arXiv subjects
Publications and source records attributed to O. Kechkin.
The Kähler formulation of 5-dimensional Einstein-Kalb-Ramond (EKR) theory admitting two commuting Killing vectors is presented. Three different Kramer-Neugebauer-like maps are established for the 2-dimensional case. A class of solutions constructed on the double Ernst one is obtained. It is shown that the double Kerr solution corresponds to a EKR dipole configuration with horizon.
The (3+d)-dimensional Einstein-Kalb-Ramond theory reduced to two dimensions is considered. It is shown that the theory allows two different Ernst-like $d \times d$ matrix formulations: the real non-dualized target space and the Hermitian dualized non-target space ones. The O(d, d) symmetry is written in a SL(2,R) matrix-valued form in both cases. The Kramer-Neugebauer transformation, which algebraically maps the non-dualized Ernst potential into the dualized one, is presented.
The Ernst-like matrix representation of the multidimensional Einstein-Kalb-Ramond theory is developed and the O(d,d)-symmetry is presented in the matrix-valued SL(2,R)-form. The analogy with the Einstein and Einstein-Maxwell-Dilaton-Axion theories is discussed.
A class of the $D=4$ gravity models describing a coupled system of $n$ Abelian vector fields and the symmetric $n \times n$ matrix generalizations of the dilaton and Kalb-Ramond fields is considered. It is shown that the Pecci-Quinn axion matrix can be entered and the resulting equations of motion possess the $Sp(2n, R)$ symmetry in four dimensions. The stationary case is studied. It is established that the theory allows a $σ$-model representation with a target space which is invariant under the $Sp[2(n+1), R]$ group of isometry transformations. The chiral matrix of the coset $Sp[2(n+1), R]/U(n+1)$ is constructed. A Kähler formalism based on the use of the Ernst $(n+1) \times (n+1)$ complex symmetric matrix is developed. The stationary axisymmetric case is considered. The Belinsky-Zakharov chiral matrix depending on the original field variables is obtained. The Kramer-Neugebauer transformation, which algebraically maps the original variables into the target space ones, is presented.
The action of the isometry subgroup which preserves the trivial values of the fields is studied for the stationary D=4 Einstein--Maxwell--Dilaton--Axion theory. The technique for generation of charges and the corresponding procedure for construction of new solutions is formulated. A solution describing the double rotating dyon with independent values of all physical charges is presented.
The Kramer--Neugebauer--like transformation is constructed for the stationary axisymmetric D=4 Einstein--Maxwell--dilaton--axion system. This transformation directly maps the dualized sigma--model equations of the theory into the nondualized ones. Also the new chiral $4 \times 4$ matrix representation of the problem is presented.
The constructed $Sp(4,R)/GL(2,R)$ matrix operator defines the family of isotropic geodesic containing vacuum point lines in the target space of the stationary D=4 Einstein--Maxwell--dilaton--axion theory. This operator is used to derive a class of solutions which describes a point center system with nontrivial values of mass, parameter NUT, as well as electric, magnetic, dilaton and axion charges. It is shown that this class contains both particular solutions Majumdar--Papapetrou--like black holes and massless asymptotically nonflat naked singularities.