Spherically symmetric quantum geometry: Hamiltonian constraint

By M. Bojowald, Rafal Swiderski. 2005

152 citations recorded by the source corpus.

Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric models. This then presents a further consistency check of the whole scheme in inhomogeneous situations, lending further credence to the physical results obtained so far mainly in homogeneous models. New applications in particular of the spherically symmetric model in the context of black hole physics are discussed.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/534f3aa75b5d3a3ca045a45e60cdf0bb20cd8fd7

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In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Introduction to Loop Quantum Cosmology (2011, background): “This problem was circumvented in [68], where the Hamiltonian constraint operator was constructed in terms of non-standard variables which mix the connection and the extrinsic curvature.”
Quantum nature of the big bang: An analytical and numerical investigation (2006, background): “Incorporation of spherical inhomogeneities seems to be within reach since significant amount of technical groundwork has already been laid [80].”
Loop quantum black hole (2005, unknown): “The form of the Gauss constraint and of the Euclidean part of the Hamiltonian constraint is [13] G ∝ A1E(2) −A2E(1), HE = 2 sin θ sgn[det(E[1])] √|Er |[(E1)2 + (E2)2] [2ArE(A1E(1) + A2E(2)) + ((A1)(2) + (A2)(2) − 1)((E(1))(2) + (E(2))(2))],”