Mustafa Halilsoy

Large family of colliding waves in the Einstein–Maxwell theory

A general class of similarity integrals of the Ernst equation with the method of Chandrasekhar and Xanthopoulos are combined to obtain a family of solutions for colliding waves in the Einstein–Maxwell theory. The family is parametrized by an arbitrary harmonic function that satisfies the Euler–Darboux equation. The first nontrivial member of the family is shown to be the cross‐polarized version of the Bell–Szekeres solution.

Similarity solution for the Ernst equation with electromagnetic fields

SummaryExact similarity solution is given for the Ernst equation coupled with electromagnetic fields in general relativity.

Cross-polarized cylindrical gravitational waves of Einstein and Rosen

SummaryUsing Einstein-Rosen’s linearly polarized waves as the seed solution, we derive an interesting solution for the Einstein’s equations that describes the evolution of such waves with the second polarization.RiassuntoUsando le onde linearmente polarizzate di Einstein-Rosen come soluzione seme, si deduce una soluzione interessante per le equazioni di Einstein che descrive l’evoluzione di tali onde con la seconda polarizzazione.РезюмеИспользуь линейно поляризованные волны Эйнштейна и Розена, как затравочное решение, мы выводим интересное решение для уравнений Эйнштейна, которое описывает эволюцию таких волн с второй поляризацией.

Studies in space‐times admitting two spacelike Killing vectors

Some properties of the space‐times admitting two spacelike Killing vectors are studied. In particular, using harmonic maps the degree of freedom on the M’ manifold is exploritd to add scalar and electromagnetic fields to Bonnor’s nonsingular solution. It is also shown that for vacuum space‐times the noncommutativity of two spacelike Killing vectors is incompatible with the self‐similarity requirement and such a self‐similar vacuum space‐time has no Taub–NUT equivalent extension.

Scalar Plane Waves in General Relativity

SummaryA more general class of scalar plane waves is presented in general relativity. It is shown that no matter how the scalar field is modified, space-time possesses an essential singularity.

Interacting superposed electromagnetic shock plane waves in general relativity

SummaryWe present a solution of the Einstein-Maxwell field equations describing the collision of superposed electromagnetic shock plane waves.

A class of transcendent solutions to Ernst system

SummaryWe present a method that generates a class of transcendent solutions to Ernst system in Einstein-Maxwell theory of general relativity.

On the generation of a class of Einstein-Maxwell solutions

We make an alternative approach to Bonnorification by making use of effective Lagrangians for the gravitational fields. Using this technique we obtain a new Einstein-Maxwell solution.