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Asymptotically Anti-de Sitter Space-times: Conserved Quantities
Abhay Ashtekar, Saurya Das
Asymptotically anti-de Sitter space-times are considered in a general dimension . As one might expect, the boundary conditions at infinity ensure that the asymptotic symmet…
Interface of General Relativity, Quantum Physics and Statistical Mechanics: Some Recent Developments
Abhay Ashtekar
The arena normally used in black holes thermodynamics was recently generalized to incorporate a broad class of physically interesting situations. The key idea is to replace the not…
Laws Governing Isolated Horizons: Inclusion of Dilaton Couplings
Abhay Ashtekar, Alejandro Corichi
Mechanics of non-rotating black holes was recently generalized by replacing the static event horizons used in standard treatments with `isolated horizons.' This framework is extend…
Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids
M. Alcubierre, S. Brandt, B. Bruegmann +4
We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-sphe…
Mechanics of Isolated Horizons
Abhay Ashtekar, Christopher Beetle, Stephen Fairhurst
A set of boundary conditions defining an undistorted, non-rotating isolated horizon are specified in general relativity. A space-time representing a black hole which is itself in e…
Isolated Horizons: the Classical Phase Space
A. Ashtekar, A. Corichi, K. Krasnov
A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are ``isolated'' near future time-like infinity or for a finite time interva…
Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context
A. Ashtekar, D. Marolf, J. Mourão +1
Osterwalder and Schrader introduced a procedure to obtain a (Lorentzian) Hamiltonian quantum theory starting from a measure on the space of (Euclidean) histories of a scalar quantu…
Quantum Mechanics of Geometry
Abhay Ashtekar
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is pre…