50 citations · 587 across the 63 of their papers we have counts for
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Some remarks on the horizon in the dust cloud collapse
Koushiki, W. Piechocki, G. Plewa
We examine the existence of an apparent horizon in the collapse of an isolated dust cloud using expansion functions. Our results indicate that in the region of spacetime far away f…
Semiclassical causal geodesics: Minkowski spacetime case
Adam Cieślik, Andrzej Góźdź, Patryk Mach +2
We use an integral quantization model based on the Heisenberg-Weyl group to describe the motion of a spinless particle in the Minkowski background spacetime. This work is a sequel…
Integral quantization based on the Heisenberg-Weyl group
Aleksandra Pȩdrak, Andrzej Góźdź, Włodzimierz Piechocki +2
We develop a relativistic framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based o…
Quantum system ascribed to the Oppenheimer-Snyder model of massive star
A. Góźdź, J. J. Ostrowski, A. Pȩdrak +1
We quantize the Oppenheimer-Snyder model of black hole using the integral quantization method. We treat spatial and temporal coordinates on the same footing both at classical and q…
Quantum dynamics of gravitational massive shell
Andrzej Góźdź, Marcin Kisielowski, Włodzimierz Piechocki
The quantum dynamics of a self-gravitating thin matter shell in vacuum has been considered. Quantum Hamiltonian of the system is positive definite. Within chosen set of parameters,…
Quantum dynamics corresponding to chaotic BKL scenario
Andrzej Góźdź, Aleksandra Pȩdrak, Włodzimierz Piechocki
We quantize the solution to the Belinski-Khalatnikov-Lifshitz (BKL) scenario using the integral quantization method. Quantization smears the gravitational singularity avoiding its…
Ascribing quantum system to Schwarzschild spacetime with naked singularity
Andrzej Góźdź, Aleksandra Pȩdrak, Włodzimierz Piechocki
We quantize the Schwarzschild spacetime with naked singularity using the affine coherent states quantization method. The novelty of our approach is quantization of both temporal an…
Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario
Piotr Goldstein, Włodzimierz Piechocki
A class of exact solutions to the Belinski-Khalatnikov-Lifshitz (BKL) scenario is derived and tested for their stability against small perturbations. These are the only regular sol…
Generic singularity of general relativity and its quantum fate
Włodzimierz Piechocki
The Belinski-Khalatnikov-Lifshitz scenario concerns the existence of generic singularity of general relativity. At the singularity, there is a breakdown of all known laws of physic…
Quantum Oppenheimer-Snyder model
Włodzimierz Piechocki, Tim Schmitz
We construct two reduced quantum theories for the Oppenheimer-Snyder model, respectively taking the point of view of the comoving and the exterior stationary observer, using affine…
Hunting for gravitational quantum spikes
Andrzej Góźdź, Włodzimierz Piechocki, Grzegorz Plewa +1
We present the result of our examination of quantum structures called quantum spikes. The classical spikes, that are known in gravitational systems, occur in the evolution of the i…
Hamiltonian formulation of dust cloud collapse
Nick Kwidzinski, Daniele Malafarina, Jan Ostrowski +2
We consider the gravitational collapse of self-gravitating spherical dust cloud in the Hamiltonian formalism. We address both homogeneous and inhomogeneous cases. Our novel derivat…
Robustness of the quantum BKL scenario
Andrzej Góźdź, Włodzimierz Piechocki
Quantum Belinski-Khalatnikov-Lifshitz scenario presents an unitary evolution of the system. However, the affine coherent states quantization applied to the quantization of the unde…
Curvature invariants for the Bianchi IX spacetime filled with tilted dust
Nick Kwidzinski, Włodzimierz Piechocki
We present an analysis of the Kretschmann and Weyl squared scalars for the general Bianchi IX model filled with tilted dust. Particular attention is given to the asymptotic regime…
Quantum Belinski-Khalatnikov-Lifshitz scenario
Andrzej Góźdź, Włodzimierz Piechocki, Grzegorz Plewa
We present the quantum model of the asymptotic dynamics underlying the Belinski-Khalatnikov-Lifshitz (BKL) scenario. The symmetry of the physical phase space enables making use of…
On the dynamics of the general Bianchi IX spacetime near the singularity
Claus Kiefer, Nick Kwidzinski, Włodzimierz Piechocki
We show that the complex dynamics of the general Bianchi IX universe in the vicinity of the spacelike singularity can be approximated by a simplified system of equations. Our analy…
Dynamical structures specific to strong gravitational field: Quantum formalism
Andrzej Góźdź, Włodzimierz Piechocki, Grzegorz Plewa
The dynamics of the general Bianchi IX spacetime, near the gravitational singularity, underlies the Belinskii, Khalatnikov and Lifshitz scenario. Asymptotically, near the singulari…
Structures arising in the asymptotic dynamics of the Bianchi IX model
Wlodzimierz Piechocki, Grzegorz Plewa
We present the analyses of the asymptotic evolution of the general Bianchi IX spacetime using Hamiltonian formulation. The dynamics reveals the existence of special structures, whi…
Do spikes persist in a quantum treatment of spacetime singularities?
Ewa Czuchry, David Garfinkle, John R. Klauder +1
The classical approach to spacetime singularities leads to a simplified dynamics in which spatial derivatives become unimportant compared to time derivatives, and thus each spatial…
Classical dynamics of the Bianchi IX model with timelike singularity
S. L. Parnovsky, W. Piechocki
We study the dynamics of the vacuum Bianchi IX model with timelike singularity and compare it with the dynamics of the Bianchi IX model with cosmological singularity. We show that…
Smooth Quantum Dynamics of Mixmaster Universe
Hervé Bergeron, Ewa Czuchry, Jean Pierre Gazeau +2
We present a quantum version of the vacuum Bianchi IX model by implementing affine coherent state quantization combined with a Born-Oppenheimer-like adiabatic approximation. The an…
Singularity avoidance in a quantum model of the Mixmaster universe
Hervé Bergeron, Ewa Czuchry, Jean-Pierre Gazeau +2
We present a quantum model of the vacuum Bianchi-IX dynamics. It is based on four main elements. First, we use a compound quantization procedure: an affine coherent state quantizat…
Level spacing distribution for the prototype of the Bianchi IX model
Jakub Mielczarek, Wlodzimierz Piechocki
Our results concern quantum chaos of the vacuum Bianchi IX model. We apply the equilateral triangle potential well approximation to the potential of the Bianchi IX model to solve t…
Comparing the dynamics of diagonal and general Bianchi IX spacetime
Ewa Czuchry, Nick Kwidzinski, Wlodzimierz Piechocki
We make comparison of the dynamics of the diagonal and nondiagonal Bianchi IX models in the evolution towards the cosmological singularity. Apart from the original variables, we us…