# Can gravity give neutrons a longer lifespan? [duplicate]

Isolated neutrons have a lifespan of about one minute yet neutrons in a neutron star can have the lifespan of the neutron star itself and not decay into proton and electron. Is the intense gravity keeping the neutrons from decaying?

• Yes it is the gravitational binding that stabilizes neutrons in neutron stars. – Lewis Miller Apr 15 '18 at 0:08
• Free neutrons have a mean lifetime of around 881 seconds, which equates to a half-life of around 611 seconds. – PM 2Ring Apr 15 '18 at 1:25
• Also, neutron stars aren't just composed of neutrons, they do have some protons and electrons mixed in, and they have a crust that contains relatively normal matter. – PM 2Ring Apr 15 '18 at 1:28
• The lifetime of neutrons is not the life of the neutron star. Beta and inverse beta decay reactions are suppressed but continue via the modified URCA process. The lifetime is probably extended by orders of magnitude though. – Rob Jeffries May 3 '18 at 21:39

In neutron stars gravity does not directly stabilise the neutrons. Rather, gravity forces the particles of matter together to a very high density where it is balanced by the degeneracy pressure (fermions cannot be in the same quantum state and this prevents them from being arbitrarily close-packed). As matter get packed together the reaction $p^+ + e^- \rightarrow n^0 + \nu$ occurs turning it into neutrons. This happens because the electrons are packed so tightly that they have to reach high energies (this is due to the Heisenberg relation $\Delta x\Delta p>h$; as the position uncertainty decreases the momentum range must increase). The reverse reaction, neutron decay, creates an electron: $n^0 \rightarrow p^+ + e^- +\bar{\nu}$. But there is no space for the electron, so this is inhibited. The chemical potential is negative: you need extra energy to make the neutrons decay here.
There is another way neutrons can be stabilised by gravity and that is time dilation. Place a neutron at a very low gravitational potential and the decay rate as measured by remote observers will decline. This is a minor effect, since it scales as $1/(1-\Delta\Phi/c^2)$ for milder fields. For neutron star surfaces this might give you a lifespan 1.4 to 1.7 times longer. For black holes it scales as $1/\sqrt{1-r_S/r}$. If we put a neutron one Planck length outside a supermassice $10^9 M_\odot$ black hole we can get a factor of $4\times 10^{23}$ - suddenly that the neutron would be very long-lasting.