Inverse square law isothermal property in relativistic charged static distributions

TL;DR

This paper investigates the inverse square law fall-off in charged, relativistic, static, spherically symmetric fluids, deriving new solutions and analyzing their physical viability, including boundary conditions and redshift constraints.

Contribution

It introduces new classes of solutions with inverse square law density fall-off in charged fluids, extending isothermal models and examining their physical properties.

Findings

Charged isothermal spheres can be bounded, unlike neutral ones.

Models satisfy physical conditions like subluminal sound speed and redshift limits.

Mass-radius bounds are consistent with established theoretical limits.

Abstract

We analyse the impact of the inverse square law fall-off of the energy density in a charged isotropic spherically symmetric fluid. Initially we impose a linear barotropic equation of state $p=\alpha \rho$ but this leads to an intractable differential equation. Next we consider the neutral isothermal metric of Saslaw, Maharaj and Dadhich (1996) in an electric field and the usual inverse square law of energy density and pressure results thus preserving the equation of state. Additionally, we discard a linear equation of state and endeavour to find new classes of solutions with the inverse square law fall off of density. Certain prescribed forms of the spatial and temporal gravitational forms result in new exact solutions. An interesting result that emerges is that while isothermal fluid spheres are unbounded in the neutral case, this is not so when charge is involved. Indeed it was found that barotropic equations of state exist and hypersurfaces of vanishing pressure exist establishing a boundary in practically all models. One model was studied in depth and found to satisfy other elementary requirements for physical admissability such as a subluminal sound speed as well as gravitational surface redshifts smaller than 2. The Buchdahl (1959), Bohmer and Harko (2007) and Andreasson (2009) mass-radius bounds were also found to be satisfied. Graphical plots utilising constants selected from the boundary conditions established that the model displayed characteristics consistent with physically viable models.