Stability of the GRS Model

TL;DR

This paper analyzes the stability of the GRS model, showing that despite violating the weak energy condition, it remains stable under small perturbations by satisfying specific conditions for graviton modes.

Contribution

It demonstrates the stability of the GRS model without the weak energy condition by establishing conditions for graviton modes to avoid tachyons and ghosts.

Findings

The GRS spacetime is stable despite violating the weak energy condition.

Stability is ensured by conditions on matter sources and graviton modes.

The lowest state is a supersymmetric vacuum with zero mass.

Abstract

We discuss the compatibility between the weaker energy condition and the stability of Gregory, Rubakov and Sibiryakov (GRS) model. Because the GRS spacetime violates the weak energy condition, it may cause the instability. In the GRS model, the four dimensional gravity can be described by the massive KK modes with the resonance. Hence, instead of considering the weaker energy condition, we require for the stability of this model: no tachyon and no ghost condition for graviton modes ($h_{\mu\nu}$). No tachyonic condition ($m^2_h \geq 0$) is satisfied because the lowest state $m_h=0$ is supersymmetric vacuum state. Further, no ghost state condition is achieved if one requires some relations for the matter source: $2T_{55}= T^{\mu}_{\mu}=3(T_{22}+T_{33})$. It turns out that, although the GRS spacetime does not satisfy the weaker energy condition, it is stable against small perturbation.