Neutron stars: compact objects with relativistic gravity

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.