Related papers: The Attractor Mechanism in Five Dimensions
We show that the attractor mechanism for generic black hole is a consequence of the double-horizon. Investigation of equations of motion shows that in the case of the double-horizon black holes, the dynamics of the geometry, the scalars and…
We generalize the description of the d=4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The…
We review recent developments concerning supersymmetric black holes in string theory. After a general introduction to the laws of black hole mechanics and to black hole entropy in string theory, we discuss black hole solutions in N=2…
The paper deals with topical issues of modern mathematical theory of dynamical chaos and its applications. At present, it is customary to assume that dynamical chaos in finitedimensional smooth systems can exist in three different forms.…
We consider the existence of robust strange nonchaotic attractors (SNA's) in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their…
This paper studies hidden oscillations appearing in electromechanical systems with and without equilibria. Three different systems with such effects are considered: translational oscillator-rotational actuator, drilling system actuated by a…
These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…
This survey is dedicated to the 100th anniversary of Mark Iosifovich Vishik and is based on a number of mini-courses taught by the author at University of Surrey (UK) and Lanzhou University (China). It discusses the classical and modern…
It is widely believed that the curvature singularities are an artifact of general relativity and may not exist in the Universe, and likely to be defined by the quantum gravity. In the absence of successful quantum gravity, significant…
Respecting the angular momentum conservation of torque-free systems, it is natural to consider rotating solutions of massive objects. Besides that, motivated by the realistic astrophysical black holes that rotate, we use the Newman-Janis…
We introduce a 'quasi-topological` term [1] in D=1+1 dimensions and the entropy for black holes is calculated [2]. The source of entropy in this case is justified by a non-null stress-energy tensor.
We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited,…
The correspondence between stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples…
The existence of light rings in a spacetime is closely related to the existence of black hole horizons and observables such as the ringdown and the shadow. Black holes, compared to nonvacuum ultracompact objects, have rather unique…
We explore spacetime torsion in a two-dimensional setting, wherein it corresponds to a vector field. Without invoking field equations of a particular gravitational theory, we develop visualization techniques for such torsion fields,…
We present an example of a new strange attractor which, as we show, belongs to a class of wild pseudohyperbolic spiral attractors. We find this attractor in a four-dimensional system of differential equations which can be represented as an…
We propose a general framework for the study of asymptotically flat black objects with $k+1$ equal magnitude angular momenta in $d\geq 5$ spacetime dimensions (with $0\leq k\leq \big[\frac{d-5}{2} \big]$). In this approach, the dependence…
Approximating regions of attraction in nonlinear systems require extensive computational and analytical efforts. In this paper, nonlinear vector fields are recasted as sum of vectors where each individual vector is used to construct an…
In the scalar-tensor theory of gravitation it seems nontrivial to establish if solutions of the cosmological equations in the presence of a cosmological constant behave as attractors independently of the initial values. We develop a general…
The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak…