45 citations · 517 across the 42 of their papers we have counts for
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Quasi-local mass on rigid or round spheres in Kerr spacetime
Jacek Jezierski, Tomasz Smołka
We introduce and analyze quasi-local mass using Hamiltonian methods. It is based on multipole decomposition for surfaces that are topological spheres. Based on the above model, tes…
Hopfion-like solutions in de Sitter spacetime
Adam Grzela, Jacek Jezierski, Tomasz Smołka
We construct electromagnetic field with non-trivial topological properties on de Sitter background. The field is closely related with Hopf fibration. We analyze energy, angular mom…
Gauge-invariant quadratic approximation of quasi-local mass and its relation with Hamiltonian for gravitational field
Jacek Jezierski, Jerzy Kijowski, Piotr Waluk
Gauge invariant, Hamiltonian formulation of field dynamics within a compact region with boundary is given for the gravitational field linearized over a Kottler met…
Quasi-local instantaneous charges asymptotics at spatial infinity
Jacek Jezierski, Tomasz Smołka
The article aims to analyze a construction of charges (conserved quantities) for the gravity field in the (3+1) decomposition. The construction is based on (3+1) splitting of confo…
Localizing Energy in Fierz-Lanczos theory
Jacek Jezierski, Jerzy Kijowski, Marian Wiatr
We calculate energy carried by the massless spin-2 field using Fierz-Lanczos representation of the theory. For this purpose Hamiltonian formulation of the field dynamic is thorough…
Charges of the gravitational field and (3+1) decomposition of CYK tensors part 2
Jacek Jezierski, Szymon Migacz
The work describes the method of construction of charges (conserved quantities) for the gravity field in the (3 + 1) decomposition. The presented construction uses tensors of the e…
Gauge invariant description of weak gravitational field on a spherically symmetric background with cosmological constant
Jacek Jezierski, Piotr Waluk
We present a formalism for analysis of linear Cauchy data on a Kottler metric. Our method removes redundancy due to gauge transformations and constraints. A set of four gauge-invar…
Simple description of generalized electromagnetic and gravitational hopfions
Tomasz Smołka, Jacek Jezierski
The generalization of electromagnetic and gravitational hopfions is performed in terms of a complex scalar field. New definition of topological charge for linearized gravity is giv…
Conformal Yano-Killing tensors for space-times with cosmological constant
Paweł Czajka, Jacek Jezierski
We present a new method for constructing conformal Yano-Killing tensors in five-di\-men\-sio\-nal Anti-de Sitter space-time. The found tensors are represented in two different coor…
Proof of Positive Energy Theorem by spacetime foliations
Jacek Jezierski, Piotr Waluk
Here we present an alternative approach, requiring only basic tools of differential geometry. This method was conceived by Kijowski and first presented during the IV Marcel Grossma…
On the existence of rigid spheres in four-dimensional spacetime manifolds
Hans-Peter Gittel, Jacek Jezierski, Jerzy Kijowski
This paper deals with the generalization of usual round spheres in the flat Minkowski spacetime to the case of a generic four-dimensional spacetime manifold . We consider geomet…
Hamiltonian dynamics in the space of asymptotically Kerr-de Sitter spacetimes
Piotr T. Chruściel, Jacek Jezierski, Jerzy Kijowski
We determine all spacetime flows which lead to a Hamiltonian dynamics in the space of general relativistic initial data sets with asymptotically Kerr-de Sitter ends. The correspond…
A geometric description of Maxwell field in a Kerr spacetime
Jacek Jezierski, Tomasz Smołka
We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein-Gordon equation called Fackerell-Ipser…
The 3+1 decomposition of Conformal Yano-Killing tensors and "momentary" charges for spin-2 field
Jacek Jezierski, Szymon Migacz
The "fully charged" spin-2 field solution is presented. This is an analog of the Coulomb solution in electrodynamics and represents the "non-waving" part of the spin-2 field theory…
The Hamiltonian mass of asymptotically Schwarzschild-de Sitter space-times
Piotr T. Chrusciel, Jacek Jezierski, Jerzy Kijowski
We derive the Hamiltonian mass for general relativistic initial data sets with asymptotically Schwarzschild-de Sitter ends.
Rigid spheres in Riemannian spaces
Hans-Peter Gittel, Jacek Jezierski, Jerzy Kijowski +1
Choice of an appropriate (3+1)-foliation of spacetime or a (2+1)-foliation of the Cauchy space, leads often to a substantial simplification of various mathematical problems in Gene…
Towards uniqueness of degenerate axially symmetric Killing horizon
Jacek Jezierski, Bartek Kamiński
We examine the linearized equations around extremal Kerr horizon and give some arguments towards stability of the horizon with respect to generic (non-symmetric) linear perturbatio…
On free general relativistic initial data on the light cone
Piotr T. Chruściel, Jacek Jezierski
We provide a simple explicit parameterization of free general relativistic data on the light cone.
The minimum length problem of loop quantum cosmology
Piotr Dzierzak, Jacek Jezierski, Przemyslaw Malkiewicz +1
The appearance of the big bounce (BB) in the evolution of the universe is analyzed in the setting of loop quantum cosmology (LQC). Making use of an idea of a minimum length turns c…
On the existence of Kundt's metrics with compact sections of null hypersurfaces
Jacek Jezierski
It is shown that Kundt's metric for vacuum cannot be constructed when two-dimensional space-like sections of null hypersurfaces are compact, connected manifolds with no boundary un…
Energy-minimizing two black holes initial data
Jacek Jezierski, Jerzy Kijowski, Szymon Leski
An attempt to construct the ``ground state'' vacuum initial data for the gravitational field surrounding two black holes is presented. The ground state is defined as the gravitatio…
Asymptotic conformal Yano-Killing tensors for asymptotic anti-de Sitter spacetimes and conserved quantities
Jacek Jezierski
Conformal rescaling of conformal Yano--Killing tensors and relations between Yano and CYK tensors are discussed. Pullback of these objects to a submanifold is used to construct all…
Conformal Yano-Killing tensors for the Taub-NUT metric
Jacek Jezierski, Maciej Łukasik
Symmetric conformal Killing tensors and (skew-symmetric) conformal Yano-Killing tensors for Euclidean Taub-NUT metric are given in explicit form. Relations between Yano and CYK ten…
Conformal Yano-Killing tensor for the Kerr metric and conserved quantities
Jacek Jezierski, Maciej Łukasik
Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed. Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime are obtained from the Yan…