Mathematics – Differential Geometry
Scientific paper
Mar 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cqgra...3..169k&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 3, March 1, 1986, p. 169-173.
Mathematics
Differential Geometry
2
Cosmology, Electromagnetic Fields, Gravitational Waves, Unified Field Theory, Differential Geometry, Einstein Equations, Maxwell Equation, Riemann Manifold, Space-Time Functions, Spin
Scientific paper
A new family of solutions to the Einstein-Maxwell equations with a cosmological constant is derived within the framework of the Newman-Penrose formalism. The solutions may be applied to the case of an electromagnetic field which is aligned (Phi0 = 0), nonradiative (Ophi2 = 0), and (Phi1 = constant) electromagnetic field. Each metric from the family contains three arbitrary real functions of the null retarded coordinate u as well as one arbitrary complex function of u and the complex variable Zeta. The main geometrical features of the solutions are discussed. It is pointed out that the Riemannian manifolds corresponding to the solutions admit the spacelike wave surfaces of a constant Gaussian curvature whose type and radius depend on the values of the cosmological constant Lambda and the invariant parameters of the electromagnetic field.
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