Abstract
We start this chapter with upto date information on divergence theorems and integral formulas. In particular, we provide new information on the validity of divergence theorem for semi-Riemannian manifolds with boundary. Then we review on the existence of Killing and affine Killing vectors and their kinematic and dynamic properties. We show that while Killing symmetry is characterized by a class of expansion-free and shear-free spacetimes, proper affine Killing symmetry is relevant to non-zero expansion and non-zero shear.
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© 1999 Springer Science+Business Media Dordrecht
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Duggal, K.L., Sharma, R. (1999). Killing and Affine Killing Vector Fields. In: Symmetries of Spacetimes and Riemannian Manifolds. Mathematics and Its Applications, vol 487. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5315-1_5
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DOI: https://doi.org/10.1007/978-1-4615-5315-1_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7425-1
Online ISBN: 978-1-4615-5315-1
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