254 SCIENCE AND CULTURE, JULY-AUGUST, 2019

P.C. VAIDYA, A GANDHIAN MATHEMATICIAN-PHYSICIST ANDPROPONENT OF ‘VAIDYA METRIC’: NEARLY IN OBLIVION

MANAS CHAKRABARTY*

The year 2018 marked the birth centenary of the Gandhian mathematician-cum-physicist, P.C.Vaidya who was an inspiring teacher, a dedicated populariser of mathematics and the proponentof Vaidya metric, a rare dynamic solution to the space time geometry around radiating stir. Sadly,however, this world famous expert in relativity and cosmology could not become a householdname in India and has nearly gone into oblivion. There was hardly any celebration of his birthcentenary across India. The life and work of this modest scientist have been presented briefly inthis article.

ARTICLE

* Former Senior Professor of Chemistry and Emeritus Scientist(CSIR) in the Department of Chemistry, Bose Institute, Kolkata700009, West Bengal.Residence: 60/13B, Gouribari Lane, P.O. Shyambazar, Kolkata700004.E-mail: chakmanas09@gmail.com

Last year (2018) was the birth centenary of PrahaladChunnilal Vaidya (PCV), a renowned Gujaratimathematician and physicist, a freedom fighter, an

inspiring Gandhian teacher and a globally recognised experton Einstein’s theory of relativity1,2. But despite his immensecontribution in the field of theory of relativity, especiallywhat is known as the ‘Vaidya metric’, PCV could notbecome a household name like C.V. Raman, S.N. Bose,Meghnad Saha, Homi Bhava, P.C. Mahalanobis, S.Chandrasekhar and the like, and he has almost gone intooblivion. In an article entitled, ‘Centenary: P.C. Vaidya, aGandhian Physicist Who Laboured in India’s Shadows’ byA. Ramnath and published in the WIRE on May 27, 2018,the author candidly confessed that he, although aprofessional historian of science, had never heard of Vaidyauntil recently when a colleague mentioned about PCVduring the course of a public lecture on the life and workof Stephen Hawking3. This statement, however shocking,bears ample testimony to the unfortunate evaluation of PCVnot only by the public at large but also by the scientificcommunity in India.

Indeed, only a few write-ups were published and evenlesser number of seminars and symposia on the life andwork of this bright Indian scientist took place last year.Regrettably, he was not covered even in a recent article,written by the present author, on the momentous incidencesthat rendered the year 1918 a truly remarkable year in thehistory of mankind4. The present write-up on the life andwork of PCV is an attempt to fill in this lacuna.

Early Life and Education

PCV was born on May 23, 1918 in Shahpur villagein Junagadh District, Gujarat. In 1931, when he was in the9th standard, his father passed away. After completing hisschool education first in Alfred High School, Bhavnagar(until 1933) and then in Mumbai, he graduated from theIsmail Yusuf College, Andheri with distinction in sciencewith physics and mathematics as major. Right from hisschool days, PCV displayed a special aptitude formathematics. He, therefore, studied applied mathematicsat the Institute of Science (formerly known as the RoyalInstitute of Science) and obtained his M.Sc. degree fromthe Bombay University where he was a topper.

Post-M.Sc. Teaching Career

In 1940, he started his career as a Lecturer inDharmendra Singhji College, Rajkot where he used to teacharithmetic and trigonometry to undergraduate students. He

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was a staunch believer in Gandhian philosophy of Ahimsa,simplicity and honesty. He took part in freedom movement,but in a different way. He resigned from the lectureship in1941 and founded a voluntary organisation, AhimsakVyayam Sangh (AVS), an institute of physical educationfor training youths for non-violent struggle. He was thePrincipal of AVS. In 1942, when the Quit India Movementwas being planned, Mahatma Gandhi wanted AVS to playa part in the planned movement. But Baba Prithvi SinghAzad, the Director of the Sangh and a one-timerevolutionary, did not want to oppose the British simplybecause he was indeed a communist and the British wereallied with the Soviets. This ideological conflict led to theclosure of the AVS sometime in 1942.

