Buchdahl type inequalities in $d$-dimensions

TL;DR

This paper derives bounds on the mass-to-radius ratio and gravitational redshift for spherically symmetric, anisotropic compact objects in higher-dimensional Einstein gravity, including effects of charge and cosmological constant.

Contribution

It extends Buchdahl inequalities to higher dimensions and various matter models, incorporating charge and cosmological constant effects.

Findings

Derived upper bounds on mass-to-radius ratio in $d ext{-}dim$

Generalized bounds with charge and cosmological constant

Identified maximum gravitational redshift at the surface

Abstract

Spherically symmetric anisotropic static compact solutions to the Einstein equations in dimension $d\geq4$ are considered. Various matter models are examined and upper bounds on the ratio of the gravitational mass to the radius in these different models are obtained. Bounds are also generalised in the presence of a non-zero charge and a positive cosmological constant. These bounds are then used to find the maximum of the gravitational redshift at the surface of the object.