Related papers: Proof of the Julia-Zee Theorem
We provide a new proof of the equality case of the spacetime positive mass theorem, which states that if a complete asymptotically flat initial data set $(M, g, k)$ satisfying the dominant energy condition has null ADM energy-momentum (that…
Properties of pure gauge theories in thermal equilibrium as calculated via standard functional integral treatments are mathematically identical to ground state properties of a theory with spatially-periodic boundary conditions imposed on…
We prove that the Cauchy problem for the Chern-Simons-Higgs equations on the (2+1)-dimensional Minkowski space-time is globally well posed for initial data with finite energy. This improves a result of Chae and Choe, who proved global…
In a previous paper [9], we proved the following singularity theorem applicable to cosmological models with a positive cosmological constant: if a four-dimensional spacetime satisfying the null energy condition contains a compact Cauchy…
In the framework of the nonlinear stability of Minkowski spacetime, we show that if the radiation field of the curvature tensor vanishes, the spacetime must be flat.
We show that the solution published in Ref.1 is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, causal symmetry and causal…
A de-Sitter gauge theory of the gravitational field is developed using a spherical symmetric Minkowski space-time as base manifold. The gravitational field is described by gauge potentials and the mathematical structure of the underlying…
We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results…
The electric and magnetic fields of an infinite straight wire carrying a steady current which is turned on abruptly are determined using Jefimenko's equations, starting from the standard assumption that the wire is electrically neutral in…
We consider a gauge theory on the 5-d $\kappa$-Minkowski which can be viewed as the noncommutative analog of a $U(1)$ gauge theory. We show that the Hermiticity condition obeyed by the gauge potential $A_\mu$ is necessarily twisted.…
We treat continuum electrodynamics as an axiomatic formal theory based on the macroscopic Maxwell--Minkowski equations applied to a thermodynamically closed system consisting of an antireflection-coated block of a simple linear dielectric…
In this note, we present a new proof of the solvability of the electrostatic Born-Infeld equation with radial charge, based on the conformal method and the Spacetime Positive Energy Theorem. An advantage of this approach is that the…
In their proof of the positive energy theorem, Schoen and Yau showed that every asymptotically flat spacelike hypersurface M of a Lorentzian manifold which is flat along M can be isometrically imbedded with its given second fundamental form…
We set up a model of an electric charge where the noninvertible metric phase of first order gravity supercedes the point charge singularity in a curved spacetime. A topological interpretation of the electric charge is provided in terms of…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
We give a new proof of the global stability of Minkowski space originally established in the vacuum case by Christodoulou and Klainerman. The new approach shows that the Einstein-vacuum and the Einstein-scalar field equations with general…
In this paper, we sketch the proof of the extension of the stability theorem of the Minkowski space in General Relativity done explicitly in previous work by the present author. We discuss solutions of the Einstein vacuum (EV) equations. We…
The concept of Euclidean time is proposed which is dual to the usual Minkowski time. The De Sitter solution is shown to be dual to the anti-De Sitter solution under the dual transformation in which Euclidean time and Minkowski time are…
We study the model theory of vector spaces with a bilinear form over a fixed field. For finite fields this can be, and has been, done in the classical framework of full first-order logic. For infinite fields we need different logical…
We prove global stability for the Charge-Scalar Field system on a background spacetime which is close to $1+3$-dimensional Minkowski space and whose outward light cones converge to those for the Schwarzschild metric at null infinity. The…