Raychaudhuri's equation and aspects of relativistic charged collapse

Abstract

We use the Raychaudhuri equation to probe certain aspects related to the gravitational collapse of a charged medium. The aim is to identify the stresses the Maxwell field exerts on the fluid and discuss their potential implications. Particular attention is given to those stresses that resist contraction. After looking at the general case, we consider the two opposite limits of poor and high electrical conductivity. In the former there are electric fields but no currents, while in the latter the situation is reversed. When the conductivity is low, we find that the main agents acting against the collapse are the Coulomb forces triggered by the presence of an excess charge. At the ideal Magnetohydrodynamic (MHD) limit, on the other hand, the strongest resistance seems to come from the tension of the magnetic forcelines. In either case, we discuss whether and how the aforementioned resisting stresses may halt the contraction and provide a set of conditions making this likely to happen.

Revised version, to appear in PRD

References in corpus (5)

• Relativistic cosmology and large-scale structure
• Nonadiabatic charged spherical gravitational collapse
• The Raychaudhuri equations: a brief review
• Gravitational collapse of spherically symmetric plasmas in Einstein-Maxwell spacetimes
• Newtonian nonlinear hydrodynamics and magnetohydrodynamics

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• Law of elasticity and fracture limit of magnetic forcelines under their gravitational deformation
• Role of a magnetic field in the context of inhomogeneous gravitational collapse