  A widespread assumption states that quantum effects of matter in curved
spacetimes become relevant only when the inverse curvature radius approaches
the Planck mass $m_{\text{P}}$. We challenge this view by showing that, relying
solely on universal properties of QFTs at high energies, the trace anomaly
becomes macroscopic instead at energy scales $ \left( m/m_{\text{P}}
\right)^{\frac{1-\alpha}{2-\alpha}} m_{\text{P}}$, where $m\ll m_{\text{P}}$
and $\alpha<1$ are, respectively, the mass scale and exponent appearing in the
matter equation of state at high energies. As an application, we consider
compact stars close to their Buchdahl limit, and examine the propagation of
scalar waves on the resulting backreacted geometries. At the aforementioned
energy scale, the curvature becomes negative within a neighborhood of the the
star's center, implying a qualitative change in the behavior of the associated
spectrum of modes.
