Showing papers by "Jerzy Lewandowski published in 2002"
TL;DR: In this article, the properties of weakly-isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g. at null infinity.
Abstract: Geometrical structures intrinsic to non-expanding, weakly-isolated and isolated horizons are analysed and compared with structures which arise in other contexts within general relativity, e.g. at null infinity. In particular, we address in detail the issue of singling out the preferred normals to these horizons required in various applications. This study provides powerful tools to extract invariant, physical information from numerical simulations of the near-horizon, strong-field geometry. While it complements the previous analysis of laws governing the mechanics of weakly-isolated horizons, prior knowledge of those results is not assumed.
228 citations
TL;DR: In this article, the axi-symmetric, vacuum and electrovac extremal isolated horizons were derived and it was shown that the induced metric tensor, the rotation 1-form potential and the pullback of the electromagnetic field necessarily coincide with those induced by the monopolar extremal Kerr-Newman solution on the event horizon.
Abstract: We derive all the axi-symmetric, vacuum and electrovac extremal isolated horizons. It turns out that for every horizon in this class, the induced metric tensor, the rotation 1-form potential and the pullback of the electromagnetic field necessarily coincide with those induced by the monopolar, extremal Kerr-Newman solution on the event horizon. We also discuss the general case of a symmetric, extremal isolated horizon. In particular, we analyze the case of a two-dimensional symmetry group generated by two null vector fields. Its relevance to the classification of all the symmetric isolated horizons, including the non-extremal once, is explained.
67 citations
TL;DR: In this paper, conditions on the geometry of a nonexpanding horizon Δ which are sufficient for the spacetime metric to coincide on Δ with the Kerr metric were formulated. But these conditions are not applicable to the non-separable horizon.
Abstract: We formulate conditions on the geometry of a nonexpanding horizon Δ which are sufficient for the spacetime metric to coincide on Δ with the Kerr metric. We introduce an invariant which can be used as a measure of how different the geometry of a given nonexpanding horizon is from the geometry of the Kerr horizon. Directly, our results concern the spacetime metric at Δ at the zeroth and the first orders. Combined with the results of Ashtekar, Beetle and Lewandowski, our conditions can be used to compare the spacetime geometry at the nonexpanding horizon with that of Kerr to every order. The results should be useful to numerical relativity in analyzing the sense in which the final black hole horizon produced by a collapse or a merger approaches the Kerr horizon.
39 citations
TL;DR: In this article, the problem of the treatment of scalar fields is addressed at the kinematic level by constructing the appropriate background independent operator algebras and Hilbert spaces.
Abstract: In loop quantum gravity, matter fields can have support only on the `polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilbert spaces. Second, to make contact with low energy physics, one has to relate this `polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.
13 citations
01 Dec 2002
TL;DR: In this paper, a new quantum representation for the Lorentzian gravity is created from the Pullin vaccum by the operators assigned to 2-complexes, using the original spinorial Ashtekar variables, the reality conditions are well posed and Thiemann's Hamiltonian is well defined.
Abstract: This is a contribution to the MG9 session QG1-a. A new quantum representation for the Lorentzian gravity is created from the Pullin vaccum by the operators assigned to 2-complexes. The representation uses the original, spinorial Ashtekar variables, the reality conditions are well posed and Thiemann’s Hamiltonian is well defined. The results on the existence of a suitable Hilbert product are partial. They were derived in collaboration with Abhay Ashtekar. The canonical gravity in terms of the Ashtekar variables is often compared to the complex representation of the harmonic oscillator. Indeed, given a 3dimensional space of the Cauchy data the Ashtekar connection [1] is + iK where, in the language of the standard ADM variables, is the Riemann connection of a 3-metric tensor defined on M, and K represents the extrinsic curvature. The variable canonically conjugate to A is an sl(2,C) � valued 2-form E. Its relation with the 3-metric can be given by the 2-area of the parallelogram formed by X, Y ∈ T(M): Area 2 (E)(XY ) = − 1 Tr(EXY EXY ). The Poisson bracket is {A i (x), Ejbc(y)} = iǫabcδ i
2 citations