Related papers: Isolated and dynamical horizons from a common pers…
We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we…
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 from the gravitational singularity, the considered system has…
From the microscopic point of view, realistic black holes are time-dependent and the teleological concept of event horizon fails. At present, the apparent or the trapping horizon seem its best replacements in various areas of black hole…
This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof…
This article translates some recent results on quasilocal horizons into the language of $(3+1)$ general relativity so as to make them more useful to numerical relativists. In particular quantities are described which characterize how…
Dynamical, non-asymptotically flat black holes are best characterized by their apparent horizons. Cosmological black hole solutions of General Relativity exhibit two types of apparent horizon behaviours which, thus far, appeared to be…
Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied…
We present numerical simulations of a Kerr black hole perturbed by a pulse of ingoing gravitational radiation. For strong perturbations we find up to five concentric marginally outer trapped surfaces. These trapped surfaces appear and…
We discuss how the surface gravity can be classically defined for dynamical black holes. In particular we focus on defining the surface gravity for locally defined horizons and compare a number definitions proposed in the literature. We…
For distant observers black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The…
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 perturbation of near horizon geometry.
When Gaussian null coordinates are adapted to a Killing horizon, the near-horizon limit is defined by a coordinate rescaling and then by taking the regulator parameter $\varepsilon$ to be small, as a way of zooming into the horizon…
This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further…
Extremal horizons satisfy an equation induced by the Einstein vacuum equations that determines the shape of the horizon and the manner in which it rotates (the EEH equation). Until recently, however, the classification of solutions required…
We propose a receding horizon control strategy that readily handles systems that exhibit interval-wise total energy constraints on the input control sequence. The approach is based on a variable optimization horizon length and contractive…
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…
The qualitative and quantitative understanding of near-horizon gravitational dynamics in the strong-field regime represents a challenge both at a fundamental level and in astrophysical applications. Recent advances in numerical relativity…
The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…