We give a unified derivation of the propagator in the gauges n.A = 0 for n timelike, spacelike or lightlike. We discuss the physical states and other physical questions.

We prove that the Lorentzian helicoid and Enneper’s surface are the unique properly embedded maximal surfaces bounded by a lightlike regular arc of mirror symmetry.

We show that the entropy created by Ohmic dissipation inside an accreting charged black hole may exceed the Bekenstein-Hawking entropy by a large factor. The second law of thermodynamics does not hold on spacelike slices inside these model black holes, even when the slices avoid Planck scale densities and curvatures. This result is distinct from, but consistent with, the fact that there is no e...

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a divisor (=hypersurface) has normal crossings if and only if it a free divisor, has a radical Jacobian ideal and a smooth normalization. Using K. Saito’s theory of free divisors, also a characterization in terms of logarithmic differential for...

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime (M0 × R, g) is equal to the index of its spatial projection as a geodesic of a Finsler metric F on M0 associated to (M0×R, g). Moreover we obtain the Morse relations of lightlike geodesics connecting a point p to a curve γ(s) = (q0, s) by using Morse theory on the Finsler manifold (M0, F ). To this end...

We analyze the bit complexity of an algorithm for computation at least one point in each connected component a smooth real algebraic set. This work is continuation our analysis hypersurface case (On finding points components hypersurface, ISSAC'20). In this paper, we extend to more general cases. Let F=(f1,…,fp) Z[X1,…,Xn]p be sequence polynomials with V=V(F)⊂Cn and equidimensional variety 〈F〉⊂...

We study the weighted ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We prove support theorems if the manifold and the weight are analytic.

Spinors are lightlike. How do they combine to make massive particles? We visit the zoo of Lagrangian singularities, or caustics, in spacetime projections from spin spacethe phase space of lightlike, 8spinor flows. We find that the species living there are the elementary particles. Codimension J = (1, 2, 3, 4) phase singularities vortex lines, sheets, tubes, and knots, are classified by the Coxe...

We present a Weierstrass-type representation formula which locally represents every regular two-dimensional lightlike surface in Lorentz-Minkowski 4-Space $\mathbb{M}^4$ by three dual functions $(\rho,f,g)$ and generalizes the for surfaces $\mathbb{M}^3$. give necessary sufficient conditions on $\rho$, $f$, $g$ to be minimal, ruled or $l$-minimal. For surfaces, we itself ruled. Furthermore, res...

The outward–pointing principal null direction of the Schwarzschild Rie-mann tensor is null hypersurface–forming. If the Schwarzschild mass spontaneously jumps across one such hypersurface then the hypersurface is the history 1 of an outgoing light–like shell. The outward– pointing principal null direction of the Kerr Riemann tensor is asymptotically (in the neighbourhood of future null infinity...