Did Einstein hold that gravity grows proportionaly with relativity mass?

Question

It is proved that mass of a body grows with growing its speed. And what about gravity caused by the mass? Does it grow with growing of the relativity mass? What Einstein thought about this?

Answer 1

The actual situation is much more complicated than simply using mass. Einstein's equation for gravity identifies a 4x4 matrix representing curvature to another 4x4 matrix called the stress-energy tensor. Because of symmetry, there are 10 independent positions in these matrices. One location in the stress energy tensor has to do with mass/energy, but the others refer to pressure and, naturally enough, stresses. In the location that depends on mass and energy, the mass that enters is the one enlarged by any relative velocities, but it is not as simple as saying that 'gravity grows proportionally to mass', but that one location of the curvature matrix will be effected by the velocity of masses close by.

Answer 2

General relativity says that space-time is curved not only by rest mass but also by energy.

In other words, a spring that is compressed will "weigh" more (it will deform space-time more) than a relaxed spring. Similarly, a stretched spring will "weigh" less (i.e., deform space-time less) than a relaxed spring. This is due to its negative energy component.

So whenever you increase the positive energy of an object, you also increase it's effect on the surrounding space-time. (and similarly, you increase the effect of distortions in space-time on it)

Answer 3

It's not actual mass, it's more like "effective" mass. It only relates to how much more energy is required to overcome it's inertia. I'll get a link

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Answer 4

A moving mass will create gravitational waves, not a static gravitational field.