2003/06/25 by Abhay Ashtekar, Ashtekar, Abhay
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0306115
Text of a plenary talk given at the conference on "Mathematical Physics, General Relativity and Cosmology", held in honor of Professor Jerzy Plebanski in Mexico city, in September of 2002. To appear in the Proceedings. Results reported here were obtained jointly with Badri Krishnan and summarized very briefly in gr-qc/0207080 . Details of proofs and extensions of these results will appear elsewhere
A summary of how black holes grow in full, non-linear general relativity is presented. Specifically, a notion of "dynamical horizons" is introduced and expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local and the energy flux is positive. Change in the horizon area is related to these fluxes. The flux formulae also give rise to balance laws analogous to the ones obtained by Bondi and Sachs at null infinity and provide generalizations of the first and second laws of black hole mechanics.