2019/12/14 by S. V. Bolokhov, Bolokhov, S. V., В. Д. Иващук +2
Mathematics · Physics and Astronomy · #Abelian group #Black Holes and Theoretical Physics #Centralizer and normalizer #Combinatorics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Lie algebra #Lie group #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Submanifold #Type (biology) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1912.08083
16 pages, 1 figure, LaTex, a semi-review paper. The changes in the v2 version: two paragraphs were added into the end of Introduction with a footnote and 8 references, several typos in the text were eliminated. arXiv admin note: text overlap with arXiv:1709.09663
openalex publication_date 2019/12/14 · arxiv created 2021/01/23 · arxiv updated 2021/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We deal with generalized Melvin-like solutions associated with Lie algebras of rank 4 (A4, B4, C4, D4, F4). Any solution has static cylindrically-symmetric metric in D dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions Hs(z) (s = 1,...,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions are polynomials of powers (n1,n2, n3, n4) = (4,6,6,4), (8,14,18,10), (7,12,15,16), (6,10,6,6), (22,42,30,16) for Lie algebras A4, B4, C4, D4, F4, respectively. The asymptotic behaviour for the polynomials at large z is governed by an integer-valued 4 × 4 matrix ν connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A4 case) the matrix representing a generator of the ℤ2-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are studied. We also present 2-form flux integrals over a 2-dimensional submanifold. Dilatonic black hole analogs of the obtained Melvin-type solutions, e.g. "fantom" ones, are also considered. The phantom black holes are described by fluxbrane polynomials under consideration.