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Roy_1981
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Can anybody recommend a reference (paper/textbook) where I can look up the Penrose diagram for multi-black hole spacetimes or multi-center solutions? Appreciate.
Roy_1981 said:Many thanks to Ben for the wonderful reference and to bcrowell for the inputs/thoughts. I was really struggling with this yesterday and got completely exhausted. Indeed more than three dimensional diagrams seem to be the way to go.
A Penrose diagram is a way of visualizing the spacetime geometry of a black hole or other curved space. It is a 2D representation of a 4D spacetime, where the horizontal and vertical axes represent space and time, respectively.
By using a Penrose diagram, we can better understand the complex spacetime structure of a multi-blackhole system, which is difficult to visualize in traditional 3D diagrams. It also allows us to study the behavior of matter and light near the event horizons of multiple black holes.
A Penrose diagram for multi-blackhole solutions is constructed by first identifying the event horizons of each black hole and mapping them onto the diagram. Then, the spacetime is divided into regions based on the behavior of light and matter inside and outside of the event horizons. The diagram is typically symmetrical and includes all relevant information about the black holes and their interactions.
One limitation is that it is a simplified representation of a complex 4D spacetime, so it may not accurately capture all aspects of the system. Additionally, the diagram may not be able to illustrate the behavior of matter and light in regions that are highly curved or near the singularity of a black hole.
Penrose diagrams for multi-blackhole solutions are used by scientists to study the dynamics and properties of these systems. They can also be used to make predictions about observable phenomena, such as gravitational lensing, that may be caused by multiple black holes. In addition, these diagrams can help researchers better understand the nature of gravity and the structure of the universe.