Bounds on M/R for Charged Objects with positive Cosmological constant

TL;DR

This paper derives bounds on the gravitational mass-to-radius ratio for charged, spherically symmetric objects in a universe with a positive cosmological constant, extending classical inequalities under specific energy and charge conditions.

Contribution

It establishes a new inequality relating mass, charge, and radius for charged objects with positive cosmological constant, considering specific pressure and energy conditions.

Findings

Derived an explicit upper bound on m_g/r involving charge and cosmological constant.

Identified conditions under which the inequality is sharp.

Extended classical bounds to include effects of charge and positive cosmological constant.

Abstract

We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant $\Lambda$. If $r$ denotes the area radius, $m_g$ and $q$ the gravitational mass and charge of a sphere with area radius $r$ respectively, we find that for any solution which satisfies the condition $p+2p_{\perp}\leq \rho,$ where $p\geq 0$ and $p_{\perp}$ are the radial and tangential pressures respectively, $\rho\geq 0$ is the energy density, and for which $0\leq \frac{q^2}{r^2}+\Lambda r^2\leq 1,$ the inequality $\frac{m_g}{r} \leq 2/9+\frac{q^2}{3r^2}-\frac{\Lambda r^2}{3}+2/9\sqrt{1+\frac{3q^2}{r^2}+3\Lambda r^2}$ holds. We also investigate the issue of sharpness, and we show that the inequality is sharp in a few cases but generally this question is open.