Showing papers by "Jerzy Lewandowski published in 2021"
TL;DR: In this article, the authors generalize a notion of "conserved charges" given by Wald and Zoupas to the asymptotically de Sitter spacetimes, and show that obtained expressions have a correct limit as Λ → 0.
Abstract: We generalize a notion of ‘conserved’ charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as Λ → 0. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at ℐ+.
12 citations
TL;DR: In this paper, the authors generalize a notion of "conserved charges" given by Wald and Zoupas to the asymptotically de Sitter spacetimes.
Abstract: We generalize a notion of 'conserved' charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as $\Lambda \to 0$. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at $\mathcal{I}^+$.
10 citations
TL;DR: In this article, all axisymmetric solutions to the near-horizon geometry equation with a cosmological constant defined on a topological 2-sphere were derived and the regularity conditions preventing cone singularity at the poles were accounted for.
Abstract: All axisymmetric solutions to the near-horizon geometry equation with a cosmological constant defined on a topological 2-sphere were derived. The regularity conditions preventing cone singularity at the poles were accounted for. The one-to-one correspondence of the solutions with the extremal horizons in the Kerr--(anti--)de Sitter spacetimes was found. A solution corresponding to the triply degenerate horizon was identified and characterized. The solutions were also identified among the solutions to the Petrov type D equation.
4 citations
Posted Content•
TL;DR: In this article, the authors analyzed the spectral properties of the spacetime of a collapsing homogeneous dust ball and showed that the backreaction effects speed up the occurrence of the bounce in comparison to the case where only a dust fluid is present.
Abstract: Quantum fields propagating on quantum spacetime of a collapsing homogeneous dust ball explore a (semiclassical) dressed geometry. When the backreaction of the field is discarded, the classical singularity is resolved due to quantum gravity effects and is replaced by a quantum bounce on the dressed collapse background. In the presence of the backreaction, the emergent (interior) dressed geometry becomes mode-dependent which scales as radiation. Semiclassical dynamics of this so-called {\em rainbow}, dressed background is analyzed. It turns out that the backreaction effects speeds up the occurrence of the bounce in comparison to the case where only a dust fluid is present. By matching the interior and exterior regions at the boundary of dust, a mode-dependent black hole geometry emerges as the exterior spacetime. Properties of such rainbow black hole are discussed. That mode dependence causes, in particular, a chromatic aberration in gravitational lensing process of which maximal magnitude is estimated via calculation of the so-called Einstein angle.
3 citations
Posted Content•
TL;DR: In this paper, the authors introduced multipole moments to characterize the geometry of non-expanding horizons (NEHs) and showed that the symmetry group of NEHs is a 1-dimensional extension of the BMS group.
Abstract: It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non-expanding horizons (NEHs). In the first part of the paper we introduce multipole moments to characterize their geometry, removing the restriction to axisymmetric situations made in the existing literature. We then show that the symmetry group $\mathfrak{G}$ of NEHs is a 1-dimensional extension of the BMS group $\mathfrak{B}$. These symmetries are used in a companion paper to define charges and fluxes on NHEs, as well as perturbed NEHs. They have physically attractive properties. Finally, it is generally not appreciated that $\mathcal{I}^\pm$ of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that $\mathcal{I}^\pm$ have a small additional structure that reduces $\mathfrak{G}$ to the BMS group $\mathfrak{B}$, and the BMS charges and fluxes can be recovered from the NEH framework; and, (ii) develop gravitational wave tomography for the late stage of compact binary coalescences: reading-off the dynamics of perturbed NEHs in the strong field regime (via evolution of their multipoles), from the waveform at $\mathcal{I}^+$.
Posted Content•
TL;DR: In this paper, a new operator representing the three-dimensional Ricci scalar curvature in loop quantum gravity is introduced, which is defined on the Hilbert space of a fixed cubical graph.
Abstract: In this article we introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. Our construction does not apply to the entire kinematical Hilbert space of loop quantum gravity; instead, the operator is defined on the Hilbert space of a fixed cubical graph. The starting point of our work is to write the spatial Ricci scalar classically as a function of the densitized triad. We pass from the classical expression to a quantum operator through a regularization procedure, in which spatial derivatives of the triad are discretized as finite differences on the cubical lattice provided by the graph. While more work is needed in order to extend our construction to encompass states based on all possible graphs, the operator presented here can be applied in models such as quantum-reduced loop gravity and effective dynamics, which are derived from the kinematical framework of full loop quantum gravity, and are formulated in terms of states defined on cubical graphs.
TL;DR: In this article, a nonsingular extension of the Kerr-NUT-de Sitter solution to Einstein's equations is proposed, which relies on an observation that in 2-dimensional algebra of Killing vector fields there exist two distinguished vector fields that may be used to define $U(1)$-principal bundle structure over the nonsinular spaces of non-null orbits.
Abstract: Due to the conical singularity along the symmetry axis Taub-NUT spacetimes suffer from a long and problematic history of physical interpretation. In 1969 Misner proposed a nonsingular interpretation taking advantage of the spacetime's topology and its underlying group-theoretic structure. We extend and refine his method to include a broader family of solutions and completely solve the outstanding issue of a nonsingular extension of the Kerr-NUT--(anti--)de Sitter solutions to Einstein's equations. Our approach relies on an observation that in 2 dimensional algebra of Killing vector fields there exist two distinguished vector fields that may be used to define $U(1)$-principal bundle structure over the nonsingular spaces of non-null orbits. For all admissible parameters we derive appropriate Killing vector fields and discuss limits to spacetimes with less parameters. The global structure of spacetime, together with nonsingular conformal geometry of the infinities is presented and (possibly also projectively nonsingular) Killing horizons is presented.