Black Hole Merger: Analytical or Numerical Solutions?

[sandy stone]

Is it not true that solutions of the EFE are stationary, in 4 dimensions? If so, it seems that the solution describing a black hole merger would be intractably complex. Are current descriptions analytical solutions, or numerical?

 

[Nugatory]

Are current descriptions analytical solutions, or numerical?

Numerical.

 

[PeterDonis]

Is it not true that solutions of the EFE are stationary, in 4 dimensions?

What do you mean by "stationary"?

 

[sandy stone]

Sorry, 'static'.

 

[martinbn]

Well, what do you mean by static? In GR static space-time is something very specific, and the answer is no, not all solutions of EFE are static.

 

[sandy stone]

My mistake, then. I thought EFE solutions all represented an unchanging (in 4 dimensions) 'block universe' type of picture. Or perhaps I am using incorrect terminology.

 

[PeterDonis]

I thought EFE solutions all represented an unchanging (in 4 dimensions) 'block universe' type of picture.

They do, yes. But that is not what "stationary" or "static" mean in GR.

 

[sandy stone]

OK, well I've learned something new today (actually, two things, and thank you Nugatory). Is there a B-level definition of 'stationary' or 'static' in GR? And is there a proper term for the idea I was trying to express?

 

[Ibix]

Stationary means that there is a way to slice up spacetime into an infinite set of "nows" that are all the same. Spacetime around an isolated eternal black hole, for example, looks the same today, tomorrow and next millenium. On the other hand two inspiralling black holes are not the same second by second and the spacetime is not stationary.

 

[sandy stone]

That makes sense, obviously I wasn't expressing myself properly. Thanks.