Backreaction of accelerated motion on spacetime curvature

[zonde]

Curvature of spacetime tells us how the body is moving when it moves inertially. But if the body is not moving inertially does it causes backreaction by affecting spacetime curvature?

Say if we compare body that is in free fall toward planet with body that is at rest on the surface of planet.

[atyy]

There is always backreaction, even when the body is moving "inertially" - ie. inertial motion is an approximation in which the finite size of the body and its backreaction is neglected.
http://arxiv.org/abs/0907.0414
http://arxiv.org/abs/0907.5197

[Passionflower]

Curvature of spacetime tells us how the body is moving when it moves inertially. But if the body is not moving inertially does it causes backreaction by affecting spacetime curvature?

Say if we compare body that is in free fall toward planet with body that is at rest on the surface of planet.
Proper acceleration implies a redistribution of mass/energy thus it must effect curvature, however it might be the other way around, a change in curvature might cause proper acceleration. In this respect Penrose's ideas on quantum 'collapse' mights be interesting.

I think the answer to those questions can only be made after unification of gravity and the 3 forces of nature.

[bcrowell]

Say if we compare body that is in free fall toward planet with body that is at rest on the surface of planet.

The answer is yes, and you don't need to worry about fancy ideas like back-reaction. The two bodies have different contributions to the stress-energy tensor, so they have different effects on the Einstein field equations.