order metric reduces to the Reissner-Nordström solution in the limit as the range parameter goes to zero. The additional terms in the g ₀₀ metric coefficient are positive, as in Reissner-Nordström, in agreement with previous numerical solutions, and hence involve naked singularities.     

A Numeric Solution for Einstein's Gravitational Theory with Proca Matter and Metric-Affine Gravity

A special case of metric-affine gauge theory of gravity (MAG) is equivalent to general relativity with Proca matter as source. We study in detail a corresponding numeric solution of the Reissner-Nordström type. It is static, spherically symmetric, and of electric type. In particular, this solution has no horizon, so it has a naked singularity at its origin.     

Finite self-energy of pointlike sources for the Reissner-Nordström metric

It is shown that charged fluid distributions, matched to the Reissner-Nordström metric, may posses finite self-energy in the point particle limit if negative energy densities are allowed and the appropriate definition of bare mass is used. Several models are analyzed to illustrate the point.On leave at: Area de Fisica Teorica, Facultad de Ciencias, Universidad de Salamanca, Salamanca 37008, Spain.     

Letter: Active Gravitational Mass and the Invariant Characterization of Reissner–Nordström Spacetime

We analyse the concept of active gravitational mass for Reissner-Nordström spacetime in terms of scalar polynomial invariants and the Karlhede classification. We show that while the Kretschmann scalar does not produce the expected expression for the active gravitational mass, both scalar polynomial invariants formed from the Weyl tensor, and the Cartan scalars, do.     

Internal instability in a Reissner-Nordström black hole

The question of the effect of asynumetries in gravitational collapse is investigated by considerations of test electromagnetic fields in an extended Reissner-Nordström background. It is found, with ths aid of computer calculations, that instabilities in the test field arise at the inner (Cauchy or anti-event) horizon, though not at the ouier (event) horizon. Thus it is reasonable to infer that in the full coupled Einstein-Maxwell theory the inner horizon will not survive as a non-singular bypersurface when asymmetric perturbations are present, but will instead become a space-time curvature singularity.     

Self-interaction and massive vector field in the Schwarzschild space-time

Using a multipole expansion, we determine formally the massive vector field generated by a point source held fixed in the Schwarzschild space-time. We prove that its limit, when the mass of the Proca field goes to zero, does not tend to the corresponding massless vector field. In this limit we evaluate the expression of the self-force acting on the particle. The result is in accordance with that of Vilenkin, without the assumption that the point source is at a large distance from the horizon, that we extend to the case of a Reissner-Nordström space-time. We also investigate a further case: a point source within a spherical shell of matter for which the Proca field tends to the corresponding massless vector field.     

Poincaré stress and the Reissner-Nordström repulsion

The Reissner-Nordström repulsion is shown to be a consequence of Poincaré stresses in a static, charged object. The strong energy condition implies that the Reissner-Nordström repulsions do not stop a neutral test particle, falling freely from rest at infinity in the fields of a charged body, before it hits the surface of the body. However, if the particle falls from rest at a sufficiently small height above the surface of the body, it will not reach the surface due to the Reissner-Nordström repulsion.     

Optical Space of the Reissner-Nordström Solutions

We present an exhaustive discussion of the embedding diagrams for the optical geometry of the Reissner-Nordström solutions. Whereas in the black hole sector there are no qualitative differences with respect to the Schwarzschild case, the diagrams are considerably different if naked singularities are present. Our treatment is sufficiently general that it can be applied also to any other static spherically symmetric spacetime.     

Event horizons in static electrovac space-times

The following theorem is established. Among all static, asymptotically flat electrovac fields with closed, simply-connected equipotential surfacesg _{0 0}=const.. the only ones which have regular event horizonsg _{0 0}=0 are the Reissner-Nordström family of spherisymmetric solutions withmG ^1/2|e|/c. In the special case where the gravitational coupling of the electromagnetic energy density is neglected (G=0) all solutions are computed explicitly, thus extending an earlier result ofGinzburg for a magnetic dipole inSchwarzschild's space-time. Possible implications for gravitational collapse are briefly discussed.On leave of absence from the Mathematics Department, University of Alberta, Edmonton, Canada.     

Letter: Generating Static Black Holes in Higher Dimensional Space-Times

In this article we extend to higher dimensional space-times a recent theorem proved by Salgado which characterizes a three-parameter family of static and spherically symmetric solutions to the Einstein Field Equations. As it happens in four dimensions, it is shown that the Schwarzschild, Reissner-Nordström and global monopole solutions in higher dimensions are particular cases from this family.     

Interpolation of the schwarzschild and Bertotti-Robinson solutions

The two well-known solutions of general relativity, the Schwarzschild and the Bertotti-Robinson solutions, are shown to be described by a common metric. In a particular coordinate system we show the connection between this metric and the metric of Reissner-Nordström.     

Limits of spacetimes

The limits of a one-parameter family of spacetimes are defined, and the properties of such limits discussed. The definition is applied to an investigation of the Schwarzschild solution as a limit of the Reissner-Nordström solution as the charge parameter goes to zero. Two new techniques — rigidity of a geometrical structure and Killing transport — are introduced. Several applications of these two subjects, both to limits and to certain other questions in differential geometry, are discussed.     

Axially symmetric solutions generated by the complexification technique

Banerjee and Andrade generated axially symmetric electrovac solutions from the spherically symmetric Reissner-Nordström solution by giving a complex translation along theZ axis. We use the same method for generating new more complicated axially symmetric solutions from known solutions. Several such examples are given.     

Globally regular solutions of a schwarzschild black hole and a Reissner-Nordström black hole

A new physical concept about globally regular solutions is suggested. The globally regular solutions corresponding to the Schwarzschild black hole and the Reissner-Nordström black hole are examined.