arXiv subjects

Alex Colling

Publications and source records attributed to Alex Colling.

5 recordsLinked to original sources

arXiv2026

Charged and rotating near-horizon geometries in five dimensions

We present new charged and rotating near-horizon geometries in five-dimensional Einstein-Maxwell theory in closed analytic form. The solutions can be parametrised by the charge and two independent angular momenta. We also generalise these near-horizon geometries to theories with an additional Chern-Simons term in the action multiplied by an arbitrary coupling constant. The new solutions have the same entropy relations as expected for charged versions of extremal Myers-Perry black holes and for rotating versions of extremal Reissner-Nordstr\"om-Tangherlini black holes, but they do not reduce to the Myers-Perry horizon in the vacuum limit. The horizon cross-sections are spherical and carry a Sasakian structure. We exploit this structure to prove a characterisation of our solutions: without any symmetry assumptions, they are the most general rotating extremal horizons for which the co-rotating electric field is a (non-zero) constant. We further extend this construction to higher dimensions, where we show that any Sasaki-Einstein manifold generates a two-parameter family of charged and rotating horizons.

hep-th↗

arXiv2025

Symmetries of extremal horizons

We prove an intrinsic analogue of Hawking's rigidity theorem for extremal horizons in arbitrary dimensions: any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing vector field. If the dominant energy condition is satisfied for null vectors, it follows that an extension of the near-horizon geometry admits an enhanced isometry group containing $SO(2,1)$ or the 2D Poincar\'e group $\mathbb{R}^2 \rtimes SO(1,1)$. In the latter case, the associated Aretakis instability for a massless scalar field is shifted by one order in the derivatives of the field transverse to the horizon. We consider a broad class of examples including Einstein-Maxwell(-Chern-Simons) theory and Yang-Mills theory coupled to charged matter. In these examples we show that the symmetries are inherited by the matter fields.

gr-qc↗

arXiv2025

Quasi-Einstein structures and Hitchin's equations

We prove (Theorem 1.1.) that a class of quasi-Einstein structures on closed manifolds must admit a Killing vector field. This extends the rigidity theorem obtained in \cite{DL23} for the extremal black hole horizons and completes the classification of compact quasi-Einstein 2-manifolds in this class. We also explore special cases of the quasi-Einstein equations related to integrability and the Hitchin equations, as well as to Einstein-Weyl structures and Kazdan-Warner type PDEs. This leads to novel explicit examples of quasi-Einstein structures on (non-compact) 2-manifolds and on $S^2 \times S^1$.

math.DG↗

arXiv2024

Rigidity of the extremal Kerr-Newman horizon

We prove that the intrinsic geometry of compact cross-sections of an extremal horizon in four-dimensional Einstein-Maxwell theory must admit a Killing vector field or is static. This implies that any such horizon must be an extremal Kerr-Newman horizon and completes the classification of the associated near-horizon geometries. The same results hold with a cosmological constant.

gr-qc↗

arXiv2024

New quasi-Einstein metrics on a two-sphere

We construct all axi-symmetric non-gradient $m$-quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon corresponding to $m=2$, as well as a family of new regular metrics with $m\neq 2$ given in terms of hypergeometric functions. We also show that in the case $m=-1$ with vanishing cosmological constant the only orientable compact solution in dimension two is the flat torus, which proves that there are no compact surfaces with a metrisable affine connection with skew Ricci tensor.

math.DG↗