Geodesics in a space with a spherically symmetric dislocation

Alcides F. Andrade, Guilherme de Berredo-Peixoto1

Abstract

We consider a defect produced by a spherically symmetric dislocation in the scope of linear elasticity theory using geometric methods. We derive the induced metric as well as the affine connections and curvature tensors. Since the induced metric is discontinuous, one can expect an ambiguity coming from these quantities, due to products between delta functions or its derivatives. However, one can obtain some well-defined physical predictions of the induced geometry. In particular, we explore some properties of test particle trajectories around the defect and show that these trajectories are curved but cannot be circular orbits. The geometric approach uses gravity methods and indicates a description of gravity theories with exotic sources containing the delta function and its derivatives.

References

  1. M. O. Katanaev and I. V. Volovich, Ann. Phys. 216(1), 1 (1992).
  2. M. O. Katanaev and I. V. Volovich, Ann. Phys. 271, 203 (1999).
  3. M. O. Katanaev, Geometric Theory of Defects, Physics-Uspekhi 48(7), 675 (2005).
  4. G. de Berredo-Peixoto and M. O. Katanaev, J. Math. Phys. 50, 042501 (2009).
  5. G. de Berredo-Peixoto, M. O. Katanaev, E. Konstantinova, and I. L. Shapiro, Nuovo Cim. 125B, 915 (2010).
  6. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, 2000).
  7. M. Kleman and J. Friedel, Rev. Mod. Phys. 80, 61 (2008).
  8. D. M. Bird and A. R. Preston, Phys. Rev. Lett. 61, 2863 (1988).
  9. C. Furtado and F. Moraes, Europhys. Lett. 45, 279 (1999).
  10. S. Azevedo and F. Moraes, Phys. Lett. 267A, 208 (2000).
  11. C. Furtado, V. B. Bezerra, and F. Moraes, Phys. Lett. 289A, 160 (2001).
  12. L. D. Landau and E.M. Lifshits, Theory of Elasticity (Pergamon, Oxford, 1970).
  13. V. C. de Andrade and J. G. Pereira, Phys. Rev. D 56, 4689 (1997).
  14. M. O. Katanaev, Point Massive Particle in General Relativity, arXiv: 1207.3481.
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