On this page are detailed some of Dr. Ashtekar's current research interests:

Quantum Gravity: Quantum geometry and its ramifications. Black hole entropy. Background independent approach and its relation to low energy physics. Potential experimental tests.
See, e.g., http://xxx.lanl.gov/abs/gr-qc/0112038

General Relativity: Mathematical theory of Black holes. Isolated horizons and their applications. Interface of analytical and numerical relativity. Asymptotics. Gravitational radiation theory.
See, e.g., http://xxx.lanl.gov/abs/gr-qc/0006006