No Ghost State in the Brane World

Abstract

We discuss the role of the trace part of metric fluctuations $h_{MN}$ in the Randall-Sundrum scenario of gravity. Without the matter, this field ($h={\eta }^{MN}{h}_{MN}$) is a gauge-dependent term, and thus it can be gauged away. But, including the uniform source ${\tilde{T}}_{MN}$, this field satisfies the linearized equation ${\square }_{4}h=16\pi G_5{T}_{\mu }^{\mu }$. This may correspond to the scalar ${\xi }^5$ in the bending of the brane due to the localized source. Considering the case of longitudinal perturbations ($h_{5\mu }=h_{55}=0$), one finds the source relation ${\tilde{T}}_{\mu }^{\mu }=2{\tilde{T}}_{55}$, which leads to the ghost states in the massive modes. In addition, if one requires $T_{44}=2(T_{22}+T_{33})$, it is found that in the limit of $m_h^2\to 0$ we have the massless spin-2 propagation without the ghost state. This exactly corresponds to the same situation as in the intermediate scales of Gregory-Rubakov-Sibiryakov (GRS) model.

7 pages, no figure, the version to appear in PLB, comments on the matter source and references added, main results unchanged

References in corpus (4)

• Gravity in the Randall-Sundrum Brane World
• Linearized Gravity in Brane Backgrounds
• Single-Brane Cosmological Solutions with a Stable Compact Extra Dimension
• Randall-Sundrum Gauge in the Brane World

Cited by in corpus (3)

• No ghost state of Gauss-Bonnet interaction in warped backgrounds
• Gravitational potential correction with Gauss-Bonnet interaction
• U(1) Gauge Field of the Kaluza-Klein Theory in the Presence of Branes