The Noether conservation laws of some Vaidiya metrics. (English) Zbl 1186.83092

Summary: In this paper, we show that a large amount information can be extracted from a knowledge of the vector fields that leave the action integral invariant, viz., Noether symmetries. In addition to a larger class of conservation laws than those given by the isometries or Killing vectors, we may conclude what the isometries are and that these form a Lie subalgebra of the Noether symmetry algebra. We perform our analysis on versions of the Vaidiya metric yielding some previously unknown information regarding the corresponding manifold. Lastly, with particular reference to this metric, we show that the only variations on \(m(u)\) that occur are \(m=0\), \(m=\text{constant}\), \(m=u\) and \(m=m(u)\).


83C57 Black holes
94A17 Measures of information, entropy
83C40 Gravitational energy and conservation laws; groups of motions
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