Entry into Research

This was the turning point in the life of PCV. Sincethe AVS was shut down, PCV had no job and his savingswere almost exhausted, he became somewhat aimless.Earlier in 1937 when PCV was an undergraduate studentof mathematics, he attended a course of lectures on generalrelativity at Bombay University by Professor V.V. Narlikar,a well known physicist of Banaras Hindu University (BHU),Varanasi and the father of famous Jayant V. Narlikar. Theselectures had two profound influences on the course of thelife of PCV. Firstly, he shifted from pure mathematics toapplied mathematics after the first semester in thepostgraduate course. Secondly, these lectures made PCVaware, for the first time, of the fact that the gravitationalfield of a radiating star had yet to be described in terms ofgeneral relativity. Inspired by these lectures, PCV becameinterested to pursue research in the general field of relativityin the school of V.V. Narlikar at BHU.

In 1939, PCV got married to Vidya Devi. In 1942,when the AVS was wound up, PCV requested V.V. Narlikar

for a berth in his research group. Narlikar immediatelyagreed, and PCV, along with his wife and six month-olddaughter Kumud, went to Banaras on the 27th June, 1942.But he could carry out research work at BHU for only tenmonths because he did not get any scholarship and hisscanty savings were almost spent by then. PCV returnedto Gujarat with his family in the April of 1943. But eventhis short period of research under the guidance of Narlikarshaped PCV into a prolific researcher and imbibed in himthe idea of developing a spacetime geometry of thegravitational field around a radiating star. Justifiably, PCVconsidered his research tenure with V.V. Narlikar as ‘KashiYatra’3 and paid homage to his Teacher-mathematician inan obituary5.

After leaving BHU, PCV taught in a number ofscience institutions in Surat, Rajkot and Bombay. He thenspent one year (1947-’48) as a Research Associate at thenewly founded Tata Institute of Fundamental Research,Bombay where he got acquainted with Homi Bhabha. Hegot his Ph.D. degree from the Bombay University in 1948.Notably, PCV was the first holder of the Ph.D. degree inmathematics in Gujarat. But long before his doctoral award,PCV became famous for his contribution, widely knownas ‘Vaidya metric’ or ‘Vaidya solution’ (vide infra).

Vaidya Metric: Major Contribution of PCV

PCV’s major interest was in the gravitational field ofradiating stars. According to the general theory of relativity,a gravitating object can be measured by the spacetimegeometry around it. When PCV started his research work,the spacetime geometry around a spherical star (with itssurrounding assumed to be empty) had already been workedout (vide the well known ‘Schwarzschild Solution’)6. Butthis geometry around a radiating star, like typical stars,was not known. A quarter of a century later when PCV

(Source: Wiki Commons) P.C. Vaidya (23.05.1918-08.04.2010) (Source: a Documentary)

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was in his early twenties, he found a solution – a metric -to this problem. His remarkable paper entitled ‘TheExternal Field of a Radiating Star in General Relativity’on this solution, called the ‘Vaidya metric’ was publishedin Current Science in 19437. Vaidya metric slowly acquireda berth in the upcoming field of relativistic astrophysics.In his public lecture titled ‘Vaidya Metric and 100 Yearsof Black Hole Solution’ held at Gujarat University onSeptember 9, 2017, Dr. Karan Jani, a gravitational waveastrophysicist and a LIGO scientist and one of the Forbeslist of ‘30 Influential Scientists Under 30’ remarked thatthe recent applications of Vadya metric, a very rare exactdynamic solution in relativity, include probing dark energy8.A video, created by Google, deals with the work of PCVin the field of general theory of relativity9.

