In linearized field equations, the metric tensor is writen as $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$, where $|h_{\mu\nu}|\ll 1$ is a small perturbation of the flat Minkowski metric $\eta_{\mu\nu}$ such that, the linearlized Einstein equations then take the form.
\begin{align} \label{eq:linearized_EFEs2} G_{\mu\nu} = \tfrac{1}{2}\left(-\partial_\mu\partial_\nu h - \square h_{\mu\nu} + \partial_\nu\partial_\rho h^\rho_\mu + \partial_\mu\partial_\rho h^\rho_\nu + \eta_{\mu\nu}\left(\square h - \partial_\rho\partial_\sigma h^{\rho\sigma}\right)\right). \end{align}
Taking a gauge transformation as below,
\begin{align} \partial_\mu h^\mu{}_\lambda - \frac{1}{2}\partial_\lambda h = 0, \qquad h \equiv \eta^{\mu\nu}h_{\mu\nu}. \end{align}
we are left with
\begin{align} G_{\mu\nu} = -\frac{1}{2}\left(\square h_{\mu\nu} -\frac{1}{2}\eta_{\mu\nu}\square h\right). \end{align}
The Einstein field equation $G_{\mu\nu} = \kappa T_{\mu\nu}$ becomes
\begin{align} \square h_{\mu\nu} -\frac{1}{2}\eta_{\mu\nu}\square h = -2\kappa T_{\mu\nu}. \end{align}
In vacuum (i.e. $T_{\mu\nu}=0)$ the trace of this equation shows that $\square h =0$, and hence the vacuum field equation becomes
\begin{align} \boxed{ \square h_{\mu\nu} = 0,} \end{align}
which is a homogeneous wave equation for each component of the metric.
My question is: What exactly is the $T_{\mu\nu}$ here; is it the energy-momentum tensor of the source (say a neutron star which is emitting gravitational waves)? Now if $T_{\mu\nu}=0$,then does that mean we are speaking of the spacetime metric in absence of the neutron star? If so, then what is the source of the perturbation $h_{\mu\nu}$ in absence of $T_{\mu\nu}$?
P.S.: I am self studying the basics of gravitational waves and had this doubt while reading Section 17.5 of "General Relativity: An Introduction for Physicists" by M.P. Hobson).
