Charging higher-dimensional spacetimes with a generalized Kerr-Schild transformation
Abstract
We explore the construction of higher-dimensional Einstein-Maxwell(-Chern-Simons) solutions from vacuum seeds by means of a generalized Kerr-Schild transformation along a geodesic null vector field k. Assuming the vector potential A to be aligned with k, and k to be a Weyl aligned null direction satisfying the ``optical constraint'', we arrive at three distinct branches of solutions. If k is expanding and twisting, then its shear must vanish -- this branch includes certain charged Taub-NUT metrics. If k is expanding and twistfree, one finds two subfamilies: Robinson-Trautman electrovac solutions with a non-null Maxwell field if the shear is zero, or shearing solutions with a null field. Finally, the case when k is non-expanding reduces to a subset of the known Kundt solutions. In all cases, the Chern-Simons term turns out to be identically zero on-shell. In passing, by relaxing the alignment assumption on A, we also obtain a six-dimensional extension of a charged Taub-NUT metric for which the magnetic part of the field strength is a linear combination of two distinct Kähler 2-forms, as opposed to the previously known examples in more than four dimensions.
Related
- Geometrically Induced Semiclassical Limit for Quasinormal Modes and Greybody Factors in Higher-Dimensional Near-Ultracold spacetimes
- Swirling spacetimes in higher dimensions: Vacuum backgrounds and black holes
- Generalized complexity and dynamical response in holographic Vaidya spacetimes
- Dimensional reduction associated with unchanged direction trajectories in flat fiber Robertson Walker spacetimes
- Reservoir computing generalized: Exploiting complex dynamics via time-invariant transformation
BibTeX
@misc{srinivasan2026charging,
title = {{Charging higher-dimensional spacetimes with a generalized Kerr-Schild transformation}},
author = {Aravindhan Srinivasan and Marcello Ortaggio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01012},
eprint = {2609.01012},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01012},
}
RIS
TY - UNPB
TI - Charging higher-dimensional spacetimes with a generalized Kerr-Schild transformation
AU - Aravindhan Srinivasan
AU - Marcello Ortaggio
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01012
UR - https://arxiv.org/abs/2609.01012
AB - We explore the construction of higher-dimensional Einstein-Maxwell(-Chern-Simons) solutions from vacuum seeds by means of a generalized Kerr-Schild transformation along a geodesic null vector field k. Assuming the vector potential A to be aligned with k, and k to be a Weyl aligned null direction satisfying the ``optical constraint'', we arrive at three distinct branches of solutions. If k is expanding and twisting, then its shear must vanish -- this branch includes certain charged Taub-NUT metrics. If k is expanding and twistfree, one finds two subfamilies: Robinson-Trautman electrovac solutions with a non-null Maxwell field if the shear is zero, or shearing solutions with a null field. Finally, the case when k is non-expanding reduces to a subset of the known Kundt solutions. In all cases, the Chern-Simons term turns out to be identically zero on-shell. In passing, by relaxing the alignment assumption on A, we also obtain a six-dimensional extension of a charged Taub-NUT metric for which the magnetic part of the field strength is a linear combination of two distinct Kähler 2-forms, as opposed to the previously known examples in more than four dimensions.
ER -