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I'm interested in studying two neutron stars orbiting each other and producing gravitational waves. In textbooks the calculation for the power of the radiation is done by considering the neutron stars as points in space. Is this an approximation? If I were to consider them as 3-dimensional objects (for example, numerically using discrete sampling), would I get different value for power or does the spherical shape make it so that this approach would give the same answer as just considering the neutron stars as points?

Edit: I'll try to clarify the problem. When calculating the energy-momentum tensor $T$ for the system of two neutron stars orbiting in a circular orbit, usually the calculation is made simpler by shrinking all of the mass of the neutron star into it's center of mass. My question is, would the result for power change if I didn't do this and instead calculated the energy-momentum tensor by considering the neutron star as it is. Hope this clarifies the question.

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Nov 23, 2022 at 22:52
  • $\begingroup$ The gravitational waves is an effect produced by small variations on the metric that describes the space-time outside of the star ($T_{\mu \nu} = 0$). So, yes, assuming a star is a point in space is simplifiying, but why would you want it to be a sphere, that doesn't give you any information at all. Remeber, the perturbations OUTSIDE the body are the ones that gives you the solution of gravitational waves. $\endgroup$ Nov 23, 2022 at 23:13
  • $\begingroup$ Yes, of course I'm interested in perturbations outside the stars, but the waves are dependent on the source. I'm asking if this simplifying step is changing the source such that the waves change. $\endgroup$ Nov 23, 2022 at 23:21
  • $\begingroup$ For example, considering a single spinning spherical neutron star as the source, making the neutron star into a point doesn't change the results, there is no gravitational waves produced. I'm asking if in my given case this makes difference. $\endgroup$ Nov 23, 2022 at 23:24
  • $\begingroup$ See this. $\endgroup$ Nov 23, 2022 at 23:45

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The calculations you a referring to are usually done as part of a post-Newtonian expansion of binary dynamics. These calculations are greatly simplified by treating the components of the binary as (spinning*) point particles. This is known to be an approximation, however the level of the approximation is well under control. Non-point particle corrections are known to enter the dynamics at the 5th post-Newtonian order, a result known as the effacement principle.

*Effects due to spin enter much earlier in the calculation, but can be included as part of the point particle approximation.

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