Related papers: On Critical Exponents for Self-Similar Collapse
This paper is devoted to the study of degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type. By means of blow-up analysis techniques, we prove an a-priori estimate in a weighted space of continuous functions. From this…
We derive new constraints on the dilaton parameter appearing in the spherically-symmetric black hole solution of Einstein-Maxwell-dilaton-axion gravity, by studying the geodesic motion of the S2 star in the Galactic Center.…
We study the nonspherical linear perturbations of the discretely self-similar and spherically symmetric solution for a self-gravitating scalar field discovered by Choptuik in the context of marginal gravitational collapse. We find that all…
In this paper, we introduce a numerical method based on Artificial Neural Networks (ANNs) for the analysis of black hole solutions to the Einstein-axion-dilaton system in a high dimensional parabolic class. Leveraging a profile root-finding…
We study both analytically and numerically the nonlinear stage of the instability of one-dimensional solitons in a small vicinity of the transition point from supercritical to subcritical bifurcations in the framework of the generalized…
We studied the influence of dilaton field on the dynamical collapse of a charged scalar one. Different values of the initial amplitude of dilaton field as well as the altered values of the dilatonic coupling constant were considered. We…
We establish the regularity in 2 dimensions of $L^2$ solutions to critical elliptic systems in divergence form involving involution operators of finite $W^{1,2}$-energy.
We explore the nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates. Using a functional renormalization group approach formulated in the Keldysh framework, we characterize the…
We solve the coupled Einstein-Vlasov system in spherical symmetry using direct numerical integration of the Vlasov equation in phase space. Focusing on the case of massless particles we study critical phenomena in the model, finding strong…
We investigate the stability of self-similar solutions for a gravitationally collapsing isothermal sphere in Newtonian gravity by means of a normal mode analysis. It is found that the Hunter series of solutions are highly unstable, while…
We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS). CSS is $L^{2}$-critical, admits solitons, and has the pseudoconformal symmetry. In this work, we consider pseudoconformal blow-up solutions under $m$-equivariance,…
We study the spherical collapse of a perfect fluid with an equation of state $P=k\rho$ by full general relativistic numerical simulations. For $0<k\alt 0.036$, it has been known that there exists a general relativistic counterpart of the…
The paper discusses a collapse of a self-interacting electrically charged scalar field in the decoupling limit of the dilatonic Gauss-Bonnet gravity. The emerging spacetimes were either non-singular or singular and containing black holes of…
Two important classes of spatio-temporal patterns, namely, spatio-temporal chaos and self-replicating patterns, for a representative three variable autocatalytic reaction mechanism coupled with diffusion has been studied. The…
The gravitational evolution of scale free initial spectra $P(k)\propto k^n$ in an Einstein-de Sitter universe is widely believed to be self-similar for $-3<n<4$. However, for $-3<n<-1$ the existence of self-similar scaling has not been…
We examine four dimensional, near-extremal black hole solutions in the presence of a finite boundary obeying conformal boundary conditions, where the conformal class of the induced metric and the trace of the extrinsic curvature are fixed.…
We report a new critical solution found at the threshold of axisymmetric gravitational collapse of a complex scalar field with angular momentum. To carry angular momentum the scalar field cannot be axisymmetric; however, its azimuthal…
Einstein-Gauss-Bonnet gravity (EGB) provides a natural higher dimensional and higher order curvature generalization of Einstein gravity. It contains a new, presumably microscopic, length scale that should affect short distance properties of…
The dynamical evolution of self-interacting scalars is of paramount importance in cosmological settings, and can teach us about the content of Einstein's equations. In flat space, nonlinear scalar field theories can give rise to localized,…
We study the critical collapse of a massive complex scalar field coupled minimally to gravity. Taking as initial data a simple gaussian pulse with a shape similar to the harmonic ansatz for boson stars, we obtain critical collapse of type…