A documentary on the life and work of PCV and arecent news article in South Asia Daily10 have describedhow the idea of Vaidya metric came into being. The storygoes as follows. One day in 1942, PCV was loitering inthe balcony waiting for a Hindi newspaper Aaj when theidea behind Vaidya metric flashed in his mind. He thoughtthat, since fluids move with velocities less than that of light,the maximum in nature, one must consider, not fluid, butradiation moving out of the star while working on the fieldof a radiating star. In other words, the velocity of light,and not that of fluid, should be considered. Once the ideacame to him, mathematics simply followed. Within a week,PCV worked out the mathematical solution of his idea, andthus came the Vaidya metric11.

PCV’s initial research with Springer ResearchScholarship of the Bombay University resulted in a paper‘Nonstatic Solutions of Einstein’s Field Equations forSpheres of Fluids Radiating Energy’ with himself as thesole author. This work, published in Physical Review in195112, was highly appreciated by none other than RobertOppenheimer, ‘the father of the atomic bomb’.

Publications of PCV

PCV’s work was focused mainly on exactsolutions, supermassive objects and black holes. Hisachievements are even more praiseworthy since he had towork with minimal infrastructural facilities. He published66 research papers and 9 related articles in reputed Indianand International journals. A complete list of his papersduring 1942-2000 is available13.

A Notable Tribute to P.C. Vaidya and AmalK. Raychaudhuri

Two pioneers in India in the field of general relativityare Professor V.V. Narlikar at BHU and Professor N. R.

Sen at the University of Calcutta. The next generation ofinfluential scientists in this domain are PCV and A.K.Raychaudhuri of Presidency College, Calcutta. Thecontribution of PCV, mainly Vaidya metric, belongs to thedomain of the study of gravitational effects around localobjects while the famous ‘Raychaudhuri equation’14,15 bylate Professor A.K. Raychudhuri belongs to the domain ofthe investigation of the global structure of spacetime – thetwo domains of general relativity. The contributions of thesetwo stalwarts in their respective fields have been amplycovered in a notable book entitled ‘A Random Walk inRelativity and Cosmology: Essays in Honour of P.C. Vaidyaand A.K. Raychaudhuri’, edited by N. Dadhich, J. KrishnaRao, J.V. Narlikar and C.V. Vishveshwara Rao who areexperts in the field of general relativity16. A review on thisbook highlighted the importance of this book and considersit to be “both useful and stimulating to any interestedreader17.”

Teaching and Science Popularisation

After getting his Ph.D. degree, PCV moved toteaching at various Colleges like Vitthalbhai Patel College,Vallabh Vidyanagar (later turned into Sardar PatelUniversity), Gujarat College, Ahmedabad, M.N. College,Visnagar, and University School of Sciences, GujaratUniversity. He became the Chairman, Gujarat PublicService Commission (1971), Chairman of the Union PublicService Commission (1977-’78), the Chancellor, GandhiVidyapeeth, Ahmedabad and also the Vice-Chancellor ofGujarat University (1978-’80).

Later in his career at Gujarat University, he once saidthat he did not want to restrict himself to teaching at M.Sc.classes since he was the highest paid teacher in mathematicsin Gujarat1. Driven by this conviction, PCV devoted himselfin spreading science in general and mathematics inparticular amongst the students, the teachers and the publicalike. He founded the Gujarat Ganit Mandal (GujaratMathematical Society) at Bhavnagar in 1964, and becameits President twice (1964, 1988). He was also instrumentalin founding the mathematics laboratory Vikram A. SarabhaiCommunity Science Centre (popularly known as CSC) inAhmedabad in the 1960s and the Indian Association forGeneral Relativity and Gravitation (IAGRG) in Ahmedabadin 1969. As recalled by his nephew Arun Vaidya, PCVwas an active organiser of sports and other activities bythe students, and his organising ability perhapsstemmed from his past experience in founding and runningthe AVS3.

