Biography

Great-grandfather, Józef Kazimierz Plebański (1831-1897) was an outstanding historian, professor at the Main School in Warsaw, editor of the “Warsaw Library”, coeditor of the “Educational Encyclopedia”, coauthor of Olgerbrand’s “Universal Encyclopedia” and author of many important scientific publications. 

Jerzy’s father, Józef Adam Plebański (1887-1967), graduated from Charlottenburg University of Technology. He was a well-known electrician-radio technician, technical director of the first Polish radio-engineering companies: Polish Radio Engineering Society, Polish Factory “Marconi”. He was the founder of the Association of Polish Radio Engineers (1921) and one of the most active Polish inventors in the field of radio technology. He had about 200 patents also known in Germany, England, France and the USA. 

Józef’s brother, beloved Jerzy’s uncle, Stanisław Plebański (1889-1954), had an engineering degree from Ecole des Ponts et Chaussées and was employed in the construction of bridges over the Amur, Boh and Dnieper. In France, he became an officer of the Foreign Legion. With the rank of captain, returned to Poland and took part in the war against the Bolsheviks in 1919 and 1920, and then in the Silesian Uprising. After the war, he takes part in the reconstruction of Warsaw and political life (he is one of the founders of the Labor Party; he has a close relationship with Władysław Sikorski). He is also a lecturer at the Warsaw University of Technology. During World War II, the Gestapo first wounded, then imprisoned and tortured him in Berlin and Pawiak in Warsaw. Arrested after the war in 1949 by the UB (Security Office – Polish Secret police). Transferred from prison to prison (under special supervision of the NKVD – Soviet secret police agency) and tortured, released after 4 years and soon dies. Stanisław Plebański had a great influence on Jerzy, after whom he was closely looking for some time. It was he who taught his nephew how to play chess, a game that Jerzy was passionate about throughout his life. 

When talking about Jerzy’s family, it is impossible not to mention his two cousins, sisters: Barbara and Janina Plebański, liaison officers in the “Zośka” battalion, who died in the Warsaw Uprising in 1944, and about cousins, 2^nd Lt. Stanisław Łopaciński, who died during the defensive war of Poland in September 1939 and his brother, 2^nd Lt. Andrzej Łopaciński, who died on the first day of the Warsaw Uprising, with whom Jerzy was very much tied. Barbara and Janina’s step sister, Zoja Plebańska (1911-2011), joined the convent Bridgettines and Jerzy maintained a cordial relationship with her until his death.

In his youth, he was also in close and cordial relations with his cousin, son of Tadeusz Plebański (1893-1976), Tomasz Plebański (1930-1994), an outstanding chemist, doctoral student of prof. Wojciech Świętosławski. He later became a professor of chemical sciences, co-founder of methods for obtaining penicillin and other antibiotics in Poland, as well as a co-creator of Polish physicochemical metrology. 

Jerzy had a younger brother, Jan, who was a multi-talented man. Jan’s daughter, Jerzy’s niece, dr hab. Jolanta Talbierska, an excellent specialist in the history of culture of the Enlightenment, especially history of graphic arts, is currently the director of the Print Room of University of Warsaw Library, continuing the family traditions from the times of Prof. Józef Kazimierz Plebański. This very limited history of Jerzy’s Plebański family provides some feeling of the atmosphere and tradition in which he was brought up and grew up and what values were dear to him throughout his life.

Jerzy education

When World War II breaks out, Jerzy is 11 years old. He studies at home and in underground education. After the war, in 1947, he was graduated from the High School in Chorzów. In the same year, he was admitted as a physics student to the University of Warsaw at the Faculty of Mathematics and Natural Sciences, receiving the student index No. 9328. This index (book of grades) shows how an outstanding student he was and how brilliant his lecturers were. Among them were professors: Wacław Sierpiński, Kazimierz Kuratowski, Andrzej Sołtan, Stefan Pieńkowski, Andrzej Mostowski, Karol Borsuk, Włodzimierz Zonn, Witold Pogorzelski, Czesław Białobrzeski, Wiktor Kemula, Wojciech Rubinowicz and Leopold Infeld. The last two played a key role in the scientific development of Jerzy Plebański. 

