Gravitational time dilation and neutron stars

Question

How great is the gravitational time dilation close to a neutron star? How would the effects of gravitational time dilation compare with the event horizon of a black hole?

Answer 1

As it says in the Wikipedia article referred to by Kyle, the relevant formula applicable to clocks situated in the gravitational field of a spherically symmetric object is that an observer at infinity sees a clock in the gravitational field slowed by a factor $(1 - r_s/r)^{-1/2}$, where $r_s$ is the Schwarzschild radius.

For a non-rotating black hole, the Schwarzschild radius marks the event horizon and at $r = r_s = 2GM/c^2$, and the time dilation becomes infinite.

Neutron stars have radii that are at least $\sim 1.5$ times their Schwarzschild radii, and more likely closer to 2 times as big. Thus typical time dilation factors at their surfaces are 1.7 to 1.4.

A clock falling towards a neutron star will appear to run slower as it falls inwards until it reaches these maximum dilation factors just as it hits the neutron star surface. Unlike for a black hole, an external observer will see objects hitting the neutron star surface in a finite time. This phenomenon is observed in X-ray bursters.