Lie Theory and Its Applications in Physics VII

General Relativity and Gravitation, 2014

The new class of the non-stationary solutions to the system of N-dimensional equations for coupled gravitational and massless scalar field is found. The model represents a single (N-1)-brane in a space-time with one large (infinite) and (N-5) small (compact) space-like extra dimensions. In some particular cases the model corresponds to the gravitational and scalar field standing waves bounded by the brane. These braneworlds can be relevant in string and other higher dimensional models.

Physical Review D, 2005

We introduce and study in some detail the properties of a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically lightlike branes for any odd world-volume dimension. Their dynamics significantly differs from that of the ordinary (conformally non-invariant) Nambu-Goto p-branes. We present explicit solutions of the Weyl-invariant lightlike brane-(WILLbrane) equations of motion in various gravitational models of physical relevance exhibiting various new phenomena. In D = 4 the WILL-membrane serves as a material and charged source for gravity and electromagnetism in the coupled Einstein-Maxwell-WILL-membrane system; it automatically positions itself on ("straddles") the common event horizon of the corresponding matching black hole solutions, thus providing an explicit dynamical realization of the membrane paradigm in black hole physics. In product spaces of interest in Kaluza-Klein theories the WILL-brane wraps nontrivially around the compact (internal) dimensions and still describes massless mode dynamics in the non-compact (space-time) dimensions. Due to nontrivial variable size of the internal compact dimensions we find new types of physically interesting solutions describing massless brane modes trapped on bounded planar circular orbits with non-trivial angular momentum, and with linear dependence between energy and angular momentum.

Foundations of Physics, 2007

We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates X µ 1 ...µn encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes the dynamics of the usual branes. Geometrically, coordinates X µ 1 ...µn and associated coordinate frame fields {γ µ 1 ...µn } extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start from 4-dimensional spacetime, then the dimension of C-space is 16. The fact that C-space has more than four dimensions suggests that it could serve as a realization of Kaluza-Klein idea. The "extra dimensions" are not just the ordinary extra dimensions, they are related to the volume degrees of freedom, therefore they are physical, and need not be compactified. Gauge fields are due to the metric of Clifford space. It turns out that amongst the latter gauge fields there also exist higher grade, antisymmetric fields of the Kalb-Ramond type, and their non-Abelian generalization. All those fields are naturally coupled to the generalized branes, whose dynamics is given by a generalized Howe-Tucker action in curved C-space. functions X µ 1 ...µ R (ξ A ) depend. In particular, the latter functions can be such that they describe just an ordinary worldsheet, swept by an ordinary brane. But in general, they describe more complicated extended objects, with an extra structure.

Central European Journal of Physics, 2009

We discuss properties of a new class of p-brane models, describing intrinsically lightlike branes for any world-volume dimension, in various gravitational backgrounds of interest in the context of black hole physics. One of the characteristic features of these lightlike p-branes is that the brane tension appears as an additional nontrivial dynamical world-volume degree of freedom. Codimension one lightlike brane dynamics requires that bulk space with a bulk metric of spherically symmetric type must possess an event horizon which is automatically occupied by the lightlike brane while its tension evolves exponentially with time. The latter phenomenon is an analog of the well known "mass inflation" effect in black holes.

Nuclear Physics B, 2000

We study gravity in backgrounds that are smooth generalizations of the Randall-Sundrum model, with and without scalar fields. These generalizations include three-branes in higher dimensional spaces which are not necessarily Anti-de Sitter far from the branes, intersecting brane configurations and configurations involving negative tension branes. We show that under certain mild assumptions there is a universal equation for the gravitational fluctuations. We study both the graviton ground state and the continuum of Kaluza-Klein modes and we find that the four-dimensional gravitational mode is localized precisely when the effects of the continuum modes decouple at distances larger than the fundamental Planck scale. The decoupling is contingent only on the long-range behaviour of the metric from the brane and we find a universal form for the corrections to Newton's Law. We also comment on the possible contribution of resonant modes. Given this, we find general classes of metrics which maintain localized four-dimensional gravity. We find that three-brane metrics in five dimensions can arise from a single scalar field source, and we rederive the BPS type conditions without any a priori assumptions regarding the form of the scalar potential. We also show that a single scalar field cannot produce conformally-flat locally intersecting brane configurations or a p-brane in greater than (p + 2)-dimensions.

Arxiv preprint hep-th/ …, 2004

We propose a new class of p-brane theories which are Weyl-conformally invariant for any p. For any odd world-volume dimension the latter describe intrinsically light-like branes, hence the name WILL-branes (Weyl-Invariant Light-Like branes). Next we discuss the dynamics ...

Physical Review D, 2014

Electronic address: [email protected] † Electronic address: [email protected] brane position gives the Nambu-Goto equations of motion which are geometrically described by the vanishing of the trace of the extrinsic curvature, and therefore, the worldsheet swept by the brane is extremal (minimal). Of course, the induced metric on a Nambu-Goto brane is finite (with the possible exception of a set of points with measure zero) which means that the bulk metric is regular at the brane position, since only then, the Nambu-Goto equations of motion are defined. When the gravitational field of the defect is taken into account the situation becomes very different and difficult since now both the bulk metric and the brane position become dynamical. It is the aim of this communication to examine anew the dynamics of a classical self-gravitating brane with a bulk metric regular on the brane. The situation with a bulk metric singular on the brane is an interesting (not in the context of a braneworld) but very different story since now the equation of motion of the defect cannot contain the induced metric which is singular. In this case, actually, the full non-perturbative equation of motion is unknown, however, there is a consensus about the equation of motion for the special case of a 0-brane (point particle) in four dimensions and only at the linearized level around an arbitrary background [2], .

Classical and Quantum Gravity, 1997

We use a simple algebraic method to find a special class of composite p-brane solutions of higher dimensional gravity coupled with matter. These solutions are composed of n constituent p-branes corresponding n independent harmonic functions. A simple algebraic criteria of existence of such solutions is presented. Relations with D = 11, D = 10 known solutions are discussed.

AIP Conference Proceedings, 2006

Geometric variables naturally occurring in a time-like foliation of brane-worlds are introduced. These consist of the induced metric and two sets of lapse functions and shift vectors, supplemented by two sets of tensorial, vectorial and scalar variables arising as projections of the two extrinsic curvatures. A subset of these variables turn out to be dynamical. Brane-world gravitational dynamics is given as the time evolution of these variables.

Physics of Particles and Nuclei Letters, 2014

The geometric approach to branes is reformulated in terms of gauge vector fields interacting with massless tensor multiplets in gravitational backgrounds. Study of nonlinear dynamics of p-branes [1-14] as well as their quantization require new tools. The geometric approach [15-17] originally developed for strings seems to be relevant for the problem. The gauge reformulation [18] of this approach using the ideas of Cartan [19], Volkov [20] and Faddeev [21] has shown that strings in D-dim. spacetime form a closed sector of states of the exactly integrable two-dimensional SO(1, 1) ×SO(D −2) gauge model. The geometric approach has turned out to be promising for investigation of integrability of branes PDEs [22-24]. Here we adopt the string gauge approach to p-branes and constuct new gauge invariant models which have brane solutions.