Vaidya Collapse with Nonzero Radial Pressure and Charge

The cosmic censorship hypothesis is regarded as one of the most important unsolved problems in classical general relativity; viz., will generic gravitational collapse of a star after it has exhausted its nuclear fuel lead to black holes only, under reasonable physical conditions. We discuss the collapse of a fluid with nonzero radial pressure within the context of the Vaidya spacetime considering a decaying cosmological parameter as well as nonzero charge. Previously, a similar analysis was done, but without considering charge. A decaying cosmological parameter may also be associated with dark energy. We found that both black holes and naked singularities can form, depending upon the initial conditions. Hence, charge does not restore the validity of the hypothesis. This provides another example of the violation of the cosmic censorship hypothesis. We also discuss some radiating rotating solutions, arriving at the same conclusion.

Electrodynamics of charged scalar solitons

The electrodynamics of a nonlinear, complex scalar field is developed from the basis of a Hamiltonian formalism. By means of a canonical transformation, the equations for a stationary state are reduced to the consideration of an equivalent problem in static equilibrium. Localized solutions are defined. For specified conditions on the self-interaction, solutions of finite energy, and finite, nonzero charge, are localized.

Classical theory of Klein–Gordon equations with logarithmic nonlinearities

The relativistic soliton theory of Bialynicki-Birula and Mycielski is reviewed, and extended by the addition of a term in [Formula: see text] to the nonlinear interaction. For suitable values of the coupling, the energy becomes a positive functional which can be treated by a variational method.Evidence is presented which suggests that all solutions with finite energy and nonzero charge are localized.