Abstract
We calculate the effective Komar angular momentum for the Kerr-Newman (KN) black hole. This result is valid at any radial distance on and outside the black hole event horizon. The effective values of mass and angular momentum are then used to derive an identity (\(K_{\chi^{\mu}}=2ST\)) which relates the Komar conserved charge (\(K_{\chi^{\mu}}\)) corresponding to the null Killing vector (χ μ) with the thermodynamic quantities of this black hole. As an application of this identity the generalised Smarr formula for this black hole is derived. This establishes the fact that the above identity is a local form of the inherently non-local generalised Smarr formula.
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Notes
For a possible justification for the anomalous factor 2 see [13].
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Acknowledgements
One of the authors (S.K.M) thanks the Council of Scientific and Industrial Research (C.S.I.R), Government of India, for financial support.
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Modak, S.K., Samanta, S. Effective Values of Komar Conserved Quantities and Their Applications. Int J Theor Phys 51, 1416–1424 (2012). https://doi.org/10.1007/s10773-011-1017-2
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DOI: https://doi.org/10.1007/s10773-011-1017-2