# Relative Mass vs Gravity

1. Sep 13, 2011

### CurvedSpace

If an object's mass increases as it nears the speed of light, would its gravitational field also change, and therefore change its affect on space time?

If this is true, would a smaller object traveling behind it be pulled faster as a result?

2. Sep 13, 2011

### Bill_K

CurvedSpace, You have been taken in by the spurious concept of "relativistic mass". We get a question like this at least once a week. More often than not, the poster also asks whether the increasing mass of a moving object will cause it to turn into a black hole.

The mass of a moving object does not increase. Why does this idea even come up? Because the relativistic expression for momentum is p = γmv, and by defining a relativistic mass M = γm you can force this expression to look like its nonrelativistic form, p = Mv.

Having said that, the gravitational field of an object is produced by its energy-momentum, not its mass, and for a rapidly moving object this does increase, and so the answer to your question indirectly, is yes. Both the energy component T00, the momentum components T0i and the stress components Tij will all contribute to the gravitational field.

3. Sep 13, 2011

### PAllen

One way to put this a little more 'invariantly' is to say the attraction between to objects in rapid relative motion is greater than for the 'same' objects in slow relative motion. If two objects are slow relative to each other, but rapid relative to something very distant, this latter rapid relative motion is irrelevant to the attraction experienced.