Does relativistic mass induce gravity?

[Lee Wang]

I've read conflicting accounts on this subject. Some say it does, some say it doesn't, some say the entire idea of relativitic mass is a "rampant pedagogical virus". So please inform me when I'm making a mistake. So does the gravity of an object it exerts on it surroundings increase with it's speed?

If so, consider the following experiment. A spaceship nearing the light speed just whooses past a star so that v->c. The captain then orders to speed up the spaceship with a precisely calculated amount so as to make the star "gain" just enough mass to collapse in a black hole, seen from the frame of reference of the space ship. However at almost exactly the same time the increased gravity the black hole exerts on it surroundings just about slows the ship down so that the mass "created" by the space ships velocity is lessened as well and makes it mass too low to remain a black hole. Would the black hole suddenly explode into a star again? ?Does this not contradict the rule that no causal influences can leave a black hole?
Or does a relativistic black hole not count? Do only black holes with a restmass large enough -or small enough, depending how you look at it- for its schwartshield radius count?

Now the best explanation I have is that when the spaceship slows down the black holes schwartshield radius recedes inward, however the black holes interior recedes inward even faster. But I'm not sure if the math adds up, since you can just deaccelerate arbitrarily fast; Obviously this doesn't really need to the gravity slowing down the ship. It could be giant magnets or just a very sturdy wall.

 

[jtbell]

Disclaimer: I am not an expert on general relativity and have not studied the subject in anywhere near the depth that I know stuff like classical electromagnetism (and there are lots of people who can run rings around me in that area! ).

Nevertheless, questions similar to yours come up over and over again here, and I've seen enough responses that I think I have a fairly good feeling for the consensus.

Bottom line: you cannot make an object into a black hole simply by going past it fast enough.

First, for "slightly" or "somewhat" relativistic velocities, at least some gravitational effects of a moving object do indeed vary approximately as \gamma m_0 (the "relativistic mass"). But note the word in bold face!

In GR, gravitational effects depend not only on energy (which is where the "relativistic mass" comes in because of E = \gamma m_0 c^2, but also on momentum. The Einstein field equations are written in terms of the stress-energy tensor whose components include both energy and momentum.

For highly relativistic velocities, momentum-dependent effects come into play which are reminiscent of the magnetic effects that influence the electromagnetic interactions of moving charges. These effects are sometimes called "gravitomagnetism," as I understand it. You cannot describe the gravitational effect of a highly relativistic object using a single number any more. Nevertheless, if the object isn't moving "too fast," you can ignore the gravitomagnetic effects as an approximation, which leads to my first statement.

Also, the Schwarzschild solution which leads to the common formula for the mass of a black hole in terms of radius, is described as a static solution, which I take to mean that it applies only in a reference frame in which the object is at rest in some sense. (I'm hedging here because I'm aware that you have to be careful when talking about reference frames in GR; maybe someone will sharpen this up for us.) It may still be useful as an approximation when the object isn't moving "too fast," but at highly relativistic velocities it is no longer useful even as an approximation.

Finally, consider this. There are an infinite number of inertial reference frames in which you satisfy the simple Schwarzschild condition for a black hole. Are you a black hole?

 

[Lee Wang]

I must be repeadetly misinformed then, thinking you can "create" black holes by going very fast.

Although I'm afraid someone needs to clarify this for me. When something goes very fast, it's gravity behaves somewhat like a magnetic field? How does that work and why does it do so? More importantly, how does it impede the creation of relativistic black holes?
"Finally, consider this. There are an infinite number of inertial reference frames in which you satisfy the simple Schwarzschild condition for a black hole. Are you a black hole?" Still how does this keep a black hole from forming?

I already mentioned this in my opening post.EDIT: Aha, I it up on wikipedia and that does make it somewhat clearer. Basically moving massive object exert their gravity like a magnetically, just like a moving electric source can be understood as a magnetic one.

 

[Lee Wang]

Ah there we go:

http://crib.corepower.com:8080/~relfaq/black_fast.html