Motion of a Test Particle in the Transverse space of Dp-Branes

TL;DR

This paper studies the motion of particles and light near Dp-branes in higher-dimensional space, revealing unique orbital behaviors and light bending effects that differ from traditional Schwarzschild black hole backgrounds.

Contribution

It provides the first leading order solutions for geodesic equations in Dp-brane backgrounds and compares light bending and orbital properties with higher-dimensional Schwarzschild spacetime.

Findings

Bound elliptic orbits exist only for p=6 in Dp-brane backgrounds.

Circular photon orbits are possible only for p ≤ 3.

Light bending differs between Dp-brane and Schwarzschild backgrounds.

Abstract

We investigate the motion of a test particle in higher dimensions due to the presence of extended sources like D$p$-branes by studying the motion in the transverse space of the brane. This is contrasted with the motion of a point particle in the Schwarzschild background in higher dimensions. Since D$p$-branes are specific to 10-dimensional space time and exact solutions of geodesic equations for this particular space time has not been possible so far for the Schwarzschild background, we focus here to find the leading order solution of the geodesic equation (for motion of light rays). This enables us to compute the bending of light in both the backgrounds. We show that contrary to the well known result of no noncircular bound orbits for a massive particle, in Schwarzschild background, for $d\geq 5$, the $Dp$-brane background does allow bound elliptic motion only for $p = 6$ and the perihelion of the ellipse regresses instead of advancement. We also find that circular orbits for photon are allowed only for $p\le 3$.