Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time Dilation at Center of a Neutron Star

  1. Dec 7, 2011 #1
    From https://www.physicsforums.com/showthread.php?t=40391 in gravitational time dilation.

    At the center of neutron star PSR J1614-2230 at 1.97 SM

    mass of Sun 1.9891×10^30 kg

    mass of PSR J1614-2230. 4 ×10^30

    gravitational constant = 6.67300 × 10-11 m3 kg-1 s-2

    radius(rough estimate) = 10000m

    phi = - 3/2 * 6.67300 × 10-11 * 4 ×10^30 / 10000

    phi = - 4 × 10^20 / 10000

    phi = - 4 × 10^16

    sqrt( 1 + 2phi/c^2 )

    sqrt( 1 - 2 * 4 × 10^16 / (3^10^8)^2

    sqrt( 1 - 8 / 9 )

    sqrt( 1/9) = .33

    so time runs perhaps three times as slowly at the center than in an area of weak gravity.

    I have read that the gravity of a neutron star owes more to its pressure than its mass. I don't know whether these figures take that into account.
  2. jcsd
  3. Dec 7, 2011 #2


    User Avatar
    Science Advisor
    Gold Member

    Presumably the M_tot includes all the contributions from pressure/energy. I'm not sure about interior solutions, but this is at least the case for the exterior Schwarzschild solution.
  4. Dec 7, 2011 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    The general form of the interior metric of a neutron star is not currently known, as far as I know, because the equation of state of the neutron degenerate matter, rho(P), is not known.


    If you did know (or assume you knew) the equation of state, for a static star solving Einstein's equations (the interior Schwarzschild solution) arising from that equation of state would give you the interior metric, and hence the time dilation. If you wanted to go beyond the static approximation (i.e. to include the effects of radiation on the stellar structure), you'd need an even more sophisticated model.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook