The Kerr theorem and multiparticle Kerr-Schild solutions

We discuss and prove an extended version of the Kerr theorem which allows one to construct exact solutions of the Einstein-Maxwell field equations from a holomorphic generating function $F$ of twistor variables. The exact multiparticle Kerr-Schild solutions are obtained from generating function of the form $F=\prod_i^k F_i,$ where $F_i$ are partial generating functions for the spinning particles $i=1...k$. Solutions have an unusual multi-sheeted structure. Twistorial structures of the i-th and j-th particles do not feel each other, forming a type of its internal space. Gravitational and electromagnetic interaction of the particles occurs via the light-like singular twistor lines. As a result, each particle turns out to be `dressed' by singular pp-strings connecting it to other particles. We argue that this solution may have a relation to quantum theory and to quantum gravity.Comment: 13 pages, 4 figures, revtex. Expressions for electromagnetic field are correcte

Complex Kerr Geometry and Nonstationary Kerr Solutions

In the frame of the Kerr-Schild approach, we consider the complex structure of Kerr geometry which is determined by a complex world line of a complex source. The real Kerr geometry is represented as a real slice of this complex structure. The Kerr geometry is generalized to the nonstationary case when the current geometry is determined by a retarded time and is defined by a retarded-time construction via a given complex world line of source. A general exact solution corresponding to arbitrary motion of a spinning source is obtained. The acceleration of the source is accompanied by a lightlike radiation along the principal null congruence. It generalizes to the rotating case the known Kinnersley class of "photon rocket" solutions.Comment: v.3, revtex, 16 pages, one eps-figure, final version (to appear in PRD), added the relation to twistors and algorithm of numerical computations, English is correcte

Rotating Black Hole, Twistor-String and Spinning Particle

We discuss basic features of the model of spinning particle based on the Kerr solution. It contains a very nontrivial {\it real} stringy structure consisting of the Kerr circular string and an axial stringy system. We consider also the complex and twistorial structures of the Kerr geometry and show that there is a {\it complex} twistor-string built of the complex N=2 chiral string with a twistorial $(x,\theta)$ structure. By imbedding into the real Minkowski $\bf M^4$, the N=2 supersymmetry is partially broken and string acquires the open ends. Orientifolding this string, we identify the chiral and antichiral structures. Target space of this string is equivalent to the Witten's `diagonal' of the $\bf CP^3\times CP^{*3}.$Comment: 19 p. 4 figures, extended version of hep-th/0412065, based on the talk given at the Conference `Symmetries and Spin'(SPIN-Praha-2004) July 200

Kerr-Schild Approach to the Boosted Kerr Solution

Using a complex representation of the Debney-Kerr-Schild (DKS) solutions and the Kerr theorem we analyze the boosted Kerr geometries and give the exact and explicit expressions for the metrics, the principal null congruences, the coordinate systems and the location of the singularities for arbitrary value and orientation of the boost with respect to the angular momentum. In the limiting, ultrarelativistic case we obtain light-like solutions possessing diverging and twisting principal null congruences and having, contrary to the known pp-wave limiting solutions, a non-zero value of the total angular momentum. The implications of the above results in various related fields are discussed.Comment: 16 pages, LaTe

Gravity vs. Quantum theory: Is electron really pointlike?

The observable gravitational and electromagnetic parameters of an electron: mass $m$, spin $J=\hbar/2$, charge $e$ and magnetic moment $ea = e\hbar /(2m)$ indicate unambiguously that the electron should had the Kerr-Newman background geometry -- exact solution of the Einstein-Maxwell gravity for a charged and rotating black hole. Contrary to the widespread opinion that gravity plays essential role only on the Planck scales, the Kerr-Newman gravity displays a new dimensional parameter $a =\hbar/(2m),$ which for parameters of an electron corresponds to the Compton wavelength and turns out to be very far from the Planck scale. Extremely large spin of the electron with respect to its mass produces the Kerr geometry without horizon, which displays very essential topological changes at the Compton distance resulting in a two-fold structure of the electron background. The corresponding gravitational and electromagnetic fields of the electron are concentrated near the Kerr ring, forming a sort of a closed string, structure of which is close to the described by Sen heterotic string. The indicated by Gravity stringlike structure of the electron contradicts to the statements of Quantum theory that electron is pointlike and structureless. However, it confirms the peculiar role of the Compton zone of the "dressed" electron and matches with the known limit of the localization of the Dirac electron. We discuss the relation of the Kerr string with the low energy string theory and with the Dirac theory of electron and suggest that the predicted by the Kerr-Newman gravity closed string in the core of the electron, should be experimentally observable by the novel regime of the high energy scattering -- the Deeply Virtual (or "nonforward")Compton Scattering".Comment: 15 pages,6 figures, proceedings of the conference QTS7, v.2 reference correcte

Four-fermion interaction from torsion as dark energy

The observed small, positive cosmological constant may originate from a four-fermion interaction generated by the spin-torsion coupling in the Einstein-Cartan-Sciama-Kibble gravity if the fermions are condensing. In particular, such a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early Universe. We study how the torsion-induced four-fermion interaction is affected by adding two terms to the Dirac Lagrangian density: the parity-violating pseudoscalar density dual to the curvature tensor and a spinor-bilinear scalar density which measures the nonminimal coupling of fermions to torsion.Comment: 6 pages; published versio

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Galaxy bulges and their massive black holes: a review

With references to both key and oft-forgotten pioneering works, this article starts by presenting a review into how we came to believe in the existence of massive black holes at the centres of galaxies. It then presents the historical development of the near-linear (black hole)-(host spheroid) mass relation, before explaining why this has recently been dramatically revised. Past disagreement over the slope of the (black hole)-(velocity dispersion) relation is also explained, and the discovery of sub-structure within the (black hole)-(velocity dispersion) diagram is discussed. As the search for the fundamental connection between massive black holes and their host galaxies continues, the competing array of additional black hole mass scaling relations for samples of predominantly inactive galaxies are presented.Comment: Invited (15 Feb. 2014) review article (submitted 16 Nov. 2014). 590 references, 9 figures, 25 pages in emulateApJ format. To appear in "Galactic Bulges", E. Laurikainen, R.F. Peletier, and D.A. Gadotti (eds.), Springer Publishin

Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking?

It is widely accepted that humans and animals minimize energetic cost while walking. While such principles predict average behavior, they do not explain the variability observed in walking. For robust performance, walking movements must adapt at each step, not just on average. Here, we propose an analytical framework that reconciles issues of optimality, redundancy, and stochasticity. For human treadmill walking, we defined a goal function to formulate a precise mathematical definition of one possible control strategy: maintain constant speed at each stride. We recorded stride times and stride lengths from healthy subjects walking at five speeds. The specified goal function yielded a decomposition of stride-to-stride variations into new gait variables explicitly related to achieving the hypothesized strategy. Subjects exhibited greatly decreased variability for goal-relevant gait fluctuations directly related to achieving this strategy, but far greater variability for goal-irrelevant fluctuations. More importantly, humans immediately corrected goal-relevant deviations at each successive stride, while allowing goal-irrelevant deviations to persist across multiple strides. To demonstrate that this was not the only strategy people could have used to successfully accomplish the task, we created three surrogate data sets. Each tested a specific alternative hypothesis that subjects used a different strategy that made no reference to the hypothesized goal function. Humans did not adopt any of these viable alternative strategies. Finally, we developed a sequence of stochastic control models of stride-to-stride variability for walking, based on the Minimum Intervention Principle. We demonstrate that healthy humans are not precisely “optimal,” but instead consistently slightly over-correct small deviations in walking speed at each stride. Our results reveal a new governing principle for regulating stride-to-stride fluctuations in human walking that acts independently of, but in parallel with, minimizing energetic cost. Thus, humans exploit task redundancies to achieve robust control while minimizing effort and allowing potentially beneficial motor variability