Suppose a body is at rest of mass m. If the same body is accelerated at velocity v, the mass increases to some definite amount. Since the mass of the body has increased, will the gravitational field of the body change in proportion to the increase in mass?
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When you accelerate a chunk of mass to some velocity, you are increasing its energy content. Since energy can bend spacetime like mass does, a more energetic chunk of mass will bend spacetime (that is, exert gravitational pull) a bit more strongly than a less energetic chunk of mass.
Explicitly separating out mass effects from energy effects (which is the way the subject is currently taught) lets physics people keep track of the basic physics in a less-complicated way than how they would if they thought of the speedy object's "intrinsic" mass as having been increased because of its velocity- which is how this subject used to be taught 50 years ago.
As long as you keep proper account of the physics, either way of thinking about the subject will yield the same (correct) solution to a problem, but the modern approach- which asserts that the intrinsic mass of an object is invariant- is the currently accepted formalism.
niels nielsen
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