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We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$…
On spacetimes that are not time orientable we construct a U(1) bundle to measure the twisting of the time axis. This single assumption, and simple construction, gives rise to Maxwell's equations of electromagnetism, the Lorentz force law…
We study the system of self-dual Maxwell field coupled to 3D gravity with torsion, with Maxwell field modified by a topological mass term. General structure of the field equations reveals a new, dynamical role of the classical central…
Maxwell's equations with massive photons and magnetic monopoles are formulated using spacetime algebra. It is demonstrated that a single non-homogeneous multi-vectorial equation describes the theory. Two limiting cases are considered and…
Using a nonlinear electrodynamics coupled to teleparallel theory of gravity, three regular charged spherically symmetric solutions are obtained. The nonlinear theory reduces to the Maxwell one in the weak limit and the solutions correspond…
Axion electrodynamics extends Maxwell's theory by postulating a hypothetical pseudoscalar axion field sourced by a scalar product of electric and magnetic fields. In this work, we demonstrate that a superposition of toroidal electromagnetic…
We prove variants of known singularity theorems ensuring the existence of a region of finite lifetime that are particularly well applicable if the solution admits a conformal extension, a property satisfied e.g. by maximal Cauchy…
The axion photon system in an external magnetic field, when for example considered with the geometry of the experiments exploring axion photon mixing (which can be represented by a 1+1 effective model) displays a continuous axion-photon…
In this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC). Specifically, we use T-duality in order to map the bounds on the charge-to-mass ratio of particles…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
We introduce a class of space-times modeling singular events such as evaporating black holes and topology changes, which we dub as semi-globally hyperbolic space-times. On these space-times we aim to study the existence of reasonable…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
Real-space singularities underpin diverse wave phenomena yet remain largely unexplored in elastic wave systems. We report the observation of real-space topological singularities in structured flexural waves on finite-sized solids. These…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
As quantum optical phenomena are based on Maxwell's equations, and it is becoming important to understand quantum optical phenomena at short distances, so it is important to analyze quantum optics using short distance corrected Maxwell's…
This work investigates alternative theories of gravity, the solutions to their field equations and the constraints that can be imposed upon them from observation and experiment. Specifically, we consider the cosmologies and spherically…
We investigate which are the independent equations of continuum electrodynamics and what is their number, beginning with the standard equations used in special and in general relativity. We check by using differential identities that there…
An analysis of the concept of orientation used in electrodynamics is presented. At least two different versions are encountered in the literature. Both are clearly identified and comparisons are made.
It is often the case that scalar fields are produced in the early Universe in the form of coherent oscillation. These scalar fields may have huge abundances and affect the evolution of the Universe. In particular, if the lifetime is long…