# Kolkata physicist who inspired the 2020 Physics Nobel laureate

## Sir Roger Penrose’s muse was Dr Amal Raychaudhuri, whose paper, known for the ‘Raychaudhuri Equation’ developed the mathematical formulation that helped him prove that black holes really can form

Kolkata is in a rare radiance as the Royal Swedish Academy of Sciences has awarded half of the Nobel Prize in Physics for 2020 to Sir Roger Penrose, emeritus professor at the Mathematical Institute, University of Oxford, UK, and Honorary Fellow and alumnus of St John’s College Cambridge for the discovery that “black hole formation is a robust prediction of the general theory of relativity”. He shares the award with Reinhard Genzel of Max Planck Institute for Extra-terrestrial Physics, Garching, Germany and University of California, Berkeley, USA, and Andrea Ghez, University of California, Los Angeles, USA for the “discovery of a supermassive compact object at the centre of our galaxy.” Half of the prize money, 10 million Swedish kronor, is to go to the British mathematical physicist.

Penrose in 1965 showed that the general theory of relativity leads to the formation of black holes, but his path of research was facilitated by a young professor of physics at Ashutosh College under the University of Calcutta in 1955. He was Amalkumar Raychaudhuri, whose paper, known famously for the ‘Raychaudhuri Equation’ developed the mathematical formulation that helped Penrose prove that black holes really can form.

But Albert Einstein who first spoke of black holes in his General Theory of Relativity himself was in grave doubts about it for 40 years until his death in 1955. Black holes, he assumed, are super-heavyweight monsters that capture everything that enters them including light. Raychaudhuri Equation assumes that the “universe is represented by a time-dependent geometry but does not assume homogeneity or isotropy at the outset”. In fact, one of its aims is to see whether non-zero rotation (spin), anisotropy (shear) and/or a cosmological constant can succeed in avoiding the initial singularity.’

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.

Professor Somak Raychaudhuri, director of the Inter-University Centre for Astronomy and Astrophysics, Pune, and an astrophysicist of global repute, noted that the Raychaudhuri Equation quantifies “certain but tricky aspects of geometry with widespread use in Albert Einstein’s general theory of relativity, essentially a geometric description of distortions and bends in space and time”.

Penrose teamed up with the celebrated late British physicist Stephen Hawking and used the Raychaudhuri Equation for a mathematical description of black holes — objects with such intense gravitational pulls that not even light escapes them — and singularities, extreme situations where laws of nature break down”.

But for Raychaudhuri’s pace-setting breakthrough, the two great British physicists might not have broken new ground in the study of compact and supermassive objects. Penrose originally belonged to the discipline of mathematics.

In a paper, ‘The Raychaudhuri equations: A brief review’ published in PRAMANA, journal of Indian Academy of Sciences(Vol. 69, No. 1 — journal of July 2007), Sayan Kar and Soumitra Sengupta, put it crisply: “In the early 1950s, Raychaudhuri began examining some of these questions in GR. One of his early works during this era involved the construction of a non-static solution of the Einstein equations for a cluster of radially moving particles in an otherwise empty space. Where he dealt with cosmological perturbations (in a sense, this article deals with what is today known as structure formation).

Subsequent to these papers, in 1955, it appeared (in) Relativistic Cosmology, which contains the derivation of the now famous Raychaudhuri equation.

Fifty years hence, the Raychaudhuri equations have been discussed and analysed in a variety of contexts. Their rise to prominence was largely due to their use (through the notion of geodesic focusing) 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.”

Small wonder, Penrose had been in touch with Raychaudhuri, especially, when he had come to Calcutta and at the Presidency College where Raychaudhuri taught for several decades. David Haviland, chair of the Nobel Committee for Physics, hailed the three recipients of the prize for physics: “The discoveries of this year’s Laureates have broken new ground in the study of compact and supermassive objects. But these exotic objects still pose many questions that beg for answers and motivate future research. Not only questions about their inner structure, but also questions about how to test our theory of gravity under the extreme conditions in the immediate vicinity of a black hole”.

Indeed, few phenomena in the universe have captivated the imaginations of both the public and the scientific community like black holes and there is still so much more we need to learn about black holes. Raychaudhuri is credited for lightening the black holes validating the Einstein’s epoch-making discovery.

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