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Honours and Achievements

Because of his achievements in the field of theory ofrelativity, he got the honour of serving various academicinstitutions as a Visiting Professor / Visiting Scientist. Thushe visited Washington State University, Pullman,Washington (USA), London University (UK), NewcastleUniversity (UK), Dublin Institute of Advanced Studies,Dublin (Ireland) and International Centre for TheoreticalPhysics, Trieste (Italy) during 1964-’73. He also delivereda course of lectures at the Institute of Henrie Poincare,Paris (France) in 1971.

Expectedly, PCV earned many feathers in his crown.In a conference in Ahmedabad in early 1969, held inhonour and felicitation of Professor V.V. Narlikar at his60th birth anniversary, PCV proposed the formation of asociety of Indian relativists. This led to the birth of theIAGRG, of which PCV was a Founder Member. He wasalso a Fellow of the Indian Academy of Sciences, a Fellowof the Indian National Science Academy, the Presidentof Calcutta Mathematical Society (for 2 years; succeededSir Asutosh Mukherjee in 1924), an Honorary Fellow of theInter-University Centre for Astronomy andAstrophysics (IUCAA), Pune, the President of the IndianMathematical Society (1976, 1977), a Founder Memberof the Springer journal General Relativity and Gravitation(1970), a Member of Indian National Committee onAstronomy (1976-’79) and the President of the UGCCommittee on Relativity and Cosmology. He also activelyparticipated in the revision of the state-level syllabi ofmathematics textbooks.

Popularisation of Mathematics and Memoirs

With a view to popularising particularly mathematicsamongst the students, he started a mathematics magazine‘Suganitam’ in the 1960s, wrote articles, mostly onmathematics, in the Gujarati cultural magazine ‘Kumar’ andauthored several popular science books (majority inGujarati) which include ‘Akhil Brahamandman’ (In theEntire Universe), ‘Dashansh Paddhati Sha Mate?’ (WhyDecimal System?), ‘Dadaji Ni Vato’ (Grandpa’s Tales),‘What is Modern Mathematics?’ and ‘Ganit Darshan’(Discourses in Mathematics). Pertinently, this last namedbook won the Gujarati Scientific Literature Prize (1970-’71) of the Govt. of Gujarat. Moreover, PCV published,inter alia, two important memoirs – ‘Chalk ane Duster’(Chalk and Duster), Suganitam Prakashan, Ahmedabad,2011, a memoir on his teaching life, and ‘America aneapne’ (America and Us), a memoir on his experience as a

Visiting Professor at Washington State University. In fact,PCV delivered the 11th IUCAA Foundation Day Lecturetitled ‘Chalk and Duster’, which was reported in theJanuary, 2000 issue of KHAGOL, the bulletin of theIUCAA18.

Why PCV could not become a householdname?

The answer to this bewildering question is two-fold.Firstly, during the era of PCV, the prestigious, burgeoningspace programmes and the atomic energy projects of theGovernment of India were eye-catching. In contrast, thefield of general relativity, pursued by PCV, was an areathat was hardly taught even in the postgraduate physicscourses in Indian Universities. Secondly, PCV himself“never yearned to be in the public eye3.” He was moreinterested to pursue research in his field of interest, to teachand to popularise particularly mathematics and lead asimplistic Gandhian life far from the madding crowd. Thenet outcome was that PCV remained relatively unknownin the centres of excellence – Universities and researchinstitutes in India and abroad. As a consequence, hiscontributions in the fields of research, teaching and sciencepopularisation, albeit invaluable, could not render him ahousehold name.

Last Period

For the last few years, PCV’s health was deteriorating.He was mostly staying at his home at Shardanagar,Ahmedabad. Since January, 2010, he was suffering fromkidney troubles. Three months later he succumbed to deathin the morning of Friday, the 12th March, 2010 inAhmedabad. He is survived by his four daughters Kumud,Ila, Smita and Hina, and their families.

Two important obituaries on the demise of PCV werewritten - one by Dr. Ajit Kembhavi, the then Director ofthe IUCAA and the other by Dr. Pankaj S. Joshi, the thenPresident of the IAGRG, and these were published inKHAGOL19.

PCV: The Astronomer

PCV considered himself as a dedicated teacher inmathematics. In 1997, when the Editor of the Bulletin ofthe Astronomical Society of India invited PCV to delivertheir Silver Jubilee Lecture, he accepted the invitation anddelivered a lecture entitled ‘Me, an Astronomer?20’ In thislecture, PCV elaborately explained how he was transforededfrom a mathematician into an astronomer. One needs to

258 SCIENCE AND CULTURE, JULY-AUGUST, 2019

go through this article in order to be able to properlyappreciate the academic contribution of PCV in the fieldof astrophysics.

Philosophy of PCV

Known as a ‘Gandhian mathematician’, PCV was astaunch follower of Gandhian principles. He believed inplain living and high thinking. A remarkable trait of PCVis that he was simple and honest in both personal and publiclife. He was a modest man of amicable nature. Even in hiseighties, “he was incredibly active, both physically andintellectually.” His teaching at classes using a chalk andblackboard used to captivate the students. He believed thatit was the best means of imparting knowledge to thestudents. That is why, perhaps, he named his memoir onteaching and research as ‘Chalk and Duster’21.

Critical Comments on PCV

In a public lecture in Gujarat University in 2017 onthe 98th birth anniversary of PCV, Dr. Karan Jani, referredto earlier, commented on the work, lifestyle and philosophyof PCV. He acknowledged that PCV was the first to writepopular science books in the Gujarat literature, he continuedto teach in primary schools even when he was a ViceChancellor of the Gujarat University, he was the firstphysicist to work on blackhole and he carried the legacyof Einstein’s Relativity in independent India. Dr. Jani furtheracknowledged that it is only Vaidya’s groundbreaking workthat proved the formation of blackhole from a stellarcollapse.

Commemoration of PCV

In commemoration of P.C. Vaidya, a 120-page SpecialIssue of Suganitam was published in 2010, and a widerange of tributes appeared in it. Vigyan Prasar, Departmentof Science and Technology, Govt. of India, in collaborationwith IUCAA, prepared a film ‘Professor Vaidya – a filmon P.C. Vaidya’ (CD: Rs. 50/-) in 201722. This film, firstconceived by Professors N. Dadhich and Ajit Kembhavi,not only “presents a unique and inspiring picture of asimple man with profound accomplishments”23 but alsoreveals Dr. Vaidya’s reminiscence on how he developedhis metric to one of Einstein’s equations. ‘Prof. P. C. VaidyaNational Conference on Mathematical Sciences’ was heldby St. Xavier’s College, Ahmedabad and Gujarat GanitMandal at Surat on Dec. 24-25, 201824. A write-up entitled‘Vaidya Metric and Bachukaka’ appeared in the South AsiaDaily on May 28, 201810. PCV’s next generation ofGujarati acquaintances used to address him as ‘Bachukaka’.

Epilogue

Quoting K.P. Jani7, “Vaidya never received any Padmaawards, nor any road or institute is named after him. Buthis legacy lives in every relativity book on earth.” He waslater remembered10 (by a journalist of South Asia Daily)as “a ramrod straight man with a slight smile who exudeda subtle sense of authority.” Professor P.C. Vaidya akaBachukaka will always be remembered as a remarkablymodest man, a lifelong Gandhian, a revered teacher, arenowned physicist and a populariser of mathematics. Thishumble scientist clad in ironed kurta and dhoti, wearing aGandhi cap and riding a black bicycle even in his old agecertainly deserves to be retrieved from near oblivion.

References

1. https://en.wikipedia.org/wiki/Prahalad_Chunnilal_Vaidya

2. A. Sherrif, “Remembering the Forgotten Scientist Who FoughtFor Freedom & For Science!,” The Better India, May 28, 2018.URL: https://www.thebetterindia. com/143176/ forgotten-indian-scientist-who-fought-for-freedom-and-for-science/.

3. A. Ramnath, “Centenary: P.C. Vaidya, a Gandhian Physicist WhoLaboured in India’s Shadows,” The Wire, May 27, 2018. URL:https://thewire.in/the-sciences/ centenary-p-c-vaidya-a-gandhian-physicist-who-laboured-in-indias-shadows.

4. M. Chakrabarty, “1918 – A Truly Remarkable Year in the Historyof Mankind,” Science and Culture, 84 (9-10), 302-309 (2018).

5. P.C. Vaidya, “Teacher-mathematician: An obituary of V. V.Narlikar,” Current Science, 60 (8), 502-503 (1991).

6. https://en.m.wikipedia.org/wiki/Schwarzschild

7. P.C. Vaidya, “The External Field of a Radiating Star in GeneralRelativity,” Current Science, 12, 183-189 (1943).

8. K. Jani, “Vaidya Metric and 100 Years of Black Hole Solution,”(P. C. Vaidya Birth Centenary Year Lecture), Gujarat University,September 9, 2017. URL: https: //twitter.com/AstroKPJ/status/734761206616084480

9. http://video.google.com/videoplay?docid=4382862622658562253#

10. ‘Vaidya Metric And Bachukaka’, South Asia Daily, May 28,2018. URL: https:// southasia.typepad.com/ south_asia_daily/2018/05/vaidya-metric-and-bachukaka.html.

11. h t t p s : / / i p f s . i o / i p f s / Q m X o y p i z j W 3 W k nF i J n K L w H C n L 7 2 v e d x j Q k D D P 1 m X Wo 6 u c o / w i k i /Vaidya_metric.html.

12. P.C. Vaidya, “Nonstatic Solutions of Einstein’s Field Equationsfor Spheres of Fluids Radiating Energy”, Physical Review, 83,10 (1951).

13. K. Jotania, “List of Papers Published by Prof. P.C. Vaidya,”Mathematics Today, 33, 1-8 (2017).

14. A.K. Raychaudhuri, “Relativistic Cosmology I,” Physical Review,98 (4), 123 (1955). DOI: 10.1103/PhysRev.98.1123.

15. E. Poisson, ‘A Relativist’s Toolkit: The Mathematics of BlackHole Mechanics’, Cambridge University Press, Cambridge, 2004,Chapter 2. ISBN 0-521-83091-5.

16. N. Dadhich, J. Krishna Rao, J.V. Narlikar and C.V. VishveshwaraRao, Eds., ‘A Random Walk in Relativity and Cosmology: Essays

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in Honour of P.C. Vaidya and A.K. Raychaudhuri’, (WileyEastern Ltd., New Delhi, 1985. ISBN: 978-0470201985).

17. http://dspace.rri.res.in/handle/2289/6624

18. ‘The Eleventh IUCAA Foundation Lecture’, KHAGOL, No. 41,January, 2000.

19. Obituaries on PCV by A, Kembhavi (Director, IUCAA) and P.S.Joshi (President, IAGRG), KHAGOL, No. 82, p.5, April, 2010.

20. P.C. Vaidya, “Me, an Astronomer?,” Bulletin of the AstronomicalSociety of India, 25, 209-212 (1997).

21. P.C. Vaidya, ‘Chalk ane Duster’ (Chalk and Duster), Suganitam

Prakashan, Ahmedabad, 2011.

22. “Professor Vaidya - a film on Prof. P. C. Vaidya,” Vigyan Prasar,Department of Science and Technology, Government of India,New Delhi, 2017. URL: https://www.youtube.com/ watch?v=bvzV3RTEkF4.

23. J.V. Narlikar, “P.C. Vaidya (1918-2010),” Current Scence, 98(10), 1389 (2010).

24. file:///C:/Users/User/Desktop/PCV-The%20Mathematics%20Consortium-2018.html by The Indian MathematicsConsortium.