I know from reading about the gravitational waves detected by Ligo, that when an object has angular acceleration, it produces gravitational waves.
I'm wondering if an object creates gravitational waves when only accelerating in one direction, however?
I'm also curious as to how the nature of the waves would differ in this case.
Answer
Any object with mass that accelerates (is it linear or angular acceleration) produces gravitational waves, though in most occasions those will be much too small to be detected. As @CuriousOne pointed out, same happens with electromagnetic waves and accelerating charges. The gravitational waves that can be detected usually come from very massive objects (such as black holes, neutron stars, etc) undergoing rapid accelerations. The situations encountered in nature where this really massive objects are accelerated tend to be related to binary stars or black hole systems orbiting each other or single stars swiftly rotating about their own axis with a noticeable irregularity like a mountain on their surface. I'd say the reason why you don't hear much about GW produced by linearly accelerating black holes/stars is that this scenario is quite unlikely to happen in nature.
You can find information about the other possible sources of GW here.
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