Related papers: Null-Field Radiationless Sources: Comment
We present an exact treatment of the influences on a quantum scalar field in its Minkowski vacuum state induced by coupling of the field to a uniformly accelerated harmonic oscillator. We show that there are no radiation from the oscillator…
For entire spacelike stationary 2-dimensional graphs in Minkowski spaces, we establish Bernstein type theorems under specific boundedness assumptions either on the W-function or on the total (Gaussian) curvature. These conclusions imply the…
We discuss the emission of radiation from general sources in quantum scalar, electromagnetic and gravitational fields using the Rindler coordinate frame, which is suitable for a uniformly accelerated observer, in the Minkowski vacuum. In…
Null cosmic strings are shown to disturb gravitational fields of massive bodies and create outgoing gravitational waves (GW). Perturbations of the metric caused by a straight null string and a point-like massive source are found as…
We consider two applications of the strata of differentials of the second kind (all residues equal to zero) with fixed multiplicities of zeros and poles: Positivity: In genus $g=0$ we show any associated divisorial projection to…
In this paper we survey some recent contributions by the authors to the theory of null holomorphic curves in the complex Euclidean space $\mathbb C^3$, as well as their applications to null holomorphic curves in the special linear group…
We review the mathematically rigorous formulation of the quantum theory of a linear field propagating in a globally hyperbolic spacetime. This formulation is accomplished via the algebraic approach, which, in essence, simultaneously admits…
Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position…
It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski 3-space R^3_1 have singularities in general. They are both characterized as zero mean curvature surfaces. We are interested in the case…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
Linearized gravitational waves in de Sitter space-time are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity.…
We consider null bosonic p-branes moving in curved space-times and develop a method for solving their equations of motion and constraints, which is suitable for string theory backgrounds. As an application, we give an exact solution for…
We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain roots of unity. In doing so, we find criteria which allow…
We study codimension two spacelike submanifolds contained into a general class of null hypersurfaces in generalized Robertson-Walker spacetimes, refer to as nullcones. In particular we analyze light cones and lightlike cylinders in…
It is classically known that the only zero mean curvature entire graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space $\boldsymbol{R}^3_1$ is called of mixed type if it changes causal…
We develop a novel approach to the Brill-Noether theory of curves endowed with a degree k cover of the projective line via Bridgeland stability conditions on elliptic K3 surfaces. We first develop the Brill-Noether theory on elliptic K3…
A new method of gauging of WZNW models is presented, leading to a class of exact string solutions with a target space metric of Minkowskian signature. The corresponding models may be interpreted as $\sigma$-model analogues of the Toda field…
We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of…
Discontinuities in non linear field theories propagate through null geodesics in an effective metric that depends on its dynamics and on the background geometry. Once information of the geometry of the universe comes mostly from photons,…
The present work describes some extensions of an approach, originally developed by V.V. Yatsyk and the author, for the theoretical and numerical analysis of scattering and radiation effects on infinite plates with cubically polarized…