Polytropic stars in bootstrapped Newtonian gravity

Abstract

We study self-gravitating stars in the bootstrapped Newtonian picture for polytropic equations of state. We consider stars that span a wide range of compactness values. Both matter density and pressure are sources of the gravitational potential. Numerical solutions show that the density profiles can be well approximated by Gaussian functions. Later we assume Gaussian density profiles to investigate the interplay between the compactness of the source, the width of the Gaussian density profile and the polytropic index. We also dedicate a section to comparing the pressure and density profiles of the bootstrapped Newtonian stars to the corresponding General Relativistic solutions. We also point out that no Buchdahl limit is found, which means that the pressure can in principle support a star of arbitrarily large compactness. In fact, we find solutions representing polytropic stars with compactness above the Buchdhal limit.

21 pages, 10 figures

References in corpus (6)

• Matter and gravitons in the gravitational collapse
• Black Hole Masses are Quantized
• Quantum black holes in bootstrapped Newtonian gravity
• Self-Consistent, Self-Coupled Scalar Gravity
• On the mass of bootstrapped Newtonian sources
• Bootstrapped Newtonian quantum gravity

Cited by in corpus (8)

• Quantum black holes in bootstrapped Newtonian gravity
• Effective metric outside bootstrapped Newtonian sources
• Quantum fields in teleparallel gravity: renormalization at one-loop
• Orbits in bootstrapped Newtonian gravity
• Binary mergers in bootstrapped Newtonian gravity: mass gap and black hole area law
• Compact sources and cosmological horizons in lower dimensional bootstrapped Newtonian gravity
• Approximating compact objects in bootstrapped Newtonian gravity: use of the canonical potential
• Newtonian approximation in (1 + 1) dimensions