LQ Stars : Modifying the Tolman -- Oppenheimer -- Volkoff equations a la LQC

Abstract

We rewrite the Tolman -- Oppenheimer -- Volkoff (TOV) equations for four and higher dimensional static spherically symmetric stars so that they resemble the equations for anisotropic cosmology. This becomes possible by treating the curvature terms of the sphere as part of the matter sector. Comparing then with the effective equations in the Loop Quantum Cosmology -- inspired models, we propose analogous modifications to the TOV equations which contain one arbitrary function. A linear function gives the TOV equations. If the function and all its derivatives are finite then the solutions are non singular. For $sin \; x \;$, an `image star' appears beyond the central region of maximal pressures in the original star. This is evocative of a bouncing universe in Loop Quantum Cosmology. We discuss possible observational consequences of these features.