Do space and time vibrate when objects accelerate?

[anubodh]

Does both space & time vibrate when objects move or when they vibrate when objects accelerate? So, what happens of these vibrations? How are they converted back into matter to maintain a cycle?Do these vibrations affect the motion of other moving objects (although negligible)?

 

[Doc Al]

Does both space & time vibrate when objects move or when they vibrate when objects accelerate?

Why would you think that?

 

[A.T.]

Does both space & time vibrate when objects move or when they vibrate when objects accelerate? So, what happens of these vibrations? How are they converted back into matter to maintain a cycle?Do these vibrations affect the motion of other moving objects (although negligible)?

You seem to be asking about gravitational waves. They are created when masses accelerate.
http://en.wikipedia.org/wiki/Gravitational_wave