  Effects of activity on glassy dynamics are fundamental in several biological
processes. Active glasses extend the scope of the equilibrium problem and
provide new control parameters to probe different theoretical aspects. In the
theory of glassy dynamics, different length scales play pivotal roles. Here,
for the first time, we present results for the static length scale, $\xi_S$, in
an active glass via large-scale molecular dynamics simulations for model active
glasses in three spatial dimensions. We show that although the relaxation
dynamics are equilibrium-like, activity has non-trivial effects on $\xi_S$.
$\xi_S$ plays the central role in the random first-order transition (RFOT)
theory. Thus, our work provides critical tests for the active RFOT theory, a
phenomenological extension of its equilibrium counterpart. We find that the two
exponents, $\theta$ and $\psi$, within the theory, become activity-dependent,
exposing the non-trivial effects of activity on $\xi_S$. However, the
combination of $\theta$ and $\psi$, which controls the relaxation dynamics,
remains nearly independent of activity leading to the effectively
equilibrium-like behavior. Interestingly, $\xi_S$ shows higher growth in an
active glass; this should help better comparison of theories with simulations
and experiments.
