If a large object is moving towards another large object at relativistic speeds, an observer on one object will measure a higher mass of the other object, but will an observer on either object measure an increased gravitational field of the other object?
I heard that the certain components of the stress-energy tensor transform so that there is no effective increase in the gravitational field of the object. Those components are apparently frame dependent.
How does this work?
I don’t know the answer - but I’m wondering, how would one measure the mass of an object moving toward one at relativistic speed, independently of measuring its gravity? Doesn’t measuring the mass of a distant body depend on measuring its gravitation effect on or from other bodies?
Qeue,
The other day the checkout girl in my local supermarket asked me this very question, and I confess I was absolutely stumped. I’ll be very glad to see a clear and concise answer from someone who knows what’s what.
Out of curiosity, where the fark do you shop? 
The last time somebody asked this, I said yes and was quickly corrected; the answer is no, but I’m not the one you want to hear it from. Apparently, relativistic mass is purely inertial.
Morpheus
I think you need to know the mass of the object and with the formula below calculate its relativistic mass.
mr = mo / sqrt(1-v^2/c^2)
mr is the relativistic mass
mo is the inertial mass
v is velocity
c is… well, you know
The quote below from John Baez is, I think, the same scenario which I’m referring. However, I don’t quite understand the details.
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html
Relativistic mass plays no role in gravitation. The simplest way to see this is to realize that If it did then a single relativistic particle could collapse stellar objects into black holes.
Achernar
Thanks for the link!
I’ve read that thread through a couple of times. If I understand correctly what JSPrinceton is saying is that it is the energy from acceleration which must be confined to a small patch of spacetime that could form an event horizon.
But once a constant velocity is attained, no horizon or extra gravitational field will be present.
I think.
Actually, I think I’m still a little confused.
Ring
Thats what I originally thought. And that is what John Baez alludes to as well in the article I linked.
And I think I understand this somewhat accurately but I just can’t put my finger on some of the details of the stress-energy tensor and how it works.
That sounds pretty cool, but I don’t understand. How could it do that?
If one uses the notion of “relativistic mass” (i.e., rest mass times [symbol]g[/symbol]), then you just need to go into the reference frame of a cosmic ray, and look at the Sun. In the cosmic ray’s reference frame, of course, it’s at rest, and the Sun is moving at an insane fraction of the speed of light. Were collapse into a black hole simply a function of “relativistic mass”, then from the cosmic ray’s frame, the Sun would be more than massive enough.
Hmmm. Well couldn’t you get the same result just from Lorentz contraction? If we had a rod the mass of the sun, and 3 km wide, and 1 AU long, it would not be a black hole in its rest frame. In a frame with gamma = 50,000,000, though, you’d have the mass of the sun within 3 km. What’s wrong with that?
If you had a flow of charged particles, Lorenz contraction enhances the electric field, right? (That’s what magnetism is, I thought.) So why wouldn’t Lorentz contraction enhance gravity?
First of all charge is an invariant so it doesn’t increase with a Lorentz contraction, but mass does if you subscribe to the concept of relativistic mass. So there’s one difference. Second, gravity doesn’t just depend on mass it also depends on momentum flux, and the combined effect of a contracted mass and the subsequent momentum prevents the object from ever reaching the black hole stage. IOW you have to take into consideration the entire stress-energy tensor.
An interesting thought…If a Lorentz contraction could change the rest volume of a hunk of U235, Saddam would have a whole new way of building a nuclear weapon.
This paper states that kinetic energy contributes to gravitational mass. That would infer relativistic mass contributes to gravitational mass, yes?
Ring, did you answer my question about the big rod? I can’t tell.
Hmmm… it does not appear that anyone disagrees with the paper I linked.
It states that kinetic energy has “weight.”
It also states that, “light falls with twice the acceleration of ordinary matter.”
Any takers?