Horace Hearne Chair in theoretical Physics,
I collaborate with Rodolfo Gambini, of the University of the Republic in Montevideo, Uruguay, our collaboration has been going on since 1990. We coauthored a book "Loops, knots, gauge theories and quantum gravity" in 1996 and the first book for undergraduates on loop quantum gravity in 2011 (available in Spanish) and have published many papers together. We study the quantization of general relativity using canonical methods. There is a small community pursuing this kind of research, which is complementary to the mainstream approach to quantum gravity: string theory. String theorists believe that one cannot quantize general relativity because it is not a fundamental theory and one has to replace it with string theory in order to quantize it. General relativity will be an "effective" "low energy" theory.
Those of us who work in canonical quantization believe that it has not been properly shown that one cannot quantize plain old general relativity in four space-time dimensions. It is clear that there are difficulties, but these are expected since we have never quantized a theory of space-time itself. Worse, we have little experience theories that are invariant under diffeomorphisms (this is the technical description for the fact that general relativity is coordinate-invariant), and mostly with theories that are considerably simpler than general relativity.
A great place to read more about the canonical vs string debate is Lee Smolin's book "Three roads to quantum gravity". Read my review for Physics Today of the book.
Canonical quantum gravity picked momentum when Ashtekar introduced a new set of variables that make the theory resemble Yang-Mills theories in 1986. Rovelli and Smolin noted in 1988 that one could use loop techniques to describe the theory. Gambini had introduced with Antoni Trias similar techniques for Yang-Mills theories in the early 80's.
With Gambini we made several discoveries, including the fact that the celebrated Jones polynomial of knot theory appeared to solve the quantum Einstein equations. More recently we have been preoccupied with the use of lattice techniques to regularize the quantum Einstein equations. We have invented a generalization of Hamiltonian mechanics that applies to discrete systems like lattice theories and applied it to gravity. Remarkably, it appears to provide a consistent quantization of general relativity. This does away with conceptual problems that have plagued the subject, but leaves us with a challenging computational problem on the lattice. The formalism emerges as a stronger alternative to Dirac's quantization procedure since it applies even in situations where Dirac's fails. More recently, we have applied the framework to spherically symmetric gravity, showing that the singularity inside black holes is removed by the quantum theory. We also showed how to quantize fields on the resulting quantum space-time and how the discreteness of space time at the quantum level naturally regulates and eliminates the infinities of field theories. In the publication list you can find several review papers we have recently writteng with Gambini on the subject.
The collision of two black holes is a central problem in gravitational physics these days since it is expected that the LIGO interferometric gravitational wave detector will be able to measure gravitational waves produced by such collisions with a frequency of a few a year.
I have made several contributions to analytic aspects of the problem of modeling a binary black hole collision on a computer. With Richard Price we developed the "close limit approximation" in which the final moments of a collision are studied as a perturbation of a single black hole. We then extended this approach to second order perturbations with Oscar Nicasio and Reinaldo Gleiser and applied it to non-head on collisions with Gaurav Khanna. The close limit approach has also been used lately by other groups to study kicks in collisions with unequal masses and spins. I also contributed with Olivier Sarbach, Manuel Tiglio and others to aspects of the hyperbolic formulation of Einstein's equations for simulations on computers.
With Reinaldo Gleiser and Richard Price we have lately been studying the decay of perturbations on the Kerr space-time, addressing the issue of the "power law tails" and the ensuing controversy.
Since moving to LSU, I have helped build a group that attempts to solve the Einstein equations for the binary black hole problem using supercomputers. My own personal interest in the subject has remained peripheral, the main players of the LSU numerical group having been Luis Lehner (currently at Perimeter Institute), Ed Seidel (currently at NCSA) and Manuel Tiglio (currently at Maryland). Still at LSU, Steve Brandt, Peter Diener and Frank Loeffler continue work in numerical relativity. You can get the latest developments of our group at the Hearne Institute homepage.
Former graduate students include Nuno Dias, now a professor in Beira, Portugal, Jose Zapata, a faculty member at UNAM-Morelia, Mexico, John Baker, a staff scientist at NASA-Goddard, Gaurav Khanna, a professor at UMass-Dartmouth, Ramon Lopez-Aleman, a professor at University of Puerto Rico, David Garrison, a professor at University of Houston Clear Lake, Gioel Calabrese, currently with Barrie & Hibbert (Edinburgh,UK), Muxin Han (M.Sc.) , currently a postdoc in Marseille.
Former postdocs include Hans-Peter Nollert, currently a C2 professor at Tuebingen University in Germany, Thorsten Schwander, working at Los Alamos, Oscar Nicasio, working for Softnet S.A., Steve Brandt working at CCT LSU, Deirdre Shoemaker, a professor at PennState, Manuel Tiglio, a professor at Maryland, Dave Neilsen, a professor at BYU, and Jason Ventrella, in private industry, Olivier Sarbach, professor at Universidad Michoacana-Morelia, Matt Anderson, instructor at BYU, Ignacio Olabarrieta, in private industry in Spain, Carlos Palenzuela at Albert Einstein Institute, Victor Taveras, a faculty member at West Kentucky Community and Technical College, Jacobo Diaz-Polo, a postdoc at University of Minho in Portugal. Current postdocs are Miguel Megevand and Ed Wilson-Ewing.
I have taught some lectures at international schools. Some of them are online in PDF and other formats:
For 11 years I was the editor of Matters of Gravity, the newsletter of American Physical Society Topical Interest Group on Gravitation. David Garfinkle has taken over the editorshipo starting fall 2006. I also run the mailing list of friends of Instituto Balseiro. I am a representative for the US in the Committee of the International Society of General Relativity and Gravitation. I am also a member of the editorial boards of the Journals Living Reviews in Relativity. In the past I was on the editorial board of the the revolutionary New Journal of Physics, for which I was the Regional Editor for North America, a journal belonging to The Institute of Physics in the United Kingdom and on the editorial board of Classical and Quantum Gravity, also an IOP journal. I am currently the managing editor of the International Journal of Modern Physics D (World Scientific). I am the founding editor of Physical Review X, launched in September 2011, the highest impact factor original research open access journal in physics. I am the past chair of the Topical Group in Gravitation of the American Physical Society. I chaired the committees that awarded the Basilis Xanthopoulos prize on gravitation (2009) and the American Physical Society's Albert Einstein Prize on gravitation (2010).
I served on the scientific advisory committee of the Perimeter Institute, the board of the Kavli Institute for Theoretical Physics at Santa Barbara, and currently serve on the board of the Center for Gravitational Wave Astronomy in Brownsville, Texas.
I have also received the prestigious Alfred P. Sloan, John Simon Guggenheim and Fulbright fellowships in 1995, 1998 and 2001 respectively. My research has been supported by the National Science Foundation starting with a CAREER grant in 1995 and continuing till today and by NATO, NASA and the Foundational Questions Institute (FQXi).
I was named Fellow of the Institute of Physics and Chartered Physicist by the Council of the Institute of Physics (UK) in 1999.
I have received the Edward Bouchet award of the American Physical Society .
I am a fellow of the American Physical Society and of the American Association for the Advancement of Science.
I was recently elected a corresponding member of the Latin American Academy of Sciences, a corresponding member of the Mexican Academy of Sciences and of the National Academy of Sciences of Argentina.