How do you project a Killing Vector onto a Schwarzschild field?

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SUMMARY

The discussion focuses on projecting a Killing vector onto a Schwarzschild field of spacetime, specifically addressing the confusion surrounding the concept of projecting a "black and white hole." Participants clarify that Schwarzschild spacetime represents a black hole and a white hole, and emphasize that simply adding solutions for individual black holes does not yield a valid binary black hole solution. For visualization, Kruskal coordinates are recommended as an effective tool for understanding the structure of maximally extended Schwarzschild spacetime.

PREREQUISITES
  • Understanding of Schwarzschild spacetime
  • Familiarity with Killing vectors in general relativity
  • Knowledge of Kruskal coordinates
  • Basic concepts of black holes and white holes
NEXT STEPS
  • Study the mathematical properties of Killing vectors in general relativity
  • Learn about the structure and implications of Schwarzschild solutions
  • Explore Kruskal coordinates for visualizing black hole spacetimes
  • Investigate the concept of binary black holes and their solutions
USEFUL FOR

Students and researchers in theoretical physics, particularly those focusing on general relativity, black hole physics, and spacetime visualization techniques.

bobrubino
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TL;DR
What is the math for projecting a Killing vector onto a Schwarzschild field of spacetime?
What is the math for projecting a Killing vector onto a Schwarzschild field of spacetime? How would you do it?
 
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What is a Schwarzschild field? Is this meant to be "B" level?
 
bobrubino said:
What is the math for projecting a Killing vector onto a Schwarzschild field of spacetime?
The question doesn't make sense. Can you give a reference that explains what you are trying to do?
 
PeterDonis said:
The question doesn't make sense. Can you give a reference that explains what you are trying to do?
I am trying to project a black and white hole onto a field of Schwarzschild spacetime and I don't know what to do. Do you have any advice?
 
bobrubino said:
I am trying to project a black and white hole onto a field of Schwarzschild spacetime and I don't know what to do. Do you have any advice?
Your question still doesn't make sense. Again, where are you getting this from? What makes you think this is even a meaningful thing to do? Why do you want to do it? A reference would be helpful.
 
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bobrubino said:
I am trying to project a black and white hole onto a field of Schwarzschild spacetime and I don't know what to do.
Schwarzschild spacetime is a black hole and a white hole. Your question makes no sense.

Are you trying to find the spacetime for a binary blackhole? You can't do it by adding together two copies of the solutions for one black hole.
 
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bobrubino said:
I am trying to project a black and white hole onto a field of Schwarzschild spacetime
The maximally extended Schwarzschild is both a black hole and a white hole. If you are just trying to visualize that, my preference is Kruskal coordinates

468px-Kruskal_diagram_of_Schwarzschild_chart.svg.png
 

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