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Add feature to compute and plot Penrose diagrams #480

@kakirastern

Description

@kakirastern

🐞 What bugs you?
Currently einsteinpy does not have the capability to compute and plot Penrose diagrams, which are 2-dimensional diagrams showing the causal relations between points in some spacetime. It would be good to implement some algorithm to add this feature. However, this will require some work on the null geodesics for Schwarzschild and Kerr Geometries (a GSoC 2020 Project idea) to have completed in order to build on top of it.

🎯 Goal

To carry out some preliminary research on Penrose diagrams and its potential implementation as an einsteinpy feature, and present the results as an EinsteinPy Proposals for Enhancement (EPE) in the einsteinpy/EinsteinPy-EPEs repo.

💡 Possible solutions
An EPE will be drafted in collaboration with @Raahul-Singh and @GTron-1729 with the theoretical background and potential solution(s) of implementation to be presented as a PR in the einsteinpy/EinsteinPy-EPEs repo.

📋 Steps to solve the problem

  • Research on the problem
  • Investigate potential implementation approaches best suited for einsteinpy to incorporate such a feature into the codebase
  • Present the findings in an EPE

📖 References

  1. J. C. Schindler, A. Aguirre (2018), Algorithms for the explicit computation of Penrose diagrams
  2. An existing implementation of a very similar idea at https://github.com/jcschindler01/xhorizon
  3. M. Walker (1970), Block Diagrams and the Extension of Timelike Two‐Surfaces
  4. A related Physics StackExchange page
  5. Penrose diagram Wikipedia page
  6. S. W. Hawking , G. F. R. Ellis (1973), The Large Scale Structure of Space-Time
  7. S. M. Carroll (2019), Spacetime and Geometry: An Introduction to General Relativity
  8. https://jila.colorado.edu/~ajsh/insidebh/penrose.html
  9. https://demonstrations.wolfram.com/PenroseDiagram/

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