Maciej Maliborski
Max Planck Society
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Featured researches published by Maciej Maliborski.
Physical Review Letters | 2013
Maciej Maliborski; Andrzej Rostworowski
We construct time-periodic solutions for a system of a self-gravitating massless scalar field, with a negative cosmological constant, in d+1 spacetime dimensions at spherical symmetry, both perturbatively and numerically. We estimate the convergence radius of the formally obtained perturbative series and argue that it is greater then zero. Moreover, this estimate coincides with the boundary of the convergence domain of our numerical method and the threshold for the black-hole formation. Then we confirm our results with a direct numerical evolution. This also gives strong evidence for the nonlinear stability of the constructed time-periodic solutions.
Physical Review Letters | 2015
Piotr Bizoń; Maciej Maliborski; Andrzej Rostworowski
We consider spherically symmetric Einstein-massless-scalar field equations with a negative cosmological constant in five dimensions and analyze the evolution of small perturbations of anti-de Sitter (AdS) spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing the instability of AdS under arbitrarily small perturbations.
Physical Review Letters | 2012
Maciej Maliborski
We consider a spherically symmetric self-gravitating massless scalar field enclosed inside a timelike worldtube R×S(3) with a perfectly reflecting wall. Numerical evidence is given that arbitrarily small generic initial data evolve into a black hole.
Physical Review D | 2014
Maciej Maliborski; Andrzej Rostworowski
We calculate the spectrum of linear perturbations of standing wave solutions discussed in [Phys. Rev. D 87, 123006 (2013)], as the first step to investigate the stability of globally regular, asymptotically AdS, time-periodic solutions discovered in [Phys. Rev. Lett. 111 051102 (2013)]. We show that while this spectrum is only asymptotically nondispersive (as contrasted with the pure AdS case), putting a small standing wave solution on the top of AdS solution indeed prevents the turbulent instability. Thus we support the idea advocated in previous works that nondispersive character of the spectrum of linear perturbations of AdS space is crucial for the conjectured turbulent instability.
International Journal of Modern Physics A | 2013
Maciej Maliborski; Andrzej Rostworowski
In these lecture notes, we discuss recently conjectured instability of anti-de Sitter space, resulting in gravitational collapse of a large class of arbitrarily small initial perturbations. We uncover the technical details used in the numerical study of spherically symmetric Einstein-massless scalar field system with negative cosmological constant that led to the conjectured instability.
Nonlinearity | 2012
Piotr Bizoń; Tadeusz Chmaj; Maciej Maliborski
We consider the exterior Cauchy–Dirichlet problem for equivariant wave maps from 3 + 1 dimensional Minkowski spacetime into the three sphere. Using mixed analytical and numerical methods we show that, for a given topological degree of the map, all solutions starting from smooth finite energy initial data converge to the unique static solution (harmonic map). The asymptotics of this relaxation process is described in detail. We hope that our model will provide an attractive mathematical setting for gaining insight into dissipation-by-dispersion phenomena, in particular the soliton resolution conjecture.
Communications in Mathematical Physics | 2017
Piotr Bizoń; Ben Craps; Oleg Evnin; Dominika Hunik; Vincent Luyten; Maciej Maliborski
We consider the conformally invariant cubic wave equation on the Einstein cylinder
Nonlinearity | 2017
Paweł Biernat; Piotr Bizoń; Maciej Maliborski
arXiv: General Relativity and Quantum Cosmology | 2013
Maciej Maliborski; Andrzej Rostworowski
{\mathbb{R} \times \mathbb{S}^3}
arXiv: General Relativity and Quantum Cosmology | 2016
Maciej Maliborski