  In this paper, we study asymptotic symmetries and algebraically special exact
solutions in the Newman-Penrose formalism. Removing the hypersurface orthogonal
condition in the well studied Newman-Unti gauge, we obtain a generic asymptotic
solution space which includes all possible origins of propagating degree of
freedom. The asymptotic symmetry of the generalized system extends the Weyl-BMS
symmetry by two independent local Lorentz transformations with non-trivial
boundary charges, which reveals new boundary degrees of freedom. The
generalized Newman-Unti gauge includes algebraically special condition in its
most convenient form. Remarkably, the generic solutions satisfying the
algebraically special condition truncate in the inverse power of radial
expansions and the non-radial Newman-Penrose equations are explicitly solved at
any order. Hence, we provide the most general algebraically special solution
space and the derivation is self-contained in the Newman-Penrose formalism. The
asymptotic symmetry with respect to the algebraically special condition is the
standard Weyl-BMS symmetry and the symmetry parameters consist only the
integration constant order. We present the Kerr solution and Taub-NUT solution
in the generalized Newman-Unti gauge in a simple form.
