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Thread: what is the gravitational time-dilation at the centre of a neutron star?

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    what is the gravitational time-dilation at the centre of a neutron star?

    At the surface it is 8/10...I think, but someone who was at or near the centre, in a impossibly strong box/room would be at the bottom of the neutron star's gravity well, so must be experiencing the highest g-time-dilation.

    In regard to this question, if this person had a meter rule, and you could somehow see him and his meter rule, what size would it appear?
    I've never really been sure about this, but knowing that gravitational time-dilation does/can lead to the self-magnifying effect, which can be visualised by thinking of the different paths that light takes between the two ends of the ruler, and the distant observer...
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    Quote Originally Posted by WaxRubiks View Post
    At the surface it is 8/10...I think, ...
    The only anecdotal data I've seen about this was from quite a few years ago, but the 511 KeV gamma rays coming from an isolated neutron star (IIRC it was Geminga), were measured at about 400 KeV. Please note that that is ONE neutron star, and that there are many neutron stars over a range of masses, so you'd have to expect a range of gravitational red shifts.
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    Quote Originally Posted by antoniseb View Post
    The only anecdotal data I've seen about this was from quite a few years ago, but the 511 KeV gamma rays coming from an isolated neutron star (IIRC it was Geminga), were measured at about 400 KeV. Please note that that is ONE neutron star, and that there are many neutron stars over a range of masses, so you'd have to expect a range of gravitational red shifts.
    yes, but I think the range isn't very large?

    I think if a neutron star were to become too massive(from infalling matter) then it would go into further collapse until it has turned into ablack hole, and if somehow were to lose mass it would return to being a white dwarf..?
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    This calculation looks correct to me, so that put it at about 1/3. (I was confident that I could find someone else who had done the math...)
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    1/3 is quite high.

    neutron star 2.jpg

    In this diagram, the man in the room has a light which flashes every second. There is a mirror one meter away from the light.
    The light flashes, and then later the light reflects off the mirror so that the distant observer can 'see' it.

    Is the time interval between the light flash and the mirror reflecting the flash, as you would expect if light would be seen as travelling at c for the distant observer, ie 1m/c seconds?]]

    Or is it something else? eg a longer time interval?
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    Quote Originally Posted by WaxRubiks View Post
    1/3 is quite high.
    It is quite high.

    Quote Originally Posted by WaxRubiks View Post
    Is the time interval between the light flash and the mirror reflecting the flash, as you would expect if light would be seen as travelling at c for the distant observer, ie 1m/c seconds?]]

    Or is it something else? eg a longer time interval?
    So, if we assume we've somehow made a transparent window all the way to the neutron star core, so an outside observer can see what's going on, everything will be slowed by the same factor of roughly 3. So the light will be observed to flash once every three seconds, the delay between each pulse and the reflected pulse will be three times as long as if the apparatus were in open space, and the wavelength of the light will be longer by a factor of 3.
    Conserve energy. Commute with the Hamiltonian.

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    Quote Originally Posted by Grey View Post
    It is quite high.

    So, if we assume we've somehow made a transparent window all the way to the neutron star core, so an outside observer can see what's going on, everything will be slowed by the same factor of roughly 3. So the light will be observed to flash once every three seconds, the delay between each pulse and the reflected pulse will be three times as long as if the apparatus were in open space, and the wavelength of the light will be longer by a factor of 3.
    what if this room is filled with cigarette smoke, and we are able to see the passage of the flash towards the mirror.
    and there is also a similar room, filled with cigarette smoke, the same distance from the observer, but away from the neutron star all together.

    Do we see the passage of the light towards the mirror, travelling at the same rate?

    If so then that might mean that things in the room have become magnified, by gravity, by the same rate as time dilation, ie the distance between the light-bulb and the mirror look like they are 3 meters apart..?

    And we know that things in gravitational fields are self magnified, when we look at it from the point of the curved path of light towards the observer...
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    Quote Originally Posted by WaxRubiks View Post
    what if this room is filled with cigarette smoke, and we are able to see the passage of the flash towards the mirror.
    and there is also a similar room, filled with cigarette smoke, the same distance from the observer, but away from the neutron star all together.

    Do we see the passage of the light towards the mirror, travelling at the same rate?

    If so then that might mean that things in the room have become magnified, by gravity, by the same rate as time dilation, ie the distance between the light-bulb and the mirror look like they are 3 meters apart..?

    And we know that things in gravitational fields are self magnified, when we look at it from the point of the curved path of light towards the observer...
    I know that distances are also distorted in a strong gravitational field. For example, I believe that the distance from any point outside a black hole to the event horizon is infinite. However, most of the work I've seen deals with the exterior of the Schwarzschild solution, not the interior. I'm not exactly sure what would be observed in the case you describe.
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    Someone correct me if I am wrong but at the center of a neutron star there would be no measurable gravitational force, just like at the center of the Earth.

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    Quote Originally Posted by billslugg View Post
    Someone correct me if I am wrong but at the center of a neutron star there would be no measurable gravitational force, just like at the center of the Earth.
    Gravitational time dilation is about potential, not apparent force.
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    Quote Originally Posted by WaxRubiks View Post
    yes, but I think the range isn't very large?
    A neutron star has a mass of at least 1.1 and perhaps up to 3 solar masses (M).[24][25] The maximum observed mass of neutron stars is about 2.01 M. But in general, compact stars of less than 1.39 M (the Chandrasekhar limit) are white dwarfs, whereas compact stars with a mass between 1.4 M and 3 M (the Tolman–Oppenheimer–Volkoff limit) should be neutron stars (though there is an interval of a few tenths of a solar mass where the masses of low-mass neutron stars and high-mass white dwarfs can overlap).
    https://en.wikipedia.org/wiki/Neutron_star#Properties
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    Quote Originally Posted by WaxRubiks View Post
    I think if a neutron star were to become too massive(from infalling matter) then it would go into further collapse until it has turned into ablack hole, and if somehow were to lose mass it would return to being a white dwarf..?
    No, a BH can't just pop back through its event horizon because it lost mass. Black holes are believed to lose mass through Hawking radiation, albeit rather slowly. A 5 M BH would radiate its mass over something like 1070 years, but would never convert back to a white dwarf.

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    Quote Originally Posted by VQkr View Post
    No, a BH can't just pop back through its event horizon because it lost mass. Black holes are believed to lose mass through Hawking radiation, albeit rather slowly. A 5 M BH would radiate its mass over something like 1070 years, but would never convert back to a white dwarf.
    no I meant a neutron star, if it somehow lost mass, would revert back to a white dwarf...I think.
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    Quote Originally Posted by WaxRubiks View Post
    no I meant a neutron star, if it somehow lost mass, would revert back to a white dwarf...I think.
    Apparently, the minimum stable mass of a neutron star is about 0.2 solar masses, or a little lower, although it's not entirely clear exactly how such a neutron star could form (or how an existing neutron star could lose that much mass). Here's one suggestion, which further suggests that dropping below the stable mass would result in an explosion.
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    Quote Originally Posted by Grey View Post
    Apparently, the minimum stable mass of a neutron star is about 0.2 solar masses, or a little lower, although it's not entirely clear exactly how such a neutron star could form (or how an existing neutron star could lose that much mass). Here's one suggestion, which further suggests that dropping below the stable mass would result in an explosion.
    I'm not surprised there might be an explosion...to go from all neutrons(mostly) back to carbon and oxygen atoms(I think) might be too complex a change..

    One way a neutron star could hypothetically lose mass is if a constant mist of antimatter fell on it for a long time....I suppose.
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