Maxwell-Proca Fields in Relativistic Astrophysical Compact Objects

Abstract

A general-relativistic model is formulated for hypothetical ultra-compact astrophysical objects composed of fluid infused with charges carrying a generalized massless Maxwell-Proca field. The chosen interior metric has the algebraic property that ; the fluid consequently possesses a negative pressure which halts gravitational collapse and establishes hydrostatic equilibrium. For an object containing a global distribution of non-interacting Maxwell - Proca charges, it is shown that physical considerations define the relationship between the charge density and the metric function uniquely, corroborating an earlier finding (for an electrostatic distribution of charge) that the interior field must increase with radial distance and the exterior field necessarily follows an inverse-square law. For the case of a charged fluid envelope surrounding a core of uncharged fluid, numerous solutions are possible. Assuming the interior field to vary as r n and requiring its strength to increase with radial distance while the charge density decreases, the range of values for n is found to be 0 < n ≤ 1 (where n is not necessarily an integer) with n = 1 denoting the special case of a continuous distribution of charge. For both continuous and stratified charge distributions, the exterior field is found to decrease as 1/ r 2 regardless of the interior field’s dependence on r .