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The pseudo-Newtonian potential of Paczynski and Wiita for particles orbitinga Schwarzschild black hole is generalized to arbitrary static and sphericallysymmetric spacetimes, including black hole solutions of alternative theories ofgravity. In addition to being more general, our prescription differssubstantially from a previous one in the literature, showing that even theassociation of a pseudo-Newtonian potential with a simple black hole metric isnot unique.

Paczynski-Wiita-like potential for any static spherical black hole in metric theories of gravity