Kumar  Shwetketu  Virbhadra Mathematics Department Korman Center Drexel University 33rd and Market Streets Philadelphia PA, 19104 USA Education Ph.D.   Physical Research Laboratory    India    Guru: Prof. P. C. Vaidya (known for the Vaidya metric - a non-static generalization to the  Schwarzschild metric.)  Click here for a video. [In Sanskrit, Gu means darkness and ru means one who dispels.] $ds^2 = -(1-\frac{2M(u)}{r}) du^2\pm 2 du dr + r^2 (d\theta^2 +\sin^2 \theta d\phi^2)$

Teaching .

•   Courses
  

  Physics & Astronomy	Institution	Pure & Applied Mathematics	Institution
  1. Classical Physics (theory)                                                  2. Classical Physics (lab)                                                     3. General Relativity                                                            4. Advanced General Relativity (ISC) )               5. Black Hole Physics (ISC)                            6 . Electric Circuits I                                                           7.  Electric Circuits II                                                          8.  Introductory Physics I  (theory)                                       9.  Introductory Physics II (theory)                                       10.. Introductory Physics I (lab)                                             11. Introductory Physics II (lab)                                            12. General Physics II (theory, Calculus based)                          13. General Physics II (lab)                                                 14. Introduction to Astronomy (theory)                                         15.  Introduction to Astronomy (lab)                                               16. Physical, Earth, and Space Sciences (theory)                    17. Physical, Earth, and Space Sciences (lab)                        18. Gravitational Lensing I   (IRC, Phy 393)                                  19. Gravitational Lensing  II (IRC, Phy 493)                                  20. Introduction to Relativity  (ISC)      21.Tensor Analysis (ISC)   22. Gravitational  Lensing (ISC)                                23. Physics II (theory and lab)                                                24. Intro. to Research in General Relativity	(Univ. of Pennsylvania) (Univ. of Pennsylvania) (Duke University) (Duke University) (Duke University) (Rutgers University) (Rutgers University) (USP, Philadelphia) (USP, Philadelphia) (USP, Philadelphia) (USP, Philadelphia) (TCNJ, NJ) (TCNJ, NJ) (TCNJ, NJ) (TCNJ, NJ) (TCNJ, NJ) (TCNJ, NJ) (TCNJ, NJ) (TCNJ, NJ) (TCNJ, NJ) (TCNJ, NJ) (TCNJ, NJ) (Rowan Univ.) (NIT, India)	25. Linear Algebra  (Math 312, Advanced level) 26. Linear Algebra  (Math 201, Elementary level)                            27. Applied Mathematical Analysis I           28. Differential Equations (Math 244)        Differential Equations  (Math 210)              29. Multivariate Calculus                                        30. Math. for Engineering Analysis II    31. Discrete Computational Structures 32. Tensor Calculus (Math 489)   33. Riemannian Geometry 34. Calculus on Manifolds 35. Differential Geometry I 36. Research in General Relativity I 37. Calculus III (Math 123) 38. Calculus II ( Math 122)                                 Calculus II ( Math 01131)     39. Practicum to Calculus II                    40.Calculus I (Math 135, Elementary level)        41.Calculus I (Math 121, Advanced level)              Calculus I (Math 1041, Advanced level)             Calculus I (Math 01130, Advanced level)       42. Introduction to Analysis II 43. Precalculus  (Math 110)                                                 Precalculus  (Math 1022)                                          Precalculus  (Math 01122)                                        44. Math. for the Liberal Arts (Pure Math.,Math 102) 45. Applied Liberal Arts Mathematics (Math 101)	(Univ. of Pennsylvania) (Drexel University) (Duke University) (Rutgers University) (Drexel University) (Drexel University) (Rowan University) (Drexel University) (Drexel University) (Drexel University) (Drexel University) (Drexel University) (Drexel University) (Drexel University) (Drexel University) (Rowan University) (Drexel University) (Rutgers University) (Drexel University) (Temple University) (Rowan University) (Drexel University)  (Drexel University) (Temple University) (Rowan University) (TCNJ, NJ) (TCNJ, NJ)

•  Teaching Evaluations [Click on the following pdf files and scroll the pages to read comments of students.]

• My collaborators (chronologically arranged)
  

Nathan Rosen (A principal collaborator of Albert Einstein, and of the Einstein-Podolsky-Rosen paradox and  the Einstein-Rosen bridge  fame.) Click here for my  joint paper with Prof.  Nathan Rosen.	G. F. R. Ellis  (A reputed cosmologist and co-author with Stephen Hawking  of a very well-known book  .)  Click here  for my  3 joint papers with Prof. G. F. R.Ellis.
Stephen L Adler (Institute of Advanced Study,       Princeton).  He is known for  the Adler-Barden theorem. Click here for my  joint paper with  him. A few other mathematical physicists.

•  Comments (published in journals) on our gravitational lensing work
• Click here  (Virbhadra-Ellis lens equation)
• Click here
• Click here. 
  

•  Terms coined by us which are used in the literature
• Relativistic images
• Relativistic Einstein rings
• Classification of naked singularities:
  Weakly (WNS), Marginally Strongly (MSNS), and Strongly Naked Singularities (SNS)
  

• Publications and Bibliometric Information (Data  fluctuate by a few percent.)

•    Top cited papers
  

• Second most cited in gravitational lensing (on INSPIRES), with over 8,000 papers written in the last 9 decades.  5 papers are in the top 50. Click here.
  (Reviews and papers with more than 25 authors have been excluded.)
  
• Renowned category (500 and above excluding self-citations) paper(s) as the leading author. Click here.
•  Famous category (250 and above  but less than  500 excluding self-citations) papers. Click here.
• 5 papers on the list of 50 most highly cited papers during 2006.  Click here.
• 3 papers on the list of 400 top cited articles of all time.              Click here.

• Ph. D.  Students

• Undergraduate Research Students 
  

•   Referee for the following journals

•      Editorial Services 
  
• Axioms (Mathematical Physics section).  Editorial board member
• Time and space. Editorial board member
  
  
• Book review

The Galactic Black Hole. Lectures on General Relativity and Astrophysics. By Heine Falcke and Friedrich W. Hehl (Eds.) 353p., Institute of Physics Publishing, Bristol and Philadelphia, 2003. ISBN 0-7503-0837-0. Gen. Relativ. Gravit. 36, pp.1983-1985 (2004). It’s About Time. Understanding Einstein’s Relativity. By N. David Mermin 192p., Princeton University Press, Princeton and Oxford, 2005. ISBN 0-691-12201-6. The Observatory: A Review of Astronomy, 126,  1194, p. 384 ( 2006).

• IAU (International Astronomical Union)