#### ohwilleke

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- Summary
- I am trying to get a sense of the magnitude of the mass contribution to the gravitational effects via the stress-energy tensor relative to other components (EM flux, kinetic energy, pressure, angular momentum) in a typical system like a solar system or galaxy.

In Newtonian gravity, non-rest mass contributions to gravitational effects are ignored and for many purposes (e.g. low precision solar system astronomy, N-body approximations of galaxy or galaxy cluster dynamics), the other contributions that enter Einstein's field equations through the stress-energy tensor can be ignored without changing the final results very much.

But, the other contributions such as electro-magnetic flux, linear momentum, pressure, and angular momentum do enter into Einstein's field equations and if you are being sufficiently precise, you need to consider them. For example, you need to consider them when calculating frame dragging effects or gravito-magnetic effects.

As a practical matter, in a typical system, like determining the gravitational pull on objects not moving at relativistic speeds in the solar system, or in a galaxy or galaxy cluster, not in the immediate vicinity of (or within) a black hole or neutron star, what percentage of gravitational effects in classical GR can be attributed to rest mass and how much can be attributed to other non-rest mass gravitational source?

Maybe specific examples would be easier to talk about. For example, the precession of Mercury is a system affected by non-mass contributions to the stress-energy tensor. What proportion of the total gravitational pull on Mercury is due to these non-mass contributions and what is simply due to mass (treated in a GR way rather than with Newton's gravity equation)? Or, what difference do non-mass contributions make to the path of the solar system around the Milky Way?

In lieu of a percentage, a sense of the order of magnitude contribution of mass v. non-mass components (and ideally of the respective non-mass components relative to each other), would be fine and helpful.

My sense is that it is usually pretty small, but that's a pretty vague understanding.

Are we talking one part in ten, one part in a thousand, or one part in millions or trillions?

But, the other contributions such as electro-magnetic flux, linear momentum, pressure, and angular momentum do enter into Einstein's field equations and if you are being sufficiently precise, you need to consider them. For example, you need to consider them when calculating frame dragging effects or gravito-magnetic effects.

As a practical matter, in a typical system, like determining the gravitational pull on objects not moving at relativistic speeds in the solar system, or in a galaxy or galaxy cluster, not in the immediate vicinity of (or within) a black hole or neutron star, what percentage of gravitational effects in classical GR can be attributed to rest mass and how much can be attributed to other non-rest mass gravitational source?

Maybe specific examples would be easier to talk about. For example, the precession of Mercury is a system affected by non-mass contributions to the stress-energy tensor. What proportion of the total gravitational pull on Mercury is due to these non-mass contributions and what is simply due to mass (treated in a GR way rather than with Newton's gravity equation)? Or, what difference do non-mass contributions make to the path of the solar system around the Milky Way?

In lieu of a percentage, a sense of the order of magnitude contribution of mass v. non-mass components (and ideally of the respective non-mass components relative to each other), would be fine and helpful.

My sense is that it is usually pretty small, but that's a pretty vague understanding.

Are we talking one part in ten, one part in a thousand, or one part in millions or trillions?

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