Neutron stars: compact objects with relativistic gravity

Abstract: General properties of neutron stars are briefly reviewed with an emphasis on the indispensability of general relativity in our understanding of these fascinating objects. In Newtonian gravity the pressure within a star merely plays the role of opposing self-gravity. In general relativity all sources of energy and momentum contribute to the gravity. As a result the pressure not only opposes gravity but also enhances it. The later role of pressure becomes more pronounced with increasing compactness, $M/R$ where $M$ and $R$ are the mass and radius of the star, and sets a critical mass beyond which collapse is inevitable. This critical mass has no Newtonian analogue; it is conceptually different than the Stoner-Landau-Chandrasekhar limit in Newtonian gravity which is attained asymptotically for ultra-relativistic fermions. For white dwarfs the general relativistic critical mass is very close to the Stoner-Landau-Chandrasekhar limit. For neutron stars the maximum mass---so called Oppenheimer-Volkoff limit---is significantly smaller than the Stoner-Landau-Chandrasekhar limit. This follows from the fact that the general relativistic correction to hydrostatic equilibrium within a neutron star is significant throughout the star, including the central part where the mass contained within radial coordinate, $m(r)$, and the Newtonian gravitational acceleration, $Gm(r)/r^2$, are small.