General Relativity and Gravitational Waves

This book serves as a textbook for senior undergraduate students who are learning the subject of general relativity and gravitational waves for the first time. Both authors have been teaching the course in various forms for a few decades and have designed the book as a one stop book at basic level including derivations and exercises.

A spectacular prediction of general relativity is gravitational waves. Gravitational waves were first detected by the LIGO detectors in 2015, hundred years after their prediction. Both authors are part of the LIGO Science Collaboration and were authors on the discovery paper. Therefore, a strong motivation for this book is to provide the essential concepts of general relativity theory and gravitational waves with their modern applications to students and to researchers who are new to the multi-disciplinary field of gravitational wave astronomy.

One of the advanced topics covered in this book is the fundamentals of gravitational wave data analysis, filling a gap in textbooks on general relativity. The topic blends smoothly with other chapters in the book not only because of the common area of research, but it uses similar differential geometric and algebraic tools that are used in general relativity.

“There is … much to like, in particular the way in which the mathematics is motivated by the underlying physics. It will make a good addition to a gravitational-wave physicist’s shelf.” (Jonathan Gair, The Observatory, Vol. 143 (1292), February, 2023)

Prof. Sanjeev Dhurandhar has published over hundred papers in top international journals such as Physical Reviews, MNRAS, Classical & Quantum Gravity, and also a review article (co-authored with M. Tinto) in Living Reviews published by Springer. About three quarters of the publications are on gravitational waves, mainly on their data analysis, and the rest are on various aspects of general relativity. The author led the gravitational wave group at IUCAA from 1989 to 2011 until he superannuated. He has taught general relativity since 1987 in the Physics Department, Pune University, several times to master’s students. Short versions of the course including gravitational waves were taught in IUCAA workshops/schools and also independently in universities around India.  He is a member of the LIGO Science Collaboration (LSC) for the past two decades. The author is a recipient of several prestigious awards which include the Vijnan Bhushan Firodia Award for Outstanding Contributions to Science, the Meghnad Saha Memorial Gold Medal (The Asiatic Society, Kolkata, India) for Outstanding Contributions to Physics, Milners breakthrough prize (Milners Foundation U.S.A.) awarded for the detection of gravitational waves (shared with the LSC), etc. He is a fellow of the American Physical Society (APS), the Indian Academy of Sciences, Bangalore, and National Academy of Sciences India, Allahabad, as well as of the Indian National Science Academy (INSA), Delhi. He has had collaborations with most of the leading detector groups in the world which include: the LIGO Lab, Caltech, USA; Albert Einstein Institute, Max Planck, Potsdam and Hannover, Germany; NAO & Osaka University, Japan; Virgo; Nice Observatory, Nice, France; and University of Western Australia, Perth, Australia.

Prof. Sanjit Mitra has been involved in gravitational wave research for twenty years. He has taught the general relativity coursefor M.Sc. and Ph.D. students for nearly ten years and given lectures on gravitational waves in several works. He has authored thirty research papers in reputed journals and is an author in more than two hundred papers by the LIGO Scientific Collaboration and also the Planck Collaboration for his research on cosmic microwave background.

The author is a recipient of several prestigious awards which include the SwarnaJayanti Fellowship (2016) by the Department of Science & Technology (DST), India, Special Breakthrough Prize in Fundamental Physics (2016) and the Gruber Cosmology Prize (2016), Princess of Asturias Award for Technical and Scientific Research (2017), for the detection of gravitational waves as part of the as part of the LIGO Scientific Collaboration (LSC), Giuseppe and Vanna Cocconi Prize (2019) awarded to the WMAP & Planck Collaborations by the European Physical Society and the Gruber Cosmology Prize (2018) for mapping the CMB anisotropies as part of the PlanckTeam.