  In this short note we explain how to adapt the construction of two Riemannian
metrics on the $\mathrm{SL}(3,\mathbb{R})$-Hitchin component to the deformation
space of globally hyperbolic anti-de Sitter structures: the pressure metric and
the Loftin metric (studied by Qiongling Li). We show that the former is
degenerate and we characterize its degenerate locus, whereas the latter is
nowhere degenerate and the Fuchsian locus is a totally geodesic copy of
Teichm\"uller space endowed with a multiple of the Weil-Petersson metric.
