Does relativistic mass create gravity?

[eNathan]

I know this question was covered here in the past, but I got some mixed answers. I hope somebody can clear this up for me.

[Hurkyl]

Energy density (effectively the "same" as relativistic mass) does indeed contribute to gravity1.

However, momentum also contributes to gravity, and in a way different from the Newtonian "pull things together" picture of gravity. Thus, you cannot simply imagine a speedy object as generating the same type of gravitational field as a stationary object.



1: What I really mean is that it affects the geometry of space-time.

[eNathan]

Well, thank you for a clear answer :) Someone told me before that it does not contribute to gravity at all. Is there an equation to express its Gravitational effects? (But of course there is, what is it?)

[Crosson]

The relativistic equations of gravity are the Einstein Field Equations. This is a set of 16 coupled non-linear partial differential equations.

[pervect]

Well, thank you for a clear answer :) Someone told me before that it does not contribute to gravity at all. Is there an equation to express its Gravitational effects? (But of course there is, what is it?)

http://lanl.arxiv.org/PS_cache/gr-qc/pdf/9909/9909014.pdf

is still the best reference I've found online.

The clearest statement that kinetic energy does indeed contribute to gravitational mass is found in the abstract of this paper.


According to the general theory of relativity, kinetic energy contributes
to gravitational mass. Surprisingly, the observational evidence for this
prediction does not seem to be discussed in the literature. I reanalyze
existing experimental data to test the equivalence principle for the
kinetic energy of atomic electrons, and show that fairly strong limits
on possible violations can be obtained.


The paper is mainly concerned with how the internal kinetic energy of a system with moving parts contributes to it's "gravitational mass" when the momentum of the system as a whole is zero. The guiding result here is that energy and pressure both cause gravity - but, for a closed system, it appears that the virial theorem requires that the appropriate intergal of energy and pressure be equal to the total energy of the system. (This is what I get from reading the paper, I've been meaning to work out some actual examples.)

If you're interested in the gravitational field of a moving object there is an unfortunate problem. As soon as the velocity gets high enough to significantly affect the gravitational field of an object, one cannot consistently view gravity as only a force - the curvature of space itself becomes important. This shows up in the curvature of light, for instance - it curves twice as much as it ought to.

A qualitiative comparison to the electric field of a moving charge can still be made if one does not want exact results. Basically one expects the field to concentrate in a transverse direction rather than to be radially uniform. To really do the problem right requires that one analyze the problem in terms of tidal forces (the Riemann tensor), rather than the "gravitational field".

[Chronos]

Under GR, the answer is simply yes. A body in motion posseses kinetic energy plus mass. Energy and mass are equivalent under GR. Particle colliders routinely confirm this prediction. Crash two particles together at relativistic velocities and you create particles with more mass than the sum of the two crashed particles.