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Background independent quantum gravity: A Status report
The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum
Quantum Nature of the Big Bang: Improved dynamics
An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail
Lectures on Non-Perturbative Canonical Gravity
Notes prepared in Collaboration with Ranjeet S Tate It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of
Loop Quantum Cosmology: A Status Report
Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum
Mathematical structure of loop quantum cosmology
Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big
Representation Theory of Analytic Holonomy C* Algebras
Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of
Asymptotically anti-de Sitter space-times
The structure of the gravitational field at infinity of asymptotically anti-de Sitter space-time is analysed in detail using conformal techniques. It is found that the situation differs from that in
Quantum nature of the big bang: An analytical and numerical investigation
Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both
Isolated and Dynamical Horizons and Their Applications
TLDR
A new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner that has introduced a more physical setting for black hole thermodynamics, suggested a phenomenological model for hairy black holes, provided novel techniques to extract physics from numerical simulations, and led to new laws governing the dynamics ofblack holes in exact general relativity.
Quantum geometry of isolated horizons and black hole entropy
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting
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