The Nobel Prize in Physics 2020 centered around rewarding the research on black holes, but the topic has been popular way before the prize announcement. The 2014 film Interstellar had it's visuals, concerning a black hole, designed under the supervision of theoretical physicist, Kip Thorne. So you see, amidst the topics on various celestial entities, black hole has got it's share of spotlight.
A lot of eminent scientists have worked on decoding black holes, one of them is Amal Kumar Raychaudhuri, whose know-how is limited to the scientific community where he is regarded as one of the Indian pioneers in popularizing relativity.
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| Prof. A K Raychaudhuri and his equation. |
Prof. Raychaudhuri's Academic Life — At a Glance
• Early education at Tirthapati Institution and completed matriculation from Hindu School, Kolkata.
• 1942: He earned B.Sc. degree from Presidency University and in 1944 M.Sc. from Rajabazar Science College, under University of Calcutta.
• 1942: He earned B.Sc. degree from Presidency University and in 1944 M.Sc. from Rajabazar Science College, under University of Calcutta.
• 1945: Joined Indian Association for the Cultivation of Science (IACS), as a research scholar and soon, in 1952, he took a research job at the same institute.
• 1955: He published a paper that included an equation addressing singularities, the equation soon came to be known as Raychaudhuri equation when it proved to be essential in the proofs of Penrose-Hawking singularity theorems.
• 1959: Received Doctor of Science degree at University of Calcutta with Prof. Archibald Wheeler, as one of the examiners, who made a special mention of Raychaudhuri's work.
• 1961: Joined the faculty of Presidency College.
Raychaudhuri and Singularity
According to Einstein's general theory of relativity, massive objects tend to bend the fabric of spacetime, as a result, bodies in proximity to that object feel an attractive force (the 'force' is essentially a consequence of the curved fabric).
As neatly summed up by John Archibald Wheeler,
Spacetime tells matter how to move,Matter tells spacetime how to curve.
When a star explodes, it spews it's reserve into space, which is known as supernova remnant. Now if the mass of this matter is greater than 2 to 3 times the mass of our Sun, all of the remnant collapses into a very dense ball known as a neutron star.
If the neutron star has falls to a certain critical radius then it collapses into a 'vanishingly small point in spacetime', known as singularity, wherein space and time aren't treated as different coordinates and all the known physical laws become indistinguishable. Pretty awesome, right?
In the 1950s, Prof. Raychaudhuri was working on the possible movement of light rays through the curvature of spacetime and how would the curvature affect the rays. To address this question, he derived an equation which has it's roots in simple geometry and presses to the fact that gravitational force is always attractive.
The equation got it's name years after Raychaudhuri published his paper in 1955 and has been an integral part in the proposition of Hawking's area theorem which relates black hole's entropy with it's surface area and Penrose-Hawking singularity theorems which pinpoints the conditions those lead to the formation of gravitational singularities.
In the original 1955 paper, Raychaudhuri assumed the Universe follows a time dependent geometry, but he refrained from considering homogeneity of space. He used a few parameters to test whether, theoretically, those can succeed in avoiding the initial singularity. His works include comoving frame, which is when an object is attached to the frame of reference, as a result, the object remains stationary with respect to the frame of reference.
Raychaudhuri used the quantity R4 ⁴, labelled as x¹, x², x³ and x⁴ where the first three represents space coordinates and the last one, time. Evaluating the quantity in two ways and then equating them, he obtained the equation for the evaluation of the expansion rate.
Raychaudhuri's work is undoubtedly crucial in the scope of general relativity, but it's not limited to it, as it deals with various geometric applications concerning flows. The most prominent contribution of his work, by far, is understanding the singularity problem. Furthermore, in astrophysics, Raychaudhuri's equations are utilized in problems related to lensing and cracking of self gravitating compact objects.
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