Trace anomaly and compact stars

TL;DR

This paper challenges the common belief that quantum effects in curved spacetime are only relevant near the Planck scale, showing instead that trace anomalies can become significant at lower, macroscopic scales in compact stars.

Contribution

It introduces a new scale at which trace anomalies become macroscopic, based on universal QFT properties, and explores their effects on the structure and wave propagation in compact stars.

Findings

Trace anomaly effects become relevant at scales lower than the Planck mass.

Negative curvature regions form inside compact stars near the Buchdahl limit.

Qualitative changes in scalar wave spectra occur due to anomaly-induced curvature.

Abstract

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.