Prof. Wojciech Rubinowicz, theoretical physicist with significant achievements in creating quantum mechanics, and a former student of Nobel laureate Arnold Sommerfeld. In 1949, proposed to Jerzy to become his assistant; it was just after Jerzy finished two years of study. (By the way, in the same year a position of an assistant was offered to Plebański by prof. Kuratowski however, with the proviso that Jerzy would move to mathematics studies. However, a father’s friend, an outstanding electronics engineer, prof. Janusz Groszkowski advised him to continue studies in physics and Jerzy heed this advice). 

In 1951 he finished studies presenting his master’s thesis, and in 1952 he was appointed an associate professor, but he does not yet have a doctoral degree. Ph.D. degree he obtained in 1954 on the basis of the dissertation: “On the state function in quantum field theory” made under the supervision of Prof. Rubinowicz. At that time he also developed more closer scientific cooperation with Prof. Leopold Infeld, who in 1950 had returned from Canada to Poland, to Warsaw. Prof. Leopold Infeld was universally recognized in the world as an authority in the field of general relativity, his fame radiated as he was a close associate of Albert Einstein and associate of other eminent scientists such as the mathematician Bartel Leendert van der Waerden or one of the founders of quantum mechanics, Nobel Prize winner Max Born. 

International career

In 1956 he was invited to the Soviet Union to the famous Lebedev Institute. Here, he meets a great Russian physicist, soon to be Nobel laureate, Igor Tamm, with whom he shared an honest friendship for many years. He also met, at that time, the future Nobel laureate, brilliant Lev D. Landau, who has been a professor at the Institute for Physical Problems in Moscow for many years. 

At the Institute of Theoretical Physics at Hoża Street (Warsaw, Poland) he is a supervisor of about 20 master’s theses, including such outstanding physicists as Andrzej Trautman or Iwo Białynicki-Birula. Furthermore, as Infeld himself will admit one day, Plebański was the scientific supervisor of doctoral dissertations of R. Michalska, W. Tulczyjew, S. Bażański and A. Trautman, but he was not a formal supervisor of these dissertations because during their defences he was already on a scholarship abroad. In the years 1956-1958, he was a Vice-Dean of the Faculty of Mathematics and Physics at the University of Warsaw. 

In 1958, he received a Rockefeller scholarship, which enabled him to go to the United States. For the first year (1958-1959) he stayed at the Institute of Advanced Studies at Princeton. He listens to the lectures of P. A. M. Dirac and C. N. Yang. He also makes friends with John Stachel, Peter Havas and John A. Wheeler. Later he will write joint papers with Stachel and Havas. He spent the second year (1959-1960) as a visiting professor in the Department of Physics at the University of California (UCLA). 

At that time, several important papers by Plebański were published, of which at least three are fundamental. One is about electromagnetic wave scattering by the gravitational field of an isolated system and also presents the general theory of the deflection of light rays (J. Plebański, Electromagnetic waves in gravitational fields, Physical Review,118, 1396 (1960)), the next two are devoted to the problem of motion in general relativity; these are, one with B. Bertotti (B. Bertotti and J. Plebański, Theory of gravitational perturbations in the fast motion approximation, Annals of Physics, 11, 169 (1960)) and the second with S. Bażański (J. Plebański and S. Bażański, The general Fokker action principle and its application in general relativity theory, Acta Physica Polonica, XVIII, 307 (1959)). 

At UCLA he met the famous Mexican physicist Alfredo Baños, who for the first time tells Jerzy about a research institution that is currently being established in Mexico City: the Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV del IPN), which is intended to be the Mexican equivalent of the Princeton Institute. As it turned out later, the meeting with A. Baños had a decisive influence on the future life of Jerzy Plebański. 

