Classical confinement of test particles in higher-dimensional models: stability criteria and a new energy condition

@article{Seahra2003ClassicalCO,
  title={Classical confinement of test particles in higher-dimensional models: stability criteria and a new energy condition},
  author={Sanjeev S Seahra},
  journal={Physical Review D},
  year={2003},
  volume={68},
  pages={104027}
}
  • S. Seahra
  • Published 8 September 2003
  • Mathematics
  • Physical Review D
We review the circumstances under which test particles can be localized around a spacetime section ${\ensuremath{\Sigma}}_{0}$ smoothly contained within a codimension-1 embedding space M. If such a confinement is possible, ${\ensuremath{\Sigma}}_{0}$ is said to be totally geodesic. Using three different methods, we derive a stability condition for trapped test particles in terms of intrinsic geometrical quantities on ${\ensuremath{\Sigma}}_{0}$ and M; namely, confined paths are stable against… 

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