https://hal-cea.archives-ouvertes.fr/cea-00825799Bena, IosifIosifBenaIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueGiusto, StefanoStefanoGiustoDipartimento di Fisica - Unipd - Università degli Studi di Padova = University of PaduaINFN, Sezione di Padova - Istituto Nazionale di Fisica Nucleare, Sezione di Padova - INFN - Istituto Nazionale di Fisica NucleareShigemori, MasakiMasakiShigemoriKobayashi-Maskawa Institute - Nagoya UniversityWarner, Nicholas P.Nicholas P.WarnerDepartment of Physics and Astronomy [USC, Los Angeles] - USC - University of Southern CaliforniaSupersymmetric Solutions in Six Dimensions: A Linear StructureHAL CCSD2012[PHYS.GRQC] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc][PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]Savelli, BrunoJeunes chercheuses et jeunes chercheurs - - String-QCD-BH2008 - ANR-08-JCJC-0001 - JCJC - VALID - String Theory, QCD and Black Holes - STRING-QCD-BH - - EC:FP7:ERC2010-01-01 - 2014-12-31 - 240210 - VALID - 2020-07-07 16:25:132023-03-24 14:53:182020-07-07 16:29:42enJournal articleshttps://hal-cea.archives-ouvertes.fr/cea-00825799/document10.1007/JHEP03(2012)084application/pdf1The equations underlying all supersymmetric solutions of six-dimensional minimal ungauged supergravity coupled to an anti-self-dual tensor multiplet have been known for quite a while, and their complicated non-linear form has hindered all attempts to systematically understand and construct BPS solutions. In this paper we show that, by suitably re-parameterizing these equations, one can find a structure that allows one to construct supersymmetric solutions by solving a sequence of linear equations. We then illustrate this method by constructing a new class of geometries describing several parallel spirals carrying D1, D5 and P charge and parameterized by four arbitrary functions of one variable. A similar linear structure is known to exist in five dimensions, where it underlies the black hole, black ring and corresponding microstate geometries. The unexpected generalization of this to six dimensions will have important applications to the construction of new, more general such geometries.