At Warsaw University

Then, however, he returned to Warsaw in 1960. The scientific collaboration of Infeld and Plebański has ended. This was due to a significant difference in their character and their approach to solving physical problems. Plebański was offended by an excessive (in his opinion) ceremonialism and the pomposity of Infeld. Infeld did not like Jerzy’s love of too much (in the opinion of Infeld) attention to formal considerations of problems to be solved. Plebański has always had a remarkable ease in making complex and tedious algebraic manipulations. It was giving an impression that the formulas obtained after many transformations have metaphysical meaning for him. Therefore, each problem solved by Jerzy was “recalculated” with all possible details and it could seem to the reader that the main issue is lost in the maze of mathematical transformations. It was the reason for Infeld’s criticism. 

Plebański, in turn, had a grudge against his mentor due to the fact that he did not include in the monograph Motion and Relativity some new results of Jerzy on the problem of the motion of extended bodies in general theory of relativity. (These results were consistent with the later results by S. Chandrasekhar). Either way, the long-standing fruitful scientific collaboration of these two prominent relativists has already gone down in history. However, this did not affect the fact that Prof. Infeld, in a letter from 1962 to the Dean of the Faculty of Mathematics and Physics of the University of Warsaw, prof. J. Bondara warmly supports the efforts of the Institute of Theoretical Physics of the University of Warsaw to award Plebański the title of an associate professor. In a few years, he will also visit Jerzy in Mexico and they have a good time together. 

From 1960 to 1962, Plebański was again the vice-dean of the Faculty of Mathematics and Physics of the University of Warsaw. He continues to work with his students Bogdan Mielnik and Joanna Ryteń (later the wife of an eminent relativist and Jerzy’s friend, Ivor Robinson) on various problems of motion in Einstein’s theory of gravity. He also collaborates with other young Polish physicists and this collaboration is not limited only to the walls of the Institute at Hoża. Very often, he moves to a cafe or restaurant, where in the fumes of cigarette smoke there is a fruitful discussion on scientific topics, but also on culture or philosophy. The result of these discussions will later be an excellent book Znane i Nie znane (Known and Unknown), popularizing contemporary theorethical physics (J. Plebański, S. Bażański, B. Mielnik, J. Ryteń, Znane i Nie znane, Iskry, Warsaw 1963). 

Plebański in the first “adolescent” period after graduation, as a rising star of theoretical physics, takes an active part in the cultural and social life of the capital. He is a frequent visitor to the Irena Krzywicka Literary Salon. There he meets many of the Polish cultural celebrities. He was there a welcome guest also because he was taking academic care of the son of Krzywicka, Andrzej Krzywicki, who studied physics at the University of Warsaw (later professor of theoretical physics at the University of Paris in Orsay).

In his book Diabelski Młyn (Ferris wheel) he writes:

...On the recommendation of Leopold Infeld, the head of the Institute of Theoretical Physics at Hoża, I was looked after by the associate professor, later professor Plebański. He gave me some readings, and my mother brought me books. The main reading, I don’t know who decided so, Plebański or Infeld, was the theoretical physics course by Landau and Lifszyc … Plebański believed that if I was worth something, I could manage…. (Andrzej Krzywicki, Ferris wheel, Reader, Warsaw 2005, pp. 66-67). 

During intensive work on the monograph Motion and Relativity, Infeld and Plebański often traveled to Nieborów. Jerzy meets there Maria Dąbrowska there. In her Diaries, fragments of the memoirs have been preserved about the discussion on Polish October, in which Plebański took an active part. Dąbrowska writes: 

May 31, 1956. Thursday. Feast of Corpus Christi “… After lunch, Infeld invited me and Pniewski to his place for black coffee, to read the draft of his speech for the general session of the Polish Academy of Sciences. He asked for an opinion. […] We need to think carefully about what we are concerned with, whether it is about talking, easing and making a “good impression” on the opposition society, or about the actual results that would be practically achievable. Infeld only partially agreed with me, but I was supported by Infeld’s assistant, associate professor Plebański. Also, in some way by Pniewski, but he was too practical. Anyway, there is to happen some ferment at the Academy …

Maria Dąbrowska, DIARIES 1951-1957, Czytelnik, 1988, vol 4, PAGES 263-264

At the end of July 1962, in Jabłonna near Warsaw the International Gravity Conference took place, which, thanks to the fame of L. Infeld, gathered the greatest relativists in the world. Jerzy takes, of course, an active part in it. He meets many physicists with whom he will meet frequently in private life and during many other conferences . With some of them, such as Ivor Robinson, Alfred Schild or Frederick Ernst, he will collaborate scientifically and publish joint papers. He also had a special bond of sympathy with Richard Feynman. In a letter written from the Grand Hotel in Warsaw to his wife, Gweneth, Feynman describes visiting a small apartment on ul. Nowolipki, which was then shared by Jerzy with his second wife Anna Łazarowicz:

Dearest Gweneth…I went one evening to the home of one of the Polish professors (young, with a young wife). People are allowed seven square yards per person in apartments, but he and his wife are lucky: they have twenty-one*—for living room, kitchen, bathroom. He was a little nervous with his guests (myself, Professor and Mrs. Wheeler, and another) and seemed apologetic that his apartment was so small. (I ask for the check. All this time the waiter has had two or three active tables, including mine.) But his wife was very relaxed and kissed her Siamese cat “Booboosh” just like you do with Kiwi. She did a wonderful job of entertaining—the table for eating had to be taken from the kitchen, a trick requiring the bathroom door to be first removed from its hinges. (There are only four active tables in the whole restaurant now, and four waiters.) Her food was very good and we all enjoyed it…

Richard P. Feynman, What do you care what other people think. Further adventures of a curious character Richard P. Feynman as told to Ralph Leighton. Bantam Books, New York, Toronto, London, Sydney, Auckland, 1989. PAGES 88-93

Soon after, Plebański will be a guest at Feynman’s home in Pasadena.

Creating a Physics Department at CINVESTAV

At the same time, he faces a completely new challenge. The outstanding Mexican neurophysiologist Arturo Rosenblueth, director of the newly established CINVESTAV, invites Jerzy to Mexico with a proposal to create a Department of Physics. Of course, Plebański’s candidacy was suggested by a previously met in the USA Alfredo Baños, on whom the brilliance and energy of the young Polish physicist made a great impression. Plebański accepts the invitation and at the end of the summer of 1962 flies to Mexico. On the way, he learns that he has been awarded the title of associate professor. He is 34 years old. 

Soon his assistant and friend Bogdan Mielnik also arrived in Mexico, and in 1963 Jerzy’s wife Anna (maiden name Łazarowicz). Jerzy Plebański is the first head of the Department of Physics in CINVESTAV. He gives a number of courses on relativity theory and quantum mechanics. Notes from these courses are published as CINVESTAV monographs. 

During this period, he worked mainly on: 

• (a) algebraic classification of the energy-momentum tensor and 
• (b) general formulation of non-linear electrodynamics. 

The energy-momentum tensor appears in Einstein’s equations and describes the effect of matter on spacetime geometry. It is therefore one of the fundamental objects of the theory of gravity. The classification based on the algebraic properties of this object was given by A. Z. Petrov in 1961. Plebański took up this topic again and prepared a detailed algebraic classification of the energy-momentum tensor using the tetrad and spinors formalism. He also analyzed possible physical realizations of the individual algebraic types. An extensive paper on this subject was published: J. Plebański, The algebraic structure of the tensor of matter, Acta Physica Polonica, XXVI, 963 (1964), aroused great interest, was repeatedly quoted and the methods used there were used by other authors in the algebraic analysis of similar objects appearing in the theory of relativity. 

Plebański’s interest, in non-linear electrodynamics, has undoubtedly its source in the famous work of M. Born and L. Infeld, devoted to the analysis of a special kind of nonlinear electrodynamics, now known as Born-Infeld nonlinear electrodynamics. Plebański pondered the theory of nonlinear electrodynamics in the general case. One of the surprising conclusions of these considerations was the possibility of propagation of field disturbances at a speed greater than the speed of light in a vacuum. This result seemed absurd to Jerzy and he refrained from publishing it. He only included it in the CINVESTAV monograph from 1966, which was a copy of his lecture notes. A similar result was obtained by G. Boillat, who, however, did not hesitate to publish it in 1966. A complete exposition of Plebański’s pioneering achievements in nonlinear electrodynamics at that time is provided in the publication of the Nordic Institute for Theoretical Physics (NORDITA): J. Plebański, Lectures on Nonlinear Electrodynamics (NORDITA, Copenhagen, 1970). 

At that time, in Mexico he had two prominent PhD students. They were Bogdan Mielnik (1964) and Rodrigo Pellicer Basañez (1968). It is worth adding that Mielnik was the first doctoral student at the Department of Physics at CINVESTAV. In 1964, Plebański’s family situation changed. The daughter Magdalena is born. (She is currently a professor at the Royal Melbourne Institute of Technology and Monash University in Melbourne. She is a world-renowned specialist in biomedicine. In particular, she is working on finding effective vaccines for malaria and cancer. Jerzy also had a son, Stanisław, born from his first marriage in 1951. He died in 2008).

Return to Poland

In 1967, Plebański’s family returned to Warsaw and Jerzy threw himself into work at the Institute on Hoża Street (Warsaw, Poland). He surrounds himself with physicists interested in various problems of physical mathematics and general relativity. Among them are Stanisław Bażański, Bogdan Mielnik, Marek Demiański, Antoni Sym, Anatol Odzijewicz, Andrzej Krasiński, Jan Slavik, Jerzy Kowalczyński, Krzysztof Rózga and, commuting from Łódź, Maciej Przanowski. Plebański is the supervisor of Andrzej’s Krasiński doctoral dissertations (1973) and Jan Slavik. The rest of Plebański’s PhD students started working on doctoral dissertations with him and finished dissertations with other supervisors, because when they were finalizing their work Plebański was already back in Mexico. 

The problems that mainly interested Plebański at that time were: 

• (c) Baker-Cambell-Hausdorff formula (BCH) in the continuous case, 
• (d) Moyal’s algebra and an alternative to the operator formulation of quantum mechanics, 
• (e) new classes of solutions of the Einstein and Einstein-Maxwell equations, 
• (f) generalization of the Goldberg-Sachs theorem and 
• (g) methods of complex analysis in relativity theory. 

The crowning achivement about considerations on the BCH formula is an extensive article: I. Białynicki-Birula, B. Mielnik and J. Plebański, Explicit solution of the continuous Baker-Cambell-Hausdorff problem and a new expression for the phase operator, Annals of Physics 51, 187 (1969), where the BCH exponent is expanded into a perturbative series. Plebański is also fascinated by the paper of J. E. Moyal from 1949, in which the author uses the earlier results of Herman Weyl and Eugene Wigner, represents quantum mechanics as a statistical theory on the phase space. Commutators of operators in quantum mechanics are replaced by a generalized Poisson’s brackets for corresponding functions, now called Moyala’s brackets. 

Jerzy devoted a whole course to students of mathematics on this topic (exercises led by Piotr Kielanowski). Notes from this lecture, were published by the University of Toruń: J. Plebański, Poisson brackets and commutators, (preprint No. 69, Institute of Physics, Nicolaus Copernicus University, Toruń, 1969). Several years later he informed Daniel Sternheimer about the ideas of Moyal. Soon Moshe Flato became interested in  this problem and in 1978 two pioneering works appeared in the Annals of Physics on a new field, quantization by deformation. It is safe to say that Plebański has opened the eyes of the mathematical community and physicists on the great importance of this new field. After 25 years, he will come back to it with his colleagues and it turns out that the formalism of quantization by deformation can also be effectively used in the field theory, string theory as well as in complex gravity.

In the “second Warsaw period”, what you can call Plebański’s stay in Poland, after returning from Mexico, he is also working intensively on finding new solutions of Einstein’s equations in a vacuum with a cosmological constant and equations Einstein-Maxwell. The first results of these searches were published in one-author articles in 1974/75 (thus already at the time of re-residence in Mexico). The final version appeared in an excellent joint paper with M. Demiański: J. F. Plebański and M. Demiański, Rotating, charged and uniformly accelerating mass in general relativity, Annals of Physics 98, 98 (1976). The solution given in this paper, known today as the Plebański-Demiański metric, contains 7 parameters and it is the most general vacuum metric (with a cosmological constant Λ) of  type D according to the Petrov-Penrose algebraic classification. The paper of Plebański and Demiański is one of the basic papers in the field of exact solutions of Einstein’s equations and has well over 650 citations. 

The next problem to which Plebański began to pay more attention was the possibility of generalizing the Goldberg-Sachs theorem in the case of the existence of matter. The original claim is that ‘The vacuum metric is algebraically special in the sense of Petrov’s classification if and only if it allows for the existence of geodetic null congruence without shear’. Keeping in mind his algebraic classification of the energy-momentum tensor, Plebański thought about examining how the Goldberg-Sachs theorem works for different types of matter. It was also about the broader problem of a relationship of the Petrov-Penrose Weyl tensor classification with the energy-momentum tensor classification. The partial results on these issues will appear after he leaft Poland. Also, after leaving Poland, the last of these problems mentioned above will be very creatively developed, i.e., whether the methods of complex analysis can significantly help in solving some problems of the theory of relativity. Plebański in his papers concerning solutions of type D  noted that the use of complex calculus greatly simplifies the analysis of these solutions. This is how Jerzy began to be interested in this topic, which will soon lead to pioneering achievements. For now, he cannot devote all his energy to solving these scientific problems because he is consumed by administrative work.

Moving to Mexico

In 1968 he was awarded the title of full professor and in the difficult period of 1969-1973 for the University of Warsaw, Plebański was chosen its vice-rector for scientific and research affairs. In 1973 he got back an invitation to Mexico and he left Poland at the end of that year, as then it turned out permanently. He holds a professorship at the Departamento de Física in CINVESTAV. However, the recent tensions related to an attempt to combine scientific and administrative work, and excessive smoking make themselves felt. Jerzy has a massive heart attack. Thanks to the quick intervention, medicine and rehabilitation, doctors manage to save his life and returned him to the old activity. However, he has to give up exhausting scientific work for a while. 

He compensates this by spending time on painting pictures. Those are symbolic images, but also portraits, e.g. of the philosopher and mystic Rudolf Steiner or his favorite writer Aldous Huxley. Many of them show cats, which for Plebański, symbolizes his relatives and friends. The cat was, anyway, Jurek’s beloved animal. The Plebański family always had cats, or rather female cats, which they called each time Bubcia (according to Jerzy, it was diminutive of the name of the Egyptian goddess of love, music and cats, Boubastis). 

Some of Jerzy’s paintings are now in the Departamento de Física in CINVESTAV. He reads a lot during his convalescence. Anyway, he always reads a lot. He loved books. He was an expert in science fiction and esoteric literature. He also plays his beloved chess a lot. He slowly returns to full strength. At that time, a copy of Jerzy’s manuscript appeared: J. Plebański, Spinors, Tetrads and Forms (Monograph of CINVESTAV, México, 1974). It was an absolute rarity in the scientific literature world. The author presented in an very clear and original way the knowledge of the methods of algebra, spinor and tetrad analysis in general relativity. It is a pity that to this day there is no book edition of this manuscript. 

H-space

At the gravity conference in Syracuse, he learns from Ted Newman about the so-called heavenly space (H-space). It is a 4-dimensional complex differential manifold endowed with a holomorphic metric satisfying the Einstein vacuum equations, for which the Weyl tensor is self-dual. Spaces of this type naturally appeared in the course of Newman’s studies of asymptotically planar space-time. It also turned out that during this conference Roger Penrose described a twistor formalism that he discovered in 1968 and intensively developed, he also introduced a celestial space, which he interpreted as a nonlinear graviton.

Plebański, after discussions with Newman and Penrose, returns with new ideas to Mexico. Because, as we have already mentioned, he has been particularly interested for some time in complex methods for Einstein’s theory, he proceeded with an unprecedented energy to work on H-spaces. Having a mathematical apparatus at his disposal, spinors and tetrads developed in the Spinors, Tetrads and Forms in very short time and in a very elegant manner he finds out a reduction of 10 vacuum Einstein’s complex equations for a holomorphic metric with a self-dual Weyl tensor to one partial nonlinear differential equation of the second order for one holomorphic function. This function defines a Heavenly space metric analogously to that known in the geometry of Kähler spaces. In the further part of this paper, he finds another form of this equation, the so-called Heavenly Equation II. He publishes his results in a fundamental article: J. F. Plebański, Some solutions of complex Einstein equations, Journal of Mathematical Physics 16, 2395 (1975). This paper outlined one of the directions for the study of heavenly spaces and in general for the complex spacetime in the following years. 

At the same time, in the same issue of the Journal of Mathematical Physics, there is another groundbreaking paper co-written with one of Jerzy’s associates, S. Hacyan: J. F. Plebański and S. Hacyan, Null geodesic surfaces and Goldberg-Sachs theorem in complex Riemannian spaces, Journal of Mathematical Physics 16, 2403 (1975). This paper generated a new wave of interest in a deeper mathematical and physical sense of the classical Goldberg-Sachs theorem, which led to further important generalizations of this theorem by Plebański’s students and associates and other mathematicians and physicists. 

Jerzy was haunted by the idea of a generalization of heavenly spaces in the case where the Weyl tensor is not self-dual. It turned out to be possible. Working on this problem with Ivor Robinson they succeeded in reducing the Einstein’s vacuum complex equations for the holomorphic metric to one partial nonlinear differential equation of second order for one holomorphic function even when the anti-self-dual (or self-dual) part of the Weyl tensor is minimally algebraically degenerated. The authors named this type of complex spacetime hyper-heavenly spaces (HH-spaces) and the appropriate differential equation hyper-heavenly equation. This equation turns out to be a generalization of the second, not the first, heavenly equation. Pioneering paper on the subject: J. F. Plebański and I. Robinson, Left-degenerate vacuum metrics, Physical Review Letters 37, 493 (1976), as well as previous paper on heavenly space, literally sparked an avalanche of papers on complex relativity theory. 

In particular, interest in this theory resulted from a certain concept formulated by Plebański, which has its origins in the pioneering paper of A. Trautman from 1962, as well as in later papers by T. Newman and others from 1965/66. This concept is summarized in the perception that physical solutions of Einstein’s vacuum equations can be realized as Lorentz real slices of complex solutions. This program, now called the Plebański program, was never fully implemented, but it did lead to some significant results and is still pursued (see, e.g., recent works by Adam Chudecki). 

It was during this period that Plebański’s works were written together with many of his associates, including: I. Robinson, D. J. Finley, A. Schild, F. J. Ernst, C. P. Boyer, S. Hacyan, A. García, G. F. Torres del Castillo, K. Rózga, A. L. Dudley, and M. Przanowski. He also does not forget his previous interests and creates works on the exact solutions of Einstein’s equations and nonlinear electrodynamics. Here, mainly with colleagues and PhD students such as: A. Krasiński, J. Kowalczyński, A. García, H. Salazar, S. Alarcón Gutiérrez, LE Morales, AL Dudley. In 1976, he published an excellent paper that turned out to be a precursor of the quantum theory of gravity according to A. Ashtekar: J. F. Plebański, On the separation of Einsteinien substructures, Journal of Mathematical Physics 18, 2511 (1977). The operation introduced there by Plebański (now called t’Hooft-Plebański) and self-dual connection (variables of Plebański-Ashtekar) play a key role in one of the quantum versions of gravity. 

It seems that the period 1974-1987 was the most creative period of the scientific research career of Plebański. In Mexico, he promoted three doctoral dissertations during this period. His doctoral students were: S. Alarcón Gutiérrez (1979), G. F. Torres del Castillo (1982) and L. E. Morales Guerrero (1984). He invites his former students and then close co-workers from Poland, as well as many foreign physicists to the Departamento de Física. The Departamento de Física at CINVESTAV is one of the top three (next to the Universities of Oxford and Pittsburgh) centers in the world dealing with complex gravity. 

More scientific collaborations 

Piotr Kielanowski, Maciej Przanowski