In advance i would like to apologise for my poor english and the fact i am just a layman in physics, so i hope i get the terminology right.

The reason for this post is that i wondered how the gravitational field of a single linear accelerated mass is deformed (i know this is an impossible thought experiment because to do this you always need a reaction mass for nullifying the total momentum).

I reasoned that the field in the direction of the acceleration should be increased, and decreased in the other direction.

The reasoning is quite simple:

The dtau/dt can be calculated with the Schwarzschild formula:

dtau= dt_{far}* sqrt( 1 - 2 * G * m / (r * cē) )

Now, obviously, in the acceleration direction of the gravitational field source, the dtau would be bigger than in the opposite direction, when calculated from a small spatial interfall. This means that the gravitational field strength calculated as:

g = cē* dētau/dx

would be changed as mentioned when the source of a gravitational field is accelerated.

Again: i did not include the reaction mass for nullifying the momentum on purpose: the change in the gravitational field would be canceled.

Does anybode know if this reasoning is correct?

Does anybode know the math for the exact solution?