Showing papers by "Jerzy Lewandowski published in 2014"
TL;DR: In this article, the authors introduce a new operator in Loop Quantum Gravity (LQG) related to the 3D scalar curvature, which is based on Regge Calculus.
Abstract: We introduce a new operator in Loop Quantum Gravity - the 3D curvature operator - related to the 3-dimensional scalar curvature. The construction is based on Regge Calculus. We define it starting from the classical expression of the Regge curvature, then we derive its properties and discuss some explicit checks of the semi-classical limit.
39 citations
TL;DR: In this article, a new scheme of defining invariant observables for general relativistic systems is presented, which is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation.
Abstract: We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The observables are invariant with respect to spatial diffeomorphisms which preserve the observer. The limited residual spatial gauge freedom is studied and fully understood. A full canonical analysis of the observables is presented: we analyze their variations, Poisson algebra and discuss their dynamics. Lastly, the observables are used to solve the vector constraint, which triggers a possible considerable reduction of the degrees of freedom of general relativistic theories.
25 citations
TL;DR: In this article, a distinguished (invariant) Bondi-like coordinate system is defined in the spacetime neighbourhood of a non-expanding horizon of arbitrary dimension via geometry invariants of the horizon.
Abstract: A distinguished (invariant) Bondi-like coordinate system is defined in the spacetime neighbourhood of a non-expanding horizon of arbitrary dimension via geometry invariants of the horizon. With its use, the radial expansion of a spacetime metric about the horizon is provided and the free data needed to specify it up to given order are determined in spacetime dimension $4$. For the case of an electro-vacuum horizon in $4$-dimensional spacetime the necessary and sufficient conditions for the existence of a Killing field at its neighbourhood are identified as differential conditions on the horizon data and data on null surface transversal to the horizon.
8 citations
TL;DR: In this article, a distinguished (invariant) Bondi-like coordinate system is defined in the spacetime neighborhood of a non-expanding horizon of arbitrary dimension via geometry invariants of the horizon.
Abstract: A distinguished (invariant) Bondi-like coordinate system is defined in the spacetime neighborhood of a non-expanding horizon of arbitrary dimension via geometry invariants of the horizon. With its use, the radial expansion of a spacetime metric about the horizon is provided and the free data needed to specify it up to a given order are determined in spacetime dimension 4. For the case of an electro-vacuum horizon in four-dimensional spacetime, the necessary and sufficient conditions for the existence of a Killing field at its neighborhood are identified as differential conditions for the horizon data and data for the null surface transversal to the horizon.
6 citations
TL;DR: In this article, a new scheme of defining invariant observables for general relativistic systems is presented, which is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation.
Abstract: We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The observables are invariant with respect to spatial diffeomorphisms which preserve the observer. The limited residual spatial gauge freedom is studied and fully understood. A full canonical analysis of the observables is presented: we analyze their variations, Poisson algebra and discuss their dynamics. Lastly, the observables are used to solve the vector constraint, which triggers a possible considerable reduction of the degrees of freedom of general relativistic theories.
1 citations