Advertisement

General Relativity and Gravitation

, Volume 34, Issue 1, pp 133–153 | Cite as

Visual Horizons in World-Models

  • W. Rindler
Article

Abstract

This paper seeks to effect a unification and generalization of various particular results on visual horizons scattered in the literature. A horizon is here defined as a frontier between things observable and things unobservable. Two quite different types of horizon exist which are here termed event-horizons and particle-horizons. These are discussed in detail and illustrated by examples and diagrams. The examples include well-known model-universes which exhibit one or the other type of horizon, both types at once, or no horizon. Proper distance and cosmic time are adopted as the main variables, and the analysis is based on the Robertson–Walker form of the line element and therefore applies to all cosmological theories using a homogeneous and isotropic substratum.

Keywords

Differential Geometry Line Element Main Variable Cosmic Time Proper Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. [1]
    The Observatory, 73, 205, 1953; 74, 36, 37, 172, 173, 1954.Google Scholar
  2. [2]
    Nature, 175, 68, 382, 808, 1955.Google Scholar
  3. [3]
    The Observatory, 74, 36, 1954.Google Scholar
  4. [4]
    A. S. Eddington, The Mathematical Theory of Relativity (2nd edition,) p. 166, Cambridge, 1924.Google Scholar
  5. [5]
    A. S. Eddington, loc. cit., pp. 157, 165.Google Scholar
  6. [6]
    E. A. Milne and G. J. Whitrow, Z. Astrophys, 15, 345, 1938.Google Scholar
  7. [7]
    E. Schrödinger, Expanding Universes, sections 4, 5, 6, 8, Cambridge, 1956.Google Scholar
  8. [8]
    W. H. McCrea, Z. Astrophys., 9, 290, 1935.Google Scholar
  9. [9]
    G. C. McVittie, Cosmological Theory, p. 54, London, 1937.Google Scholar
  10. [10]
    E. A. Milne, Relativity, Gravitation and World Structure, p. 327, Oxford, 1935.Google Scholar
  11. [11]
    H. P. Robertson, Astrophys. J., 82, 284, 1935.Google Scholar
  12. [12]
    A. G. Walker, Proc. Lond. Math. Soc. (2) 42, 90, 1937.Google Scholar
  13. [13]
    W. Rindler, M.N., 116, 335, 1956.Google Scholar
  14. [14]
    H. Bondi, Cosmology, formula (10_18), Cambridge, 1952.Google Scholar
  15. [15]
    H. Bondi, loc. cit., pp. 82 and 104.Google Scholar
  16. [16]
    A. S. Eddington, loc. cit., p. 166.Google Scholar
  17. [17]
    E. Schrödinger, loc. cit., p. 21 et seq.Google Scholar
  18. [18]
    E. A. Milne, Kinematic Relativity, section 16, Oxford, 1948.Google Scholar
  19. [19]
    A. S. Eddington, The Expanding Universe, chapter III, section VI, Cambridge, 1932.Google Scholar
  20. [20]
    W. H. McCrea, loc. cit., formula (15).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • W. Rindler
    • 1
  1. 1.Department of PhysicsUniversity of Texas at DallasRichardsonU.S.A

Personalised recommendations