New gravitational instanton: shadow of an extra dimension
Abstract
We present an exact gravitational instanton solution on a five-dimensional, conformally invariant, Kerr-like warped Riemannian brane-world manifold. The geometry can be described as the Kähler manifold ℂ1×ℂ1× ℝ. By applying a double cover of S3 through stereographic projection onto ℂP1× ℂP1 of the effective four-dimensional manifold, together with the Klein surface construction, we exploit the underlying ℤ2 symmetry. The instanton is then obtained by fibering over the antipodal S2. The metric is determined by a first-order differential equation containing an integer parameter, while the equation governing the angular momentum component decouples from the remaining field equations. Finally, we show that our solution admits an analytic complex transformation to a locally conformally related Kähler manifold possessing a Kähler potential, thereby making the self-dual structure manifest.
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BibTeX
@misc{slagter2026gravitational,
title = {{New gravitational instanton: shadow of an extra dimension}},
author = {Reinoud Jan Slagter},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.03536},
eprint = {2608.03536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.03536},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New gravitational instanton: shadow of an extra dimension
AU - Reinoud Jan Slagter
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.03536
UR - https://arxiv.org/abs/2608.03536
AB - We present an exact gravitational instanton solution on a five-dimensional, conformally invariant, Kerr-like warped Riemannian brane-world manifold. The geometry can be described as the Kähler manifold ℂ^1×ℂ^1× ℝ. By applying a double cover of S^3 through stereographic projection onto ℂP^1× ℂP^1 of the effective four-dimensional manifold, together with the Klein surface construction, we exploit the underlying ℤ_2 symmetry. The instanton is then obtained by fibering over the antipodal S^2. The metric is determined by a first-order differential equation containing an integer parameter, while the equation governing the angular momentum component decouples from the remaining field equations. Finally, we show that our solution admits an analytic complex transformation to a locally conformally related Kähler manifold possessing a Kähler potential, thereby making the self-dual structure manifest.
ER -