  In this study, we provide some classifications for half-conformally flat
gradient $f$-almost Ricci solitons, denoted by $(M, g, f)$, in both Lorentzian
and neutral signature. First, we prove that if $||\nabla f||$ is a non-zero
constant, then $(M, g, f)$ is locally isometric to a {warped product} of the
form $I \times_{\varphi} N$, where $I \subset \mathbb{R}$ and $N$ is of
constant sectional curvature. On the other hand, if $||\nabla f|| = 0$, then it
is locally a {Walker manifold}. Then, we construct an example of 4-dimensional
steady gradient $f$-almost Ricci solitons in neutral signature. At the end, we
give more physical applications of gradient Ricci solitons endowed with the
standard static spacetime metric.
