Hypervelocity stars and RX J0822-4300

[Redsummers]

I was wondering what would be the gravitational force caused by stars with high speed. As an example, I was trying to compute the gravitational force exerted by RX J0822-4300. This radio-quiet neutron star has a radial velocity of 1500Km/s (i.e. 0.5% c).

The thing is that I am not quite sure which equations should be used in this problem. My guess would be to use General Relativity, since I need to bring relativity in the Universal Law of Gravity. Still, I don't know how should I proceed.

Imagine that you are the observer outside the RX J0822-4300.


P.S. This is not homework, just that I am wondering if this would be an application for General Relativity.

 

[Dale]

At 0.005 c you are not going to have much in the way of relativistic effects due to velocity. So you can essentially just use the Schwarzschild metric if you are looking at forces very close to the star. If you are outside of a few Schwarzschild radii then I think that you can probably get away with just using Newtonian gravity. All depending, of course, on the sensitivity/accuracy needed.

 

[Redsummers]

Oh okay, I think I can live with this approximation then. I have another question, if we were to find the gravitational force by a pulsar, rotating very rapidly, would there be any variation compared to the way you just mentioned above?

Thanks for the answer, DS.

 

[Dale]

Well, for a rotating star you would want to use the Kerr metric instead of the Schwarzschild solution, but other than that the comments are the same. It all depends on how close you are and how sensitive/accurate you need to be.

 

[Redsummers]

That's great, thank you for your input.