On generalized Melvin solutions for Lie algebras of rank 4
Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198, Moscow, Russian Federation
2 Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya St., 119361, Moscow, Russian Federation
Accepted: 3 February 2021
Published online: 17 February 2021
We deal with generalized Melvin-like solutions associated with Lie algebras of rank 4 (, , , , ). Any solution has static cylindrically symmetric metric in D dimensions in the presence of four Abelian two-form and four scalar fields. The solution is governed by four moduli functions () of squared radial coordinate obeying four differential equations of the Toda chain type. These functions are polynomials of powers for Lie algebras , , , , , respectively. The asymptotic behaviour for the polynomials at large z is governed by an integer-valued matrix connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in case) the matrix representing a generator of the -group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are studied. We also present two-form flux integrals over a two-dimensional submanifold. Dilatonic black hole analogs of the obtained Melvin-type solutions, e.g. “phantom” ones, are also considered. The phantom black holes are described by fluxbrane polynomials under consideration.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021