in [n.p.] .
Written in English
reprinted from Annals of Mathematics, Vol. 35, No. 4, 1934, p. 705-713.
|The Physical Object|
Republication of: On the deviation of geodesics and null-geodesics, particularly in relation to the properties of spaces of constant curvature and indefinite line-element - NASA/ADS This Golden Oldie is a reprinting of a paper by J. L. Synge first published in Cited by: 2. Editorial note to: J. L. Synge, On the deviation of geodesics and null geodesics, particularly in relation to the properties of spaces of constant curvature and indefinite line-element and to: F. The geodesic deviation equation (“GDE”) provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the Friedmann—LemaîtreRobertson—Walker (“FLRW”) models, where we assume the sources to be given by a noninteracting mixture of incoherent matter and radiation, and we also take a nonzero cosmological Cited by: Synge’s paper , published in in the prestigious Annals of Mathematics, is the first publication where deviation of null geodesics is considered.
The radial motion along null geodesics in static charged black hole space-times, in particular, the Reissner-Nordström and stringy charged black holes, are studied. We analyzed the properties of the effective potential. The circular photon orbits in these space-times are investigated. Abstract: The radial motion along null geodesics in static charged black hole space-times, in particular, the Reissner-Nordstr\"om and stringy charged black holes are studied. We analyzed the properties of the effective potential. The circular photon orbits in these space-times are investigated. We found that the radius of circular photon orbits in both charged black holes are different and Cited by: Congruences of timelike geodesics are then presented in Section , and the case of null geodesics is treated in Section Recommend this book Email your librarian or administrator to recommend adding this book to your organisation's collection. 6. GEODESICS In the Euclidean plane, a straight line can be characterized in two different ways: (1) it is the shortest path between any two points on it; (2) it bends neither to the left nor the right (that is, it has zero curvature) as you travel along it. We will transfer these ideas to a regular surface in 3-space,File Size: KB.
For this reason we stick to smooth congruences of causal geodesics with spacelike S only. The following theorem shows that, actually, geodesic deviation of timelike geodesics, or equivalently, geodesic deviation of null geodesics, encodes all information on the curvature. Theorem Consider a spacetime (M,g). The following facts are equivalent. The point the book is trying to make about the null geodesics is that unlike for time-like or space-like geodesics, one can not use arc-length as a parameter along null geodesic curves since that parameter is 0 along the entire curve. So one must use some (arbitrary) affine parameter to parametrize the curve. The deviation from Einstein gravity appears as a new parameter in the black hole solution, which is called the gravitational hair parameter. In order to clarify the consequences of the deviation, we investigate the null geodesics and the deflection angles of the null geodesics in the black hole spacetime with the gravitational hair parameter 1 Cited by: 3. curvature,Geodesics. I. INTRODUCTION A central element in Einstein’s theory of general rel-ativity (GR) is that ideal point-like test-particles fol-low time-like or null geodesics in a four-dimensional (4D) relativistic space-time which is curved as a pseudo-Riemannian manifold in connection with a File Size: KB.