Does increased velocity increase gravity?

[michael879]

I know it increases mass, since KE = 1/2 mv^2 and as you approach the speed of light KE keeps going up meaning mass must go up. I've been told that this is simply an increase in relativistic mass (the e=mc^2 type) and gravity is based on rest mass. But isn't it kind of weird for everything except gravity to use total mass while gravity only uses rest mass?

 

[pervect]

Strictly speaking, when a body starts to move at a relativistic speed, the entire idea of gravity as a "force" needs to be revisited. However, the error involved in continuing to think of gravity as a force is only about 2:1, so if one isn't too demaning of the model, it's possible to come up with a hand-waving description of the gravitational field of a relativistically moving body (with the understanding that this description will only be approximately correct and not really mathematically rigorous).

With the understanding that the concept isn't totally well defined, the general behavior of the "gravitational field" of a relativistically moving mass will NOT be the same in all directions. It will greatly resemble the eletcric field of a relativistically moving electron. This means that the field will be stronger in the transverse direction than in the direction of motion. Because the field isn't uniform, one has to define the total field strength by some sort of average. Gauss's law for the electric field defines a notion of an average field that is independent of velocity - applying the same notion to the "field" of a moving mass will yield an average field that increases with velocity, so the "average" field of a moving mass is stronger.

Of course the field in a frame co-moving WITH the mass will not be changed! Only the field in a frame moving relative to the mass, or the mass moving relative to the frame, will be changed.

 

[michael879]

well according to that something approaching the speed of light will become a black hole right? I've heard arguments agreeing with this and some opposing it tho...

 

[pervect]

well according to that something approaching the speed of light will become a black hole right?

NO!

I've heard arguments agreeing with this and some opposing it tho...

Read the sci.physics.faq on the topic, you should be able to dig up the URL. (I've quoted it a bunch of times personally, so you can always search this board for my deathless, or at least archived, prose).

also, re-read what I said in my last long post, particularly the part about how I specifically mentioned that the gravitational field in a frame co-moving with the body is not affected, in an attempt to head off just this sort of misunderstanding.

 

[Doc Al]

If you go too fast do you become a black hole?

If you go too fast do you become a black hole?

 

[pervect]

Here's a thought experiment that might help.

Imagine a pair of bodies with both mass and charge. The bodies attract each other because they are massive, and repel each other because they have charge. The charge is set to such a value that there is no net force between the bodies when they are both at rest.

Now, accelerate one of the bodies so it is moving. The electrostatic field of the body will be distorted by its motion when looked at from a frame in which it appears to be moving, so will it's "gravitational field".

Note again that neither the electrostatic field nor the "gravitational field" will change from the point of view of the body itself - it can't tell that it's moving! The fields will only appear to be distorted when looked at by an observer with relative motion.

(Repeat the above statement for emphasis if necessary :-)).

The main point I want to make is that the electrostatic and gravitational fields will change in a different manner, so that the net force between the bodies will no longer be zero when one body is set in motion. (Both fields will exhibit the same sort of general behavior, but they will not transform identically!).

Caveat - it's easy to measure the force on a body that's exerted by a charge directly (you can compare the force exerted on a charged body to the force exerted on a non-charged body), but measuring the gravitational field of a body requires an external frame of reference - because gravity affects all objects equally, there is no such thing as an "uncharged" reference point. The details of setting up a frame of reference makes the idea of a 'gravitational field" mathematically a bit suspect, but since it's a familiar notion, I talk about gravitational fields transforming, even though the math is not handled that way.

 

[pmb_phy]

I know it increases mass, since KE = 1/2 mv^2 and as you approach the speed of light KE keeps going up meaning mass must go up. I've been told that this is simply an increase in relativistic mass (the e=mc^2 type) and gravity is based on rest mass.

That is absolutley incorrect. Gravity is not based on rest mass. Its based on relativistic mass (which is described completely by a second rank tensor).

To answer your question - Yes. In general the gravitational field is a function of speed. See the example at

http://www.geocities.com/physics_world/gr/moving_body.htm

See also
Measuring the active gravitational mass of a moving object, D.W. Olson, R.C. Guarino, Am. J. Phys. 53(7), July 1985

Pete

 

[Zanket]

well according to that something approaching the speed of light will become a black hole right? I've heard arguments agreeing with this and some opposing it tho...

If some object somewhere moves at close to the speed of light relative to you, you don't become a black hole from its perspective right?

 

[pmb_phy]

If some object somewhere moves at close to the speed of light relative to you, you don't become a black hole from its perspective right?

If you mean from its rest frame then yup. That's right.

Whether an object is a black hole is not determined by its mass. Too many people make this false assumption and this is why they make the error that an object moving fast enough would become a black hole.

Take as an example micro-black holes and a normal black hole whose mass is the mass of the sun. A micro-black hole has a mass of about Mt. Everest (this is not a fixed number but simply an order of magnitude range). Now we all know that Mt. Everest is not a black hole in its own rest frame. So here we have an example of two objects of identical mass in the rest frame - one is a black hole and the other isn't. The Earth has evern more mass and it too is not a black hole. The sun has even more mass and it also is not a black hole. Yet the micro-black hole is possible and is a black hole and has much less mass than the earth, which is not a black hole.

So why would you associate the large mass of an object with whether it being a black hole?

Pete

 

[Zanket]

Did I do that? My question to michael879 is rhetorical.

 

[Myriad209]

Black holes only form from one perspective and will not form from any other perspective. Rest-mass determines whether something will become a black hole or not. Read Doc's link.