An algebraic technique generates rotating black holes and multi-source solutions from static ones by transforming to AdS×S asymptotics, applying a rotating frame shift, and returning to flat asymptotics.
Generalized Weyl Solutions
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl's construction is generalized here to arbitrary dimension $D\ge 4$. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplace's equation in three-dimensional flat space or by D-4 independent solutions of Laplace's equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat ``black ring'' with an event horizon of topology S^1 x S^2 held in equilibrium by a conical singularity in the form of a disc.
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2026 3verdicts
UNVERDICTED 3representative citing papers
New exact solutions to d-dimensional Einstein-scalar gravity are generated in Weyl form that incorporate multipolar scalars and magnetic fields, with limits matching scalar versions of Schwarzschild-Melvin and Fisher-Janis-Newman-Winicour spacetimes.
Essentially all known analytical exact single black hole solutions in four-dimensional Einstein-Maxwell theory belong to the accelerating Kerr-Newman-NUT family placed in backgrounds that are subcases of the conjugated Kerr-Newman-NUT spacetime with arbitrary angular topology.
citing papers explorer
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Generating Rotation in a Snap
An algebraic technique generates rotating black holes and multi-source solutions from static ones by transforming to AdS×S asymptotics, applying a rotating frame shift, and returning to flat asymptotics.
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Weyl-type solutions with multipolar scalar fields
New exact solutions to d-dimensional Einstein-scalar gravity are generated in Weyl form that incorporate multipolar scalars and magnetic fields, with limits matching scalar versions of Schwarzschild-Melvin and Fisher-Janis-Newman-Winicour spacetimes.
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Black holes in rotating, electromagnetic backgrounds and topological Kerr-Newman-NUT spacetimes
Essentially all known analytical exact single black hole solutions in four-dimensional Einstein-Maxwell theory belong to the accelerating Kerr-Newman-NUT family placed in backgrounds that are subcases of the conjugated Kerr-Newman-NUT spacetime with arbitrary angular topology.