Quasilocal energy, Komar charge and horizon for regular black holes

We study the Brown–York quasilocal energy for regular black holes. We also express the identity that relates the difference of the Brown–York quasilocal energy and the Komar charge at the horizon to the total energy of the spacetime for static and spherically symmetric black hole solutions in a convenient way which permits us to understand why this identity is not satisfied when we consider nonlinear electrodynamics. However, we give a relation between quantities evaluated at the horizon and at infinity when nonlinear electrodynamics is considered. Similar relations are obtained for more general static and spherically symmetric black hole solutions which include solutions of dilaton gravity theories.