Abstract
Using Lie approximate symmetry methods for differential equations second-order approximate symmetries of the geodesic equations for the Kerr–Newman-AdS (KN-AdS) spacetime are investigated. For this purpose the KN-AdS metric is considered as a second perturbation of the AdS metric. A rescaling of the arc length parameter for consistency of the trivial second-order approximate symmetries of the geodesic equations indicates that the energy in the KN-AdS spacetime has to be rescaled. There is an extra contribution to the energy of the KN-AdS spacetime due to the cosmological constant. This energy expression is compared with that for the Kerr–Newman (KN) spacetime.
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Hussain, I. Energy of the Kerr–Newman-AdS black hole by using approximate Lie symmetries. Gen Relativ Gravit 43, 1037–1045 (2011). https://doi.org/10.1007/s10714-010-0961-0
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DOI: https://doi.org/10.1007/s10714-010-0961-0