Raychaudhuri's equation and aspects of relativistic charged collapse

TL;DR

This paper investigates how electromagnetic stresses influence the gravitational collapse of charged fluids using Raychaudhuri's equation, analyzing different conductivity regimes and their potential to prevent collapse.

Contribution

It provides a detailed analysis of electromagnetic stresses in charged collapse, highlighting the roles of Coulomb forces and magnetic tension in resisting contraction.

Findings

Coulomb forces oppose collapse in low conductivity regimes.

Magnetic tension resists contraction in high conductivity (ideal MHD) limit.

Conditions are identified under which electromagnetic stresses can halt 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.