Contemporary Mathematics
Volume 127, 1992
NULL DIRECTIONS AND CURVATURE
1
John
K.
Beem and Phillip E. Parker
ABSTRACT. Let (M, g) be a Lorentzian manifold. The
sectional curvature is related to tidal accelerations. The
tidal accelerations generally become unbounded near null
directions. Special null directions corresponding to
directions where tidal accelerations are bounded for objects
near the speed of light are investigated. In the Ricci
flat case they can be related to principal null directions.
1. INTRODUCTION. In this paper we consider the sectional
curvature function for a Lorentzian manifold (M, g) near null (i.e.,
degenerate) sections. In general, the sectional curvature is unbounded
near these sections. This geometric result has an interesting physical
implication. Generically, tidal accelerations become unbounded for
objects of positive rest-mass when these objects approach the speed of
light.
Section 2 contains some preliminary definitions.
In
Section 3 we
1980 Mathematics Subject Classification: 53B30, 53B50.
1partially supported by NSF grant DMS-8803511.
The final version of this paper will be submitted for publication elsewhere.
1
©
1992 American Mathematical Society
0271-4132/92 $1.00
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http://dx.doi.org/10.1090/conm/127/1155405
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