Time-like Extra Dimensions without Tachyons or Ghosts

TL;DR

This paper constructs a 3-brane solution in a 5D gravity model with a time-like extra dimension, achieving localized gravity without tachyons or ghosts, thus avoiding typical instabilities associated with time-like extra dimensions.

Contribution

It presents a novel solitonic 3-brane solution in Einstein-Gauss-Bonnet gravity with a time-like extra dimension, ensuring stable localized gravity without tachyonic or ghost states.

Findings

Gravity is fully localized on the brane.

No propagating tachyonic or negative norm states.

The model avoids instabilities typically associated with time-like extra dimensions.

Abstract

Some time ago Dvali, Gabadadze and Senjanovic (hep-ph/9910207) discussed brane world scenarios with time-like extra dimensions. In this paper we construct a solitonic 3-brane solution in the 5-dimensional Einstein-Hilbert-Gauss-Bonnet theory with the space-time signature (-,+,+,+,-). The direction transverse to the brane is the second time-like direction. The solitonic brane is $\delta$-function like, and has the property that gravity is completely localized on the brane. That is, there are no propagating degrees of freedom in the bulk, while on the brane we have purely 4-dimensional Einstein gravity. In particular, there are no propagating tachyonic or negative norm states even though the extra dimension is time-like.