Uniformly accelerated motion in General Relativity: completeness of inextensible trajectories

详细信息    查看全文

• 作者：Daniel de la Fuente (1)
  Alfonso Romero (2)
  
  1. Departamento de Matem谩tica Aplicada ; Universidad de Granada ; 18071 ; Granada ; Spain
  2. Departamento de Geometr铆a y Topolog铆a ; Universidad de Granada ; 18071 ; Granada ; Spain
  
• 关键词：Uniformly accelerated motion ; General Relativity ; Fermi鈥揥alker connection ; Third ; order differential equation ; Completeness of inextensible trajectories ; 83C10 ; 83C75 ; 53C50
• 刊名：General Relativity and Gravitation
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：47
• 期：4
• 全文大小：179 KB
• 参考文献：1. Beem, J.K., Ehrlich, P.E., Easley, K.L.: Global Lorentzian Geometry. Marcel Dekker, Pure and Applied Mathematics 202, (1996)
  2. Candela, A.M., Romero, A., S谩nchez, M.: Completeness of trajectories of relativistic particles under stationary magnetic fields. Int. J. Geom. Methods Mod. Phys., 10, 1360007(1鈥?), (2013)
  3. Candela, AM, Romero, A, S谩nchez, M (2013) Completeness of the trajectories of particles coupled to a general force field. Arch. Ration. Mech. Anal. 208: pp. 255-274 external" href="http://dx.doi.org/10.1007/s00205-012-0596-2" target="_blank" title="It opens in new window">CrossRef
  4. Chen, BY (1981) Geometry of Submanifolds and Its Applications. Science University of Tokyo, Tokyo
  5. Kobayashi, S, Nomizu, K (1969) Foundations of Differential Geometry. Wiley, New York
  6. Friedman, Y., Scarr, T.: Making the relativistic dynamics equation covariant: explicit solutions for motion under a constant force. Phys. Scr. 86, 065008(7pp) (2012)
  7. Friedman, Y., Scarr, T.: Spacetime transformations from a uniformly accelerated frame, Phys. Scr. 87, 055004 (8 pp) (2013)
  8. Ikawa, T (1985) On curves and submanifolds in an indefinite-Riemannian manifold. Tsukuba. J. Math. 9: pp. 353-371
  9. Marder, L (1957) On uniform acceleration in special and general relativity. Math. Proc. Camb. Phil. Soc. 53: pp. 194-198 external" href="http://dx.doi.org/10.1017/S0305004100032114" target="_blank" title="It opens in new window">CrossRef
  10. Mashhoon, B, Muench, U (2002) Length measuremente in accelerated systems. Ann. Phys. 11: pp. 532-547 external" href="http://dx.doi.org/10.1002/1521-3889(200208)11:7<532::AID-ANDP532>3.0.CO;2-3" target="_blank" title="It opens in new window">CrossRef
  11. McMillan, EM (1957) The 鈥渃lock paradox鈥?and space travel. Science 126: pp. 381-384 external" href="http://dx.doi.org/10.1126/science.126.3270.381" target="_blank" title="It opens in new window">CrossRef
  12. Misner, CW, Thorne, KS, Wheeler, JA (1973) Gravitation. W.H. Freeman and Co., London
  13. Nomizu, K, Yano, K (1974) On circles and spheres in Riemannian geometry. Math. Ann. 210: pp. 163-170 external" href="http://dx.doi.org/10.1007/BF01360038" target="_blank" title="It opens in new window">CrossRef
  14. O鈥橬eill, B (1983) Semi-Riemannian Geometry. Academic Press, Massachusetts
  15. Ponge, R, Reckziegel, H (1993) Twisted products in pseudo-Riemannian geometry. Geom. Dedicata 48: pp. 15-25 external" href="http://dx.doi.org/10.1007/BF01265674" target="_blank" title="It opens in new window">CrossRef
  16. Rindler, W (1960) Hyperbolic motion in curved space time. Phys. Rev. 119: pp. 2082-2089 external" href="http://dx.doi.org/10.1103/PhysRev.119.2082" target="_blank" title="It opens in new window">CrossRef
  17. Rindler, W (1961) Length contraction paradox. Am. J. Phys. 24: pp. 365-366 external" href="http://dx.doi.org/10.1119/1.1937789" target="_blank" title="It opens in new window">CrossRef
  18. Romero, A, S谩nchez, M (1995) Completeness of compact Lorentz manifolds admitting a timelike conformal Killing vector field. Proc. Am. Math. Soc. 123: pp. 2831-2833 external" href="http://dx.doi.org/10.1090/S0002-9939-1995-1257122-3" target="_blank" title="It opens in new window">CrossRef
  19. Sachs, RK, Wu, H (1977) General Relativity for Mathematicians. Springer, New York
  20. S谩nchez, M (1998) On the geometry of Generalized Robertson鈥揥alker spacetimes: geodesics. Gen. Relativ. Gravit. 30: pp. 914-932 external" href="http://dx.doi.org/10.1023/A:1026664209847" target="_blank" title="It opens in new window">CrossRef
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Relativity and Cosmology
  Differential Geometry
  Quantum Physics
  Astronomy, Astrophysics and Cosmology
  
• 出版者：Springer Netherlands
• ISSN：1572-9532

文摘

The notion of a uniformly accelerated motion of an observer in a general spacetime is analysed in detail. Such a observer may be seen as a Lorentzian circle, providing a new characterization of a static standard spacetime. The trajectories of uniformly accelerated observers are seen as the projection on the spacetime of the integral curves of a vector field defined on a certain fiber bundle over the spacetime. Using this tool, we find geometric assumptions to ensure that an inextensible uniformly accelerated observer does not disappear in a finite proper time.