Andrzej Rostworowski

Time-Periodic Solutions in an Einstein AdS–Massless-Scalar-Field System

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.

Pion light cone wave function in the nonlocal NJL model

We use the simple instanton motivated NJL-type model to calculate the leading twist pion light cone wave function. The model consists in employing the momentum dependent quark mass in the quark loop entering the definition of the wave function. The result is analytical up to a solution of a certain algebraic equation. Various properties including the kT dependence of the pion wave function are discussed. The resulting kT integrated wave function is not asymptotic and is in agreement with recent analysis of the CLEO data.

AdS collapse of a scalar field in higher dimensions

We show that the weakly turbulent instability of anti-de Sitter space, recently found in P. Bizon and A. Rostworowski, Phys. Rev. Lett. 107, 031102 (2011) for 3+1-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant, is present in all dimensions d+1 for d{>=}3.

Resonant Dynamics and the Instability of Anti-de Sitter Spacetime

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.

What drives AdS spacetime unstable

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.

TURBULENT INSTABILITY OF ANTI-DE SITTER SPACE–TIME

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.

Asymptotic stability of the Skyrmion

We study the asymptotic behavior of spherically symmetric solutions in the Skyrme model. We show that the relaxation to the degree-one soliton (called the Skyrmion) has a universal form of a superposition of two effects: exponentially damped oscillations (the quasinormal ringing) and a power-law decay (the tail). The quasinormal ringing, which dominates the dynamics for intermediate times, is a linear resonance effect. In contrast, the polynomial tail, which becomes uncovered at late times, is shown to be a nonlinear phenomenon.

Comment on "Holographic Thermalization, Stability of Anti-de Sitter Space, and the Fermi-Pasta-Ulam Paradox".

A recent interesting paper [1] revisits the problem of (in)stability of AdS under spherically symmetric massless scalar field perturbations, first studied in [2]. The authors claim that the set of initial data which do not trigger instability is larger than originally envisioned in [2], in particular it comprises small amplitude two-mode initial data with energy equally distributed among the modes. To support this claim, the long time numerical evolution of these data was shown to be stable against black hole formation. The aim of this comment is to demonstrate that this numerical result is incorrect. Hereafter, we use the notation and references to equations of [1]. Using our code (see [3] for the detailed description), we solved the system of equations (2-4) for the two-mode initial data (20) with κ = 3/5 and ε = 0.09 used in Fig. 3 in [1]. The comparison of our result with the one of [1] is shown in Fig. 1 which depicts the upper envelope of the quantity Π(t, 0) (related linearly to the Ricci scalar at the origin).

Late-time tails of a Yang-Mills field on Minkowski and Schwarzschild backgrounds

We study the late-time behavior of spherically symmetric solutions of the Yang-Mills equations on Minkowski and Schwarzschild backgrounds. Using nonlinear perturbation theory we show in both cases that solutions having smooth compactly supported initial data posses tails which decay as

Saddle-point dynamics of a Yang–Mills field on the exterior Schwarzschild spacetime

t^{-4}