B\"acklund transforms of the extreme Kerr near-horizon geometry
Reinhard Meinel, Andreas Kleinw\"achter
TL;DR
This paper uses Bäcklund transformations to generate a hierarchy of exact vacuum Einstein solutions based on the extreme Kerr near-horizon geometry, allowing for multiple free parameters.
Contribution
It introduces a novel application of Bäcklund transformations to produce a new class of solutions with flexible parameters in the context of extreme Kerr geometries.
Findings
Generated a hierarchy of exact solutions with arbitrary parameters.
Extended the solution space of the vacuum Einstein equations near the extreme Kerr horizon.
Demonstrated the method's capability to produce solutions with specific asymptotics.
Abstract
We apply the method of B\"acklund transformations to generate a new hierarchy of exact solutions to the vacuum Einstein equations starting from the extreme Kerr near-horizon geometry. Solutions with extreme Kerr near-horizon asymptotics containing an arbitrary number of free parameters are included.
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