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Here we have developed the general parametrization for spherically symmetricand asymptotically flat black-hole spacetimes in an arbitrary metric theory ofgravity. The parametrization is similar in spirit to the parametrizedpost-Newtonian (PPN) approximation, but valid in the whole space outside theevent horizon, including the near horizon region. This generalizes thecontinued-fraction expansion method in terms of a compact radial coordinatesuggested by Rezzolla and Zhidenko [Phys.Rev.D 90 8, 084009 (2014)] for thefour-dimensional case. As the first application of our higher-dimensionalparametrization we have approximated black-hole solutions of theEinstein-Lovelock theory in various dimensions. This allows one to write downthe black-hole solution which depends on many parameters (coupling constants infront of higher curvature terms) in a very compact analytic form, which dependsonly upon a few parameters of the parametrization. The approximate metricdeviates from the exact (but extremely cumbersome) expressions by fractions ofone percent even at the first order of the continued-fraction expansion, whichis confirmed here by computation of observable quantities, such as quasinormalmodes of the black hole.

General parametrization of higher-dimensional black holes and its application to Einstein-Lovelock theory