Q) In general relativity, the Raychaudhuri equation is a fundamental result describing the motion of nearby bits of matter. Discuss how the equation contributed to the discovery of black holes. (150 words)

Why this question?

  • Roger Penrose was rewarded with the Nobel Prize in Physics for his work on black holes. Penrose won half the Prize. The other half is shared by Andrea Ghez of the US and German astronomer Reinhold Genzel. Thus the question.

Introduction: After the announcement of the 2020 physics Nobel to Penrose for discovery related to Black Holes, the Raychaudhuri Equation in General Relativity, derived by Raychaudhuri (AKR), has come into the spotlight.

Body: discuss  the following aspects

  • Research  by Penrose: Penrose, in collaboration with cosmologist Stephen Hawking, used an equation that Raychauduri had published in the journal Physical Review in 1955, for a mathematical description of Black Holes in 1969.
  • Contribution of Raychaudhuri Equation: It assumes that the “universe is represented by a time-dependent geometry but does not assume homogeneity or isotropy at the outset”. 
  • Using the Einstein equations (with a cosmological constant Λ) and, using the geometric definition of rotation, Dr. Raychaudhuri also introduced the definitions of shear and rotation.

Conclusion: The Raychaudhuri equations have been discussed in the proofs of the seminal Hawking-Penrose singularity theorems of General Relativity. Today, the importance of this set of equations, as well as their applicability in diverse scenarios, is a well-known fact.