If we consider the AdS-Schwarzschild manifold, defined by $M^n=[s_0,\infty)\times\mathbb{S}^{n-1}$ equipped with the Riemannian metric $$\overline{g}=\frac{1}{1-ms^{2-n}+s^2}ds\otimes ds+s^2g_{\mathbb{S}^{n-1}},$$ where $m>0$ is a fixed positive number, $s_0$ is the unique positive solution of the equation $1+s_0^2-ms_0^{2-n}=0$ and $g_{\mathbb{S}^{n-1}}$ is the standard round metric on the unit sphere $\mathbb{S}^{n-1}$. The scalar curvature of $M$ is equals $-n(n-1)$.

My question is:

There exists some spin structure on $M$ ?

Since the Hyperbolic space is a particular case when $m\to0$ and the hyperbolic space admits a spin structure, is natural asking for a spin structure on the AdS- Schwarschild space?