Metin Gürses

Lorentz covariant treatment of the Kerr–Schild geometry

It is shown that a Lorentz covariant coordinate system can be chosen in the case of the Kerr–Schild geometry which leads to the vanishing of the pseudo energy–momentum tensor and hence to the linearity of the Einstein equations. The retarded time and the retarded distance are introduced and the Lienard–Wiechert potentials are generalized to gravitation in the case of world‐line singularities to derive solutions of the type of Bonnor and Vaidya. An accelerated version of the de Sitter metric is also obtained. Because of the linearity, complex translations can be performed on these solutions, resulting in a special relativistic version of the Trautman–Newman technique and Lorentz covariant solutions for spinning systems can be derived, including a new anisotropic interior metric that matches to the Kerr metric on an oblate spheroid.

On construction of recursion operators from Lax representation

In this work we develop a general procedure for constructing the recursion operators for nonlinear integrable equations admitting Lax representation. Several new examples are given. In particular, we find the recursion operators for some KdV-type systems of integrable equations.

A super AKNS scheme

Abstract A super extension of the AKNS scheme is presented by proposing a super sl(2, R) valued connection. A class of super integrable equations, containing the super extension of the Lax hierarchy, is found.

Perfect Fluid Sources in 2+1 Dimensions

We show that a class of metrics of Einstein theory with perfect fluid sources are also the solutions of the Deser--Jackiw--Templeton (DJT) theory with a cosmological constant. Because of this analogy we interpret a recently found black hole solution of the DJT equations as a rotating fluid solution of the Einstein theory in three dimensions.

Integrable KdV systems: Recursion operators of degree four

Abstract The recursion operator and bi-Hamiltonian formulation of the Drinfeld-Sokolov system are given.

AdS Waves as Exact Solutions to Quadratic Gravity

We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.

Boundary conditions for integrable equations

The problem of constructing boundary conditions for nonlinear equations compatible with higher symmetries is considered. In particular, this problem is discussed for the sine - Gordon, Jiber - Shabat, Liouville and KdV equations. New results are obtained for the last two ones. The boundary condition for the KdV contains two arbitrary constants. The substitution maps it onto the boundary condition with linear dependence on t for the potentiated KdV.

Hamiltonian equations in R3

Hamiltonian formulation of N=3 systems is considered in general. The Jacobi equation is solved in three classes. Compatible Poisson structures in these classes are determined and explicitly given. The corresponding bi-Hamiltonian systems are constructed and some explicit examples are given.

The exterior gravitational field of a charged spinning source in the poincaré gauge theory: A Kerr-newman metric with dynamic torsion☆

Abstract We present a new exact solution of the Poincare gauge theory, namely a charged Kerr-NUT metric with an effective cosmological constant which is consistently coupled to a dynamic torsion field. The solution is given in terms of an orthonormal basis in Boyer-Lindquist coordinates and depends on the constants m0 (mass), j0 (angular momentum), q0 (electric charge), and n0 (NUT parameter). Whereas m0,j0, and q0 can be specified arbitrarily, the NUT parameter and the effective cosmological constant are determined by the coupling constants of our model. The torsion of the solution is centered around the coordinate origin and vanishes asymptotically for large radial distance. For n0=0, we find the exterior gravitational field of a charged spinning source.

Integrable coupled KdV systems

We give the conditions for a system of N-coupled Korteweg de Vries (KdV) type of equations to be integrable. We find the recursion operators of each subclass and give all examples for N=2.