Classical general relativity Ashtekar's work in classical general relativity includes studies of the asymptotic structure of spacetime,
gravitational radiation, and
black hole dynamics. With collaborators including Richard Hansen and Anne Magnon, he identified the asymptotic symmetry group at spatial infinity, known as the Spi group, and analyzed associated conserved quantities, especially the subtleties in the notion of angular momentum of space-times with gravitational waves. His research on gravitational waves demonstrated that their physical content is encoded in the curvature of a connection defined on Penrose's conformal boundary of
spacetime. These ideas provided the foundation for later work on infrared effects, gravitational memory and
celestial holography and recent efforts to improve gravitational waveform modeling for
LIGO–Virgo data analysis. Ashtekar and collaborators, including Badri Krishnan introduced quasi-local horizons, including isolated and dynamical horizons, which are now widely used in numerical simulations of black hole formation and mergers, and in investigations of the black hole evaporation due to emission of quantum radiation discovered by
Stephen Hawking. He has also studied asymptotic properties of gravitational fields in spacetimes with nonzero cosmological constant.
Quantum gravity and Ashtekar variables Ashtekar's research on quantum gravity began with work on quantum field theory in curved spacetime, including algebraic and Kähler-geometric methods. In the 1980s, he developed a non-perturbative quantization of the radiative modes of gravity and identified connections between infrared issues and asymptotic symmetries. In 1986, he reformulated general relativity using self-dual connections, now known as
Ashtekar variables. This reformulation simplified Einstein's equations and cast general relativity in a gauge-theoretic form, enabling the development of loop quantum gravity. In 2011, the international conference
Loops 11: Celebrating 25 Years of Loop Quantum Gravity was held in
Madrid to commemorate the 25th anniversary of Ashtekar's landmark paper introducing the variables that helped launch the loop quantum gravity research program.
Loop quantum gravity and cosmology Loop quantum gravity predicts a quantum geometry in which geometric operators corresponding to area and volume have discrete spectra. The theory was further developed by numerous researchers, including Ivan Agullo,
Jerzy Lewandowski,
Carlo Rovelli,
Lee Smolin, and Thomas Thiemann, many of whom are former members of Ashtekar's research group, and by their own students. In loop quantum cosmology, Ashtekar and collaborators showed that quantum geometric effects resolve the classical Big Bang singularity, replacing it with a cosmological bounce. They also showed that these quantum geometric effects can modify the evolution of primordial perturbations and may leave observable imprints in the cosmic microwave background, potentially accounting for certain large-scale anomalies. In black hole physics, loop quantum gravity provides a microscopic account of black hole entropy. It has also been applied to the study of black hole evaporation through frameworks based on quantum geometry and quasi-local or isolated horizons. == Outreach, service, and mentoring ==