SO(n + 1) Symmetric Solutions of the Einstein Equations in Higher Dimensions
M. Jakimowicz, J. Tafel
TL;DR
This paper introduces a method for solving Einstein equations with scalar fields, applied to find higher-dimensional vacuum metrics with SO(n + 1) symmetry acting on spheres.
Contribution
It presents a novel approach to derive higher-dimensional vacuum solutions with specific symmetry properties in Einstein's equations.
Findings
Derived new higher-dimensional vacuum metrics with SO(n + 1) symmetry.
Demonstrated the applicability of the method to scalar field-involved Einstein equations.
Provided explicit solutions invariant under SO(n + 1) group actions.
Abstract
A method of solving the Einstein equations with a scalar field is presented. It is applied to find higher dimensional vacuum metrics invariant under the group SO(n + 1) acting on n-dimensional spheres.
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