Related papers: Inverse problem for Einstein-scalar field equation…
Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known…
We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…
We study inverse problems for the Einstein-Maxwell equations. We prove that it is possible to generate gravitational waves from the nonlinear interactions of electromagnetic waves. By sending electromagnetic waves from a neighborhood of a…
In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new…
We consider the existence of Einstein-Maxwell-dilaton plus fluid system for the case of stationary cylindrically symmetric spacetimes. An exact inhomogeneous $ \epsilon$-order solution is found, where the parameter $\epsilon$ parametrizes…
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a…
The inhomogeneous distribution of matter in the non-linear regime of galaxies, clusters of galaxies and voids is described by an exact, spherically symmetric inhomogeneous solution of Einstein's gravitational field equations, corresponding…
We consider the problem of determining the shape and location of an unknown penetrable object in a perfectly conducting electromagnetic waveguide. The inverse problem is posed in the frequency domain and uses multistatic data in the near…
We study the Lie point symmetries of Einstein's equations for the Friedmann-Roberstson-Walker Cosmology. They form either a two - dimensional or a three - dimensional solvable group depending on the form of the self interacting potential.…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
We consider an inverse problem for a non-linear hyperbolic equation. We show that conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evaluated along a single timelike curve. We use the microlocal…
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
The rotational metric provides an exact solution to Einstein's clock-rate problem in curved spacetime, specifically, whether time flows more slowly at the equator of a compact object such as a neutron star than at its poles. It features a…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period $T$ yet mimic with good approximation, or even…
We propose a robust numerical method to find the coefficient of the creation or depletion term of parabolic equations from the measurement of the lateral Cauchy information of their solutions. Most papers in the field study this nonlinear…
Investigations of spherically symmetric motions of self-gravitating gaseous stars governed by the non-relativistic Newtonian gravitation theory or by the general relativistic theory lead us to a certain type of non-linear hyperbolic…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…