# Is relative mass making gravitational field?

by marshallaw
Tags: field, gravitational, mass, relative
 P: 1 Hello When you have something and it gains a lot of mass m due to its high kinetic energy, so it gains a lot of relative energy. So, every object has its own gravitational field. So is the RELATIVE mass making a gravitatinal field? mathematically if g=GM/Rˇ2 does work, where you MUST add relative mass Well this would be very amazing, strange, bizzare if this was true
 Emeritus Sci Advisor PF Gold P: 5,597 If I'm understanding correctly, then you're using the terms "relative energy" and "relative mass" to mean what is referred to in standard terminology as mass-energy. In standard (modern) terminology, "mass" is absolute, not relative. What we now call mass is what people used to refer to as rest mass. The source of the gravitational field is the stress-energy tensor, not mass-energy. You can sometimes get away with estimating gravitational effects by plugging mass-energy into Newton's law of gravity, but it won't always work. For example, parallel beams of light exert zero gravitational force on one another, but antiparallel ones exert nonzero force.
 Sci Advisor PF Gold P: 5,059 A next level of approximation is invariant mass. It is often accurate up to the point where self gravitation is important, for simple systems. For example it 'explains' the anti-parallel vs. parallel beams. In the former, the invariant mass of the system adds the beam energy because the momentum cancels. In the parallel case, the invariant mass is zero. Similarly, the KE of an isolated body (no matter how fast it is moving in some frame) has no relevance for any curvature invariant produced by it. However, as part of confined system of bodies (e.g. particles in a box), the invariant mass of the system will tend to include much of the KE of each body due to momentum cancellation. Just don't take this too far - the real source, as mentioned, is the stress energy tensor.
 Sci Advisor P: 5,437 Is relative mass making gravitational field? this question could be studied using the Aichelburg–Sexl ultraboost metric http://en.wikipedia.org/wiki/Aichelb...exl_ultraboost
 Sci Advisor P: 899 I would like to nominate that as the metric with the most beautiful name.
 Emeritus Sci Advisor P: 7,622 I tend to view energy (sometimes called relativistic mass) as a better approximation for gravity in most circumstances than invariant mass. Examples where this approach works reasonably well. particles in a box moving thermally velocities induced by a relativistic flyby. In fact, the velocities induced by a relativistic flyby increase MORE rapidly than the approximation usig energy- see http://dx.doi.org/10.1119/1.14280 . So using invariant mass to compute velocities due to a relativistic flyby is a very bad approximation, it's off by a factor of 2*gamma, whereas the using energy is only off by a factor of 2:1 or so. But as everyone has pointed out, the actual situation is more complex, it's really the stress energy tensor that causes gravity, and if you want to get truly accurate answers that's what you need to use. Which leads to the other reason I like to use energy. It's easier to justify as an approximation - you're approximating the stress-energy tensor by just the energy part, and throwing away the others (the momentum part, and the stress part). Invariant mass isn't part of the stress energy tensor the way energy is. The other thing that's worth mentioning is that F=GmM/r^2 doesn't work at all for relativistically moving bodies. The "field" from a moving body isn't at all spherically symmetric. Some insight into this can be gained by considering the electric field of a rapidly moving body. A search should find a lot of posts on this topic.
P: 5,632
Marshallaw.....WOW you got great replies here,,,,,sometimes an initially insigthful answer spawns others.....
As usual when members of this group reply I have some recollecting to do. If you are
that way, check out the first section here:
http://en.wikipedia.org/wiki/Invariant_mass
for a bit of background.....especially 'frames'.

 The source of the gravitational field is the stress-energy tensor, not mass-energy.
took me by surprise when I first read it several years ago. Later I realized that it meant the mass-energy was only a piece of the source....as pervect illustrated while I was typing!