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 rn 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/r2 regardless of the interior field’s dependence on r.
Highlights
Until quite recently, it was believed that astrophysical objects more compact than neutron stars could not exist; no physically plausible mechanism had been conceived that could halt the gravitational collapse and establish equilibrium inside such an object, leading inevitably to its collapse to a singularity and the formation of a classical black hole
For an object containing a global distribution of non-interacting MaxwellProca charges, it is shown that physical considerations define the relationship between the charge density and the metric function uniquely, corroborating an earlier finding that the interior field must increase with radial distance and the exterior field necessarily follows an inverse-square law
This has led to models for two classes of such hypothetical compact objects: For those collapsing to an equilibrium radius, R, that is smaller than their Schwarzschild radius rS, the result is a nonsingular black hole; and those for which R > rS at equilibrium are referred to as ultra-compact objects
Summary
It was believed that astrophysical objects more compact than neutron stars could not exist; no physically plausible mechanism had been conceived that could halt the gravitational collapse and establish equilibrium inside such an object, leading inevitably to its collapse to a singularity and the formation of a classical black hole This began to change as research into entities such as vacuum energy and dark energy progressed (and evidence for their existence mounted): These entities all possess the equation of state p = –ρ, meaning that for a positive mass-energy density the pressure must be negative (sometimes called a tension) and act as an “anti-gravity” mechanism to oppose the collapse of a compact object. One such family of compatible entities consists of the massless, non-self-interacting Maxwell-Proca (M-P) fields, and these are the subject of our investigation in this paper
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