Swirling spacetimes in higher dimensions: Vacuum backgrounds and black holes
Abstract
We construct higher-dimensional swirling spacetimes in vacuum General Relativity using the hidden symmetries of the dimensionally reduced theory. Working directly with the coset-space formulation, we perform in five dimensions a reduction along the two independent axial Killing vectors, obtaining an SL(3,ℝ)/SO(3) sigma model and a genuinely five-dimensional background with two independent swirling parameters. The same transformation yields doubly swirling Schwarzschild--Tangherlini and Myers--Perry geometries. A distinctive feature of the new background is its multidirectional asymptotic structure. Correlated radial-angular limits reveal directional curvature singularities that are invisible in the usual large-radius limit at fixed angle. We further exhibit causal geodesics that reach such singular asymptotic ends in finite affine parameter. Finally, we describe the maximally axial extension of this construction to higher dimensions: five dimensions are maximal for an entirely axial reduction to three dimensions, while six dimensions admit an additional nontrivial translational deformation, with further dimensions contributing only flat spectator directions.
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BibTeX
@misc{barrientos2026swirling,
title = {{Swirling spacetimes in higher dimensions: Vacuum backgrounds and black holes}},
author = {José Barrientos and Adolfo Cisterna and Carlos Herdeiro and Konstantinos Pallikaris},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12372},
eprint = {2610.12372},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12372},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Swirling spacetimes in higher dimensions: Vacuum backgrounds and black holes
AU - José Barrientos
AU - Adolfo Cisterna
AU - Carlos Herdeiro
AU - Konstantinos Pallikaris
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12372
UR - https://arxiv.org/abs/2610.12372
AB - We construct higher-dimensional swirling spacetimes in vacuum General Relativity using the hidden symmetries of the dimensionally reduced theory. Working directly with the coset-space formulation, we perform in five dimensions a reduction along the two independent axial Killing vectors, obtaining an SL(3,ℝ)/SO(3) sigma model and a genuinely five-dimensional background with two independent swirling parameters. The same transformation yields doubly swirling Schwarzschild--Tangherlini and Myers--Perry geometries. A distinctive feature of the new background is its multidirectional asymptotic structure. Correlated radial-angular limits reveal directional curvature singularities that are invisible in the usual large-radius limit at fixed angle. We further exhibit causal geodesics that reach such singular asymptotic ends in finite affine parameter. Finally, we describe the maximally axial extension of this construction to higher dimensions: five dimensions are maximal for an entirely axial reduction to three dimensions, while six dimensions admit an additional nontrivial translational deformation, with further dimensions contributing only flat spectator directions.
ER -