On a local study of star boundaries

Abstract In this paper, we will present a local study of star boundaries along three different routes. Firstly, we will develop a local algorithm based on curvature scalars for identifying invariantly the boundary of a star; we will distinguish between the cases of stars supported by fluids with either isotropic or anisotropic pressure, and we will successfully test our proposal for a number of available analytical spacetimes not necessarily stationary. Our method will be based on the trace anomaly, the variation of volume along a geodesic and the skewness of the matter content. Next, restricting to some Tolman’s metrics, we will recast the Buchdahl’s bound for global and physical quantities, as the mass and radius of the star, into a local inequality between Weyl and Ricci curvature scalars at the boundary: our results will allow to inspect the required interplay between pure gravitational and pure matter energy in supporting the equilibrium. Lastly, we will relate the non-local complexity factor of the matter content for those Tolman’s solutions to a local Weyl scalar in a unified manner. We will compare and contrast our paradigm with the geometric horizon conjecture for black holes also in the context of the no-hair theorem and holographic principle. From the physical perspective, our present research scrutinizes which global properties of bounded compact objects can actually be fully accounted for by local measurements, while from the mathematical side, it provides a transparent foundation via the formalism of differential geometry to some numerical relativity techniques adopted in astrophysical simulations.