Classical tests of General Relativity in thick branes

TL;DR

This paper examines how the thickness of a brane influences classical tests of General Relativity, such as light deflection and time delay, within a braneworld scenario, revealing energy-dependent effects and potential gravitational rainbow phenomena.

Contribution

It introduces a model for thick branes based on a regularized black hole solution and derives explicit solutions for light deflection and time delay considering transverse motion effects.

Findings

Light deflection depends on light ray energy due to transverse motion.

Time delay in gravitational tests is influenced by brane thickness.

Potential gravitational rainbow effect caused by energy-dependent light propagation.

Abstract

Classical tests of General Relativity in braneworld scenarios have been investigated recently with the purpose of posing observational constraints on parameters of some models of infinitely thin brane. Here we consider the motion of test particles in a thick brane scenario that corresponds to a regularized version of the Garriga-Tanaka solution, which describes a black hole solution in RSII model, in the weak field regime. By adapting a mechanism previously formulated in order to describe the confinement of massive tests particles in a domain wall (that simulates classically the trapping of the Dirac field in a domain wall), we study the influence of the brane thickness on the four-dimensional (4D) path of massless particles. Although the geometry is not warped and, therefore, the bound motion in the transverse direction is not decoupled from the movement in the 4D-world, we can find an explicit solution for the light deflection and the time delay, if the motion in the fifth direction is a high frequency oscillation. We verify that, owing to the transverse motion, the light deflection and the time delay depend on the energy of the light rays. This feature may lead to the phenomenon of gravitational rainbow. We also consider the problem from a semi-classical perspective, investigating the effects of the brane thickness on the motion of the zero-mode in the 4D-world.