Buchdahl limit of compact stars in presence of Weyl anomaly

Abstract

We setup an anisotropic compact star model in presence of Weyl ``trace" anomaly. We derive an exact interior solution which determines the contribution of the vacuum trace anomaly. We introduce a dimentionless parameter, $\beta$, to characterize this contribution. Applying appropriate matching conditions with the exterior solution, we determine the model parameters in terms of the Weyl anomaly parameter $\beta$ and the compactness parameter, $C=\frac{2GM}{c^2 \mathcal{R}}$ where $M$ and $\mathcal{R}$ are the mass and the radius of the star. We investigate the parameter space $\{\beta, C\}$ and the corresponding modifications of Buchdahl limit on the maximum compactness. We use astrophysical observations of mass and radius of the pulsar PSR J0740+6620 to constrain the Weyl anomaly parameter $\beta$. Also, we investigate the Mass-Radius diagram with other observational constraints from NICER and LIGO/Virgo collaboration.