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, β , to characterize this contribution. Applying appropriate matching conditions with the exterior solution, we determine the model parameters in terms of the Weyl anomaly parameter β and the compactness parameter, C = 2 G M c 2 R where M and R are the mass and the radius of the star. We investigate the parameter space { β , 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 β . Also, we investigate the Mass-Radius diagram with other observational constraints from NICER and LIGO/Virgo collaboration.