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Jan Gutowski

Publications and source records attributed to Jan Gutowski.

9 recordsLinked to original sources
arXiv2026

Classification of Killing Horizons in D=11 Supergravity

We initiate the classification of supersymmetric degenerate Killing horizons, with closed spatial cross section, away from the near-horizon limit in D=11 supergravity. We prove that all such solutions fall into two distinct classes, depending on lightcone chirality with respect to a Gaussian null coordinate system. For the first class of solutions, the negative lightcone chirality part of the Killing spinor is non-zero on the Killing horizon, and we prove that all such solutions are isometric to supersymmetric near-horizon geometries. In the second class, the negative lightcone chirality part of the Killing spinor vanishes on the Killing horizon. In this case, we prove that the spinorial Lie derivative of the Killing spinor with respect to the Killing vector which generates the Killing horizon vanishes, and that all such solutions with more than 13 supersymmetries are pp-waves.

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arXiv2025

Extremal Black Holes from Homotopy Algebras

The uniqueness and rigidity of black holes remain central themes in gravitational research. In this work, we investigate the construction of all extremal black hole solutions to the Einstein equation for a given near-horizon geometry, employing the homotopy algebraic perspective, a powerful and increasingly influential framework in both classical and quantum field theory. Utilising Gau{\ss}ian null coordinates, we recast the deformation problem as an analysis of the homotopy Maurer-Cartan equation associated with an $L_\infty$-algebra. Through homological perturbation theory, we systematically solve this equation order by order in directions transverse to the near-horizon geometry. As a concrete application of this formalism, we examine the deformations of the extremal Kerr horizon. Notably, this homotopy-theoretic approach enables us to characterise the moduli space of deformations by studying only the lowest-order solutions, offering a systematic way to understand the landscape of extremal black hole geometries.

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arXiv2019

From Static to Cosmological Solutions of N=2 Supergravity

We obtain cosmological solutions with Kasner-like asymptotics in N=2 gauged and ungauged supergravity by maximal analytic continuation of planar versions of non-extremal black hole solutions. Initially, we construct static solutions with planar symmetry by solving the time-reduced field equations. Upon lifting back to four dimensions, the resulting static regions are incomplete and bounded by a curvature singularity on one side and a Killing horizon on the other. Analytic continuation reveals the existence of dynamic patches in the past and future, with Kasner-like asymptotics. For the ungauged STU-model, our solutions contain previously known solutions with the same conformal diagram as a subset. We find explicit lifts to five, six, ten and eleven dimensions which show that in the extremal limit, the underlying brane configuration is the same as for STU black holes. The extremal limit of the six-dimensional lift is shown to be BPS for special choices of the integration constants. We argue that there is a universal correspondence between spherically symmetric black hole solutions and planar cosmological solutions which can be illustrated using the Reissner-Nordström solution of Einstein-Maxwell theory.

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arXiv2016

Einstein--Weyl Spaces and Near-Horizon Geometry

We show that a class of solutions of minimal supergravity in five dimensions is given by lifts of three--dimensional Einstein--Weyl structures of hyper-CR type. We characterise this class as most general near--horizon limits of supersymmetric solutions to the five--dimensional theory. In particular, we deduce that a compact spatial section of a horizon can only be a Berger sphere, a product metric on $S^1\times S^2$ or a flat three-torus. We then consider the problem of reconstructing all supersymmetric solutions from a given near--horizon geometry. By exploiting the ellipticity of the linearised field equations we demonstrate that the moduli space of transverse infinitesimal deformations of a near--horizon geometry is finite--dimensional.

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arXiv2013

Enhanced Euclidean supersymmetry, 11D supergravity and $SU(\infty)$ Toda equation

We show how to lift solutions of Euclidean Einstein-Maxwell equations with non-zero cosmological constant to solutions of eleven-dimensional supergravity theory with non-zero fluxes. This yields a class of 11D metrics given in terms of solutions to $SU(\infty)$ Toda equation. We give one example of a regular solution and analyse its supersymmetry. We also analyse the integrability conditions of the Killing spinor equations of N=2 minimal gauged supergravity in four Euclidean dimensions. We obtain necessary conditions for the existence of additional Killing spinors, corresponding to enhancement of supersymmetry. If the Weyl tensor is anti-self-dual then the supersymmetric metrics satisfying these conditions are given by separable solutions to the $SU(\infty)$ Toda equation. Otherwise they are ambi-Kähler and are conformally equivalent to Kähler metrics of Calabi type or to product metrics on two Riemann surfaces.

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arXiv2010

Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Anti-Self-Dual Solutions

We classify super-symmetric solutions of the minimal $N=2$ gauged Euclidean supergravity in four dimensions. The solutions with anti-self-dual Maxwell field give rise to anti-self-dual Einstein metrics given in terms of solutions to the $SU(\infty)$ Toda equation and more general three-dimensional Einstein--Weyl structures. Euclidean Kastor--Traschen metrics are also characterised by the existence of a certain super covariantly constant spinor.

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arXiv2007

The return of the four- and five-dimensional preons

We prove the existence of 3/4-BPS preons in four- and five-dimensional gauged supergravities by explicitly constructing them as smooth quotients of the AdS_4 and AdS_5 maximally supersymmetric backgrounds, respectively. This result illustrates how the spacetime topology resurrects a fraction of supersymmetry previously ruled out by the local analysis of the Killing spinor equations.

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arXiv1999

Generalized Calibrations

We present a generalization of calibrations in which the calibration form is not closed. We use this to examine a class of supersymmetric p-brane worldvolume solitons.As an example we consider M5-brane worldvolume solitons in an AdS background.

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