# Accelerated spacetimes in type D spacetimes

Are accelerated spacetimes in General Relativity "vacuum solutions"? Why are they not integrable as the Kerr-NUT-dS? After all, the following cube of metrics seems to mean that every Kerr-type metric can be derived from the accelerated versions,...Why are accelerated solutions "hard" to handle with? Any physical meaning of them, specifically the C-metric? I mean, I did know that Kerr metrics are rotating black holes, or the NUT parameter is some type of gravitomagnetic mass term, but what is the physical picture of, e.g., the C-metric (and more generally accelerated spacetimes)?

• Where does this graph come from? What is the meaning of various parameters? – magma Jan 3 '18 at 2:04

One thing to note, is that this type of solutions exhibits conical singularity along (half)axis (in a given patch of a space-time), which could be interpreted as semi-infinite cosmic string pulling the Schwarzschild black hole and thus providing the source of acceleration. This also answers your question on whether this solution is vacuum solution: yes, it is, except for the cosmic string which correspond to $\delta$-like singularity of Ricci tensor.