Strong Brane Gravity and the Radion at Low Energies

TL;DR

This paper analyzes the bulk geometry of the Randall-Sundrum 2-brane model under strong gravity and low matter density, deriving effective theories and exploring astrophysical implications of brane dynamics and radion behavior.

Contribution

It extends the analysis of the Randall-Sundrum model to strong gravity regimes, deriving a scalar-tensor effective theory and examining radion effects and brane collisions.

Findings

Derived bulk geometry for strong gravity in low-density regime.

Found a scalar-tensor effective theory with a specific coupling function.

Numerically illustrated brane behavior in static star solutions.

Abstract

For the 2-brane Randall-Sundrum model, we calculate the bulk geometry for strong gravity, in the low matter density regime, for slowly varying matter sources. This is relevant for astrophysical or cosmological applications. The warped compactification means the radion can not be written as a homogeneous mode in the orbifold coordinate, and we introduce it by extending the coordinate patch approach of the linear theory to the non-linear case. The negative tension brane is taken to be in vacuum. For conformally invariant matter on the positive tension brane, we solve the bulk geometry as a derivative expansion, formally summing the `Kaluza-Klein' contributions to all orders. For general matter we compute the Einstein equations to leading order, finding a scalar-tensor theory with $\omega(\Psi) \propto \Psi / (1 - \Psi)$, and geometrically interpret the radion. We comment that this radion scalar may become large in the context of strong gravity with low density matter. Equations of state allowing $(\rho - 3 P)$ to be negative, can exhibit behavior where the matter decreases the distance between the 2 branes, which we illustrate numerically for static star solutions using an incompressible fluid. For increasing stellar density, the branes become close before the upper mass limit, but after violation of the dominant energy condition. This raises the interesting question of whether astrophysically reasonable matter, and initial data, could cause branes to collide at low energy, such as in dynamical collapse.