Solutions of Einstein ’ s field equations related to Jacobi ’ s inversion problem R . Meinel and G . Neugebauer Max – Planck
نویسندگان
چکیده
A new class of exact solutions to the axisymmetric and stationary vacuum Einstein equations containing n arbitrary complex parameters and one arbitrary real solution of the axisymmetric three–dimensional Laplace equation is presented. The solutions are related to Jacobi's inversion problem for hyperelliptic Abelian integrals.
منابع مشابه
Gravitational fields of rotating disks and black holes
The two known exact solutions of Einstein’s field equations describing rotating objects of physical significance – a black hole and a rigidly rotating disk of dust – are discussed using a single mathematical framework related to Jacobi’s inversion problem. Both solutions can be represented in such a form that they differ in the choice of a complex parameter and a real solution of the axisymmetr...
متن کاملEffects of Hall Current and Rotation in Modified Couple Stress Generalized Thermoelastic Half Space due to Ramp-Type Heating
The objective is to study the deformation in a homogeneous isotropic modified couple stress thermoelastic rotating medium in the presence of Hall current and magnetic field due to a ramp-type thermal source. The generalized theories of thermoelasticity developed by Lord Shulman (L-S, 1967) and Green Lindsay (G-L, 1972) are used to investigate the problem. Laplace and Fourier transform technique...
متن کاملInvariant Wave Maps from Gödel’s Universe
Gödel’s metric is a solution g↵ to the Einstein field equations, with cosmological constant, in the presence of an incoherent matter distribution. Gödel’s universe G4 ↵ = R4 , g↵ is the total space of a principal bundle R ! G4 ↵ ! M3 over a 3dimensional nondegenerate CR manifold M3 = G4 ↵/K got as the space of orbits of a null Killing vector field K on G4 ↵. Invariant wave maps : G4 ↵ ! N are p...
متن کاملThe (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2
Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...
متن کامل0 On billiard weak solutions of nonlinear PDE ’ s and Toda flows ∗
A certain class of partial differential equations possesses singular solutions having discontinuous first derivatives (“peakons”). The time evolution of peaks of such solutions is governed by a finite dimensional completely integrable system. Explicit solutions of this system are constructed by using algebraic-geometric method which casts it as a flow on an appropriate Riemann surface and reduc...
متن کامل