Relativistic Stars in Randall-Sundrum Gravity

TL;DR

This paper numerically investigates static, spherically symmetric stars in Randall-Sundrum gravity, revealing an upper mass limit, localized geometries, and consistency with 4D General Relativity for large stars, despite the non-compact extra dimension.

Contribution

It provides a numerical solution to 5D Einstein equations for stars in Randall-Sundrum gravity, demonstrating the localization of geometry and the recovery of 4D GR behavior for large stars.

Findings

Existence of an upper mass limit for small stars

Geometry remains localized near the brane at high densities

Large stars exhibit 4D General Relativity behavior

Abstract

The non-linear behaviour of Randall-Sundrum gravity with one brane is examined. Due to the non-compact extra dimension, the perturbation spectrum has no mass gap, and the long wavelength effective theory is only understood perturbatively. The full 5-dimensional Einstein equations are solved numerically for static, spherically symmetric matter localized on the brane, yielding regular geometries in the bulk with axial symmetry. An elliptic relaxation method is used, allowing both the brane and asymptotic radiation boundary conditions to be simultaneously imposed. The same data that specifies stars in 4-dimensional gravity, uniquely constructs a 5-dimensional solution. The algorithm performs best for small stars (radius less than the AdS length) yielding highly non-linear solutions. An upper mass limit is observed for these small stars, and the geometry shows no global pathologies. The geometric perturbation is shown to remain localized near the brane at high densities, the confinement interestingly increasing for both small and large stars as the upper mass limit is approached. Furthermore, the static spatial sections are found to be approximately conformal to those of AdS. We show that the intrinsic geometry of large stars, with radius several times the AdS length, is described by 4-dimensional General Relativity far past the perturbative regime. This indicates that the non-linear long wavelength effective action remains local, even though the perturbation spectrum has no mass gap. The implication is that Randall-Sundrum gravity, with localized brane matter, reproduces relativistic astrophysical solutions, such as neutron stars and massive black holes, consistent with observation.