Showing papers by "Jerzy Lewandowski published in 2019"
TL;DR: In this paper, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex.
Abstract: To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex. The Hamiltonian operator ${\stackrel{^}{H}}_{v}$ is chosen to be graph-preserving, and the matrix elements of ${\stackrel{^}{H}}_{v}$ are explicitly worked out in a suitable basis. The nontrivial Euclidean part ${\stackrel{^}{H}}_{v}^{E}$ of ${\stackrel{^}{H}}_{v}$ is studied in details. It turns out that by choosing a specific symmetrization of ${\stackrel{^}{H}}_{v}^{E}$, the dynamics driven by the Hamiltonian give a picture of bouncing evolution. Our result in the model of full loop quantum gravity gives a significant echo of the well-known quantum bounce in the symmetry-reduced model of loop quantum cosmology, which indicates a closed relation between singularity resolution and quantum geometry.
19 citations
TL;DR: In this paper, a spin-foam model is derived from the canonical model of Loop Quantum Gravity coupled to a massless scalar field, and generalized to the full theory of loop quantum cosmology by Ashtekar, Campiglia and Henderson, later developed by Henderson, Rovelli, Vidotto and Wilson-Ewing.
Abstract: A spin-foam model is derived from the canonical model of Loop Quantum Gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of Loop Quantum Cosmology by Ashtekar, Campiglia and Henderson, later developed by Henderson, Rovelli, Vidotto and Wilson-Ewing.
9 citations
TL;DR: In this article, it was shown that every solution to Einstein's equations with possibly non-zero cosmological constant that is foliated by non-expanding null surfaces transversal to a single nonexpanding surface belongs to family of the near (extremal) horizon geometries.
Abstract: We prove that every solution to Einstein's equations with possibly non-zero cosmological constant that is foliated by non-expanding null surfaces transversal to a single non-expanding null surface belongs to family of the near (extremal) horizon geometries. Our results are local, hold in a neighborhood of the single non-expanding null surface.
6 citations
TL;DR: In this paper, the volume operator of loop quantum cosmology and all its positive powers are shown to be ill-defined on physical states, and it was recently shown that almost every step in the procedure is illdefined and relies heavily upon a (seemingly premature) numerical truncation.
Abstract: It was recently shown that the volume operator of loop quantum cosmology (LQC) and all its positive powers are ill-defined on physical states. In this paper, we investigate how it effects predictions of cosmic microwave background (CMB) power spectra obtained within dressed metric approach for which expectations values of $\hat{a}$ are the key element. We find that almost every step in the procedure is ill-defined and relies heavily upon a (seemingly premature) numerical truncation. Thus, it suggests that more care is needed in making predictions regarding pre-inflationary physics. We propose a new scheme which contains only well-defined quantities. The surprising agreement of the hitherto models with observational data, especially at low angular momenta $l$ is explained.
5 citations
TL;DR: In this article, the authors consider NE-SF null surface geometries embeddable as extremal Killing horizons to the second order in Einstein vacuum spacetimes and derive the constraints implied by the existence of an embedding.
Abstract: We consider nonexpanding shear-free (NE-SF) null surface geometries embeddable as extremal Killing horizons to the second order in Einstein vacuum spacetimes. A NE-SF null surface geometry consists of a degenerate metric tensor and a consistent torsion free covariant derivative. We derive the constraints implied by the existence of an embedding. The first constraint is well known as the near-horizon geometry equation. The second constraint we find is new. The constraints lead to a complete characterization of those NE-SF null geometries that are embeddable in the extremal Kerr spacetime. Our results are also valid for spacetimes with a cosmological constant.
4 citations
TL;DR: In this paper, the Petrov type D equation was studied in the context of isolated horizons (IHs) generated by null curves that form nontrivial $U(1)$ bundles.
Abstract: We consider $3$-dimensional isolated horizons (IHs) generated by null curves that form nontrivial $U(1)$ bundles. We find a natural interplay between the IH geometry and the $U(1)$-bundle geometry. In this context we consider the Petrov type D equation introduced and studied in previous works \cite{DLP1,DLP2,LS,DKLS1}. From the $4$-dimensional spacetime point of view, solutions to that equation define isolated horizons embeddable in vacuum spacetimes (with cosmological constant) as Killing horizons to the second order such that the spacetime Weyl tensor at the horizon is of the Petrov type D. From the point of view of the $U(1)$-bundle structure, the equation couples a $U(1)$-connection, a metric tensor defined on the base manifold and the surface gravity in a very nontrivial way. We focus on the $U(1)$-bundles over $2$-dimensional manifolds diffeomorphic to $2$-sphere. We have derived all the axisymmetric solutions to the Petrov type D equation. For a fixed value of the cosmological constant they set a $3$-dimensional family as one could expect. A surprising result is, that generically our horizons are not embeddable in the known exact solutions to Einstein's equations. It means that among the exact type D spacetimes there exists a new family of spacetimes that generalize the properties of the Kerr- (anti) de Sitter black holes on one hand and the Taub-NUT spacetimes on the other hand.
3 citations