arXiv subjects

Ivan Kolář

Publications and source records attributed to Ivan Kolář.

At least 19 recordsLinked to original sources

arXiv2026

Rotating near-horizon extreme geometries in quadratic gravity

Rotating near-horizon extreme solutions of quadratic gravity are analyzed combining power series expansions and numerical calculations. Restricting to geometries with symmetries of the near-horizon extreme Kerr black hole (i.e., with the $\mathrm{AdS_2}$-structure), spherical horizon topology, and equatorial reflection symmetry, we introduce conformal coordinates simplifying the field equations of Einstein--Weyl gravity, i.e., quadratic gravity with vanishing scalar curvature. Employing the Frobenius analysis, we classify all power series solutions expanded around the equator as well as the poles, and obtain the recurrence relations. With the help of numerical analysis, we study fine-tuning of the free parameter to satisfy the global constraints on regular near-horizon extreme geometries. Computations of the horizon area, horizon scalar curvature, and rotational scalar reveal strong horizon deformations in some Bachian branches. Moreover, the absence of regular Bachian near-horizon geometries above a finite horizon area suggests an upper bound on the size of the corresponding extremal rotating black holes.

gr-qc↗

arXiv2026

Quasi-topological gravity for 4-dimensional Taub-NUT, near-horizon extreme Kerr, and swirling symmetries

We classify 4-dimensional gravitational theories with integrability properties analogous to quasi-topological gravity, but for metrics with the symmetries of spherical, hyperbolic, and planar Schwarzschild and Taub-NUT solutions, their double-Wick-rotated counterparts - the B-metrics, the near-horizon extreme Kerr, and the swirling universe - and the Eguchi-Hanson instanton. These are the symmetries that allow consistent reductions (principle of symmetric criticality) with 4 Killing vectors and 3-dimensional orbits. Considering theories depending only on the Riemann tensor, we show that, for these metrics, only those with third-order equations (second-order after trivial integration) can be analytic in the Riemann tensor. We show that there is a unique theory with first-order field equations (algebraic after trivial integration, with the same integrability as general relativity) at each order in curvature and construct regular static black holes from infinite towers of these high-energy corrections to general relativity. For these theories, we obtain closed-form solutions for all the symmetries listed above, which we analyze to ensure they have a clear physical interpretation.

gr-qc↗

arXiv2026