Gravitational Stability and Screening Effect from Extra Timelike Dimensions

TL;DR

This paper investigates how extra timelike dimensions influence gravitational stability and screening effects, revealing conditions for stability of spherical bodies and demonstrating gravitational force screening at short distances due to Kaluza-Klein modes.

Contribution

It provides an analytically rigorous analysis of gravitational stability and screening effects caused by a single extra timelike dimension, including conditions for stability and force screening mechanisms.

Findings

Spherical bodies of radius R can be stable at R=2πLp for positive integers p.

Gravitational force is screened at short distances R ≤ πL due to tachyonic Kaluza-Klein modes.

Stability depends on the radius being a multiple of the extra dimension scale.

Abstract

We discuss extra timelike dimensions and their effects on the gravitational stability of spherical massive bodies. Here we specifically report our results for the case of one extra timelike dimension where we have made analytically rigorous investigations on the tachyonic graviton exchange due to the infinite tower of the Kaluza-Klein mode. With the scale $L$ of the extra timelike dimension we find that some spherical bodies of radius $R$ can be stable at critical radii $R=2\pi Lp$ for some positive integer $p$. We also obtain the generic property of massive bodies that for the short distance range $0<R\leq \pi L$ the gravitational force due to the ordinary massless graviton exchange is screened by the Kaluza-Klein mode exchange of tachyonic gravitons.