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ISCO, Lyapunov exponent and Kolmogorov-Sinai entropy for Kerr-Newman Black hole

We compute the principal Lyapunov exponent and Kolmogorov-Sinai(KS) entropy for Kerr-Newman black hole space-times and investigate the stability and instability of the equatorial circular geodesics via these exponents. We also show that the principal Lyapunov exponent and KS entropy can be expressed in terms of the radial equation of ISCO(innermost stable circular orbit) for timelike circular geodesics. The other aspect we have studied that among the all possible circular geodesics, which encircle the central black-hole, the timelike circular geodesics has the longest orbital period i.e. T_{timelike} > T_{photon}, than the null circular geodesics (photon sphere) as measured by asymptotic observers. Thus, the timelike circular geodesics provide the slowest way to circle the Kerr-Newman black-hole. In fact, any stable timelike circular geodesics other than the ISCO traverses more slowly than the null circular geodesics.