Neutrons stars can be analyzed in a very similar manner to white-dwarf stars. In fact, the previous analysis can be simply modified by letting and . Thus, we conclude that non-relativistic neutrons stars satisfy the mass-radius law:

(8.218) |

It follows that the radius of a typical solar mass neutron star is a mere 10km. In 1967, Antony Hewish and Jocelyn Bell discovered a class of compact radio sources, called

When relativistic effects are taken into account,
it is found that there is
a critical mass above which a neutron star cannot be maintained against
gravity.
According to our analysis,
this critical mass, which is known as the *Oppenheimer-Volkoff
limit*, is given by

(8.219) |

A more realistic calculation, which does not assume constant density, does not treat the neutrons as point particles, and takes general relativity into account, gives a somewhat lower value of

1.5-2.5 | (8.220) |

A star whose mass exceeds the Oppenheimer-Volkoff limit cannot be maintained against gravity by degeneracy pressure, and must ultimately collapse to form a black-hole.