  In this work, we mainly consider the Cauchy problem for the reverse
space-time nonlocal Hirota equation with the initial data rapidly decaying in
the solitonless sector. Start from the Lax pair, we first construct the basis
Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation.
Furthermore, using the approach of Deift-Zhou nonlinear steepest descent, the
explicit long-time asymptotics for the reverse space-time nonlocal Hirota is
derived. For the reverse space-time nonlocal Hirota equation, since the
symmetries of its scattering matrix are different with the local Hirota
equation, the $\vartheta(\lambda_{i})(i=0, 1)$ would like to be imaginary,
which results in the $\delta_{\lambda_{i}}^{0}$ contains an increasing
$t^{\frac{\pm Im\vartheta(\lambda_{i})}{2}}$, and then the asymptotic behavior
for nonlocal Hirota equation becomes differently.
