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We demonstrate that the fermions in Reissner-Nordstr\"{o}m-anti-de Sitterblack hole background in the chiral limit $m=0$, are related to an $N=4$extended one dimensional supersymmetry with non-trivial topological charges. Wealso show that the $N=4$ extended supersymmetry is unbroken and we extend thetwo $N=2$ one dimensional supersymmetries that the system also possess, to havea trivial central charge. The implications of the trivial central charge on theWitten index are also discussed.

Fermions in a Reissner-Nordstr\"{o}m-anti-de Sitter Black Hole Background and $N=4$ Supersymmetry with non-trivial Topological Charges