Black Hole Merger: Analytical or Numerical Solutions?

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Discussion Overview

The discussion revolves around the nature of solutions to the Einstein Field Equations (EFE) in the context of black hole mergers, specifically questioning whether these solutions are analytical or numerical. Participants explore concepts of "stationary" and "static" solutions in General Relativity (GR) and their implications for understanding black hole dynamics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that solutions of the EFE are stationary in four dimensions, while others challenge this by stating that not all solutions are static.
  • A participant expresses confusion regarding the terminology of "stationary" and "static," suggesting a misunderstanding of their specific meanings in GR.
  • There is a clarification that "stationary" refers to a spacetime that can be sliced into identical "nows," contrasting with the dynamic nature of inspiralling black holes.
  • One participant acknowledges learning about the definitions and expresses a desire for a clearer understanding of the terms used in GR.

Areas of Agreement / Disagreement

Participants demonstrate a lack of consensus on the definitions of "stationary" and "static" in GR, with some agreeing on the need for precise terminology while others maintain differing interpretations of EFE solutions.

Contextual Notes

There are unresolved issues regarding the definitions of "stationary" and "static," as well as the implications of these terms for the understanding of black hole mergers. The discussion reflects varying levels of familiarity with GR terminology among participants.

sandy stone
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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?
 
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sandy stone said:
Are current descriptions analytical solutions, or numerical?
Numerical.
 
sandy stone said:
Is it not true that solutions of the EFE are stationary, in 4 dimensions?

What do you mean by "stationary"?
 
Sorry, 'static'.
 
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.
 
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.
 
sandy stone said:
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.
 
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?
 
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.
 
  • #10
That makes sense, obviously I wasn't expressing myself properly. Thanks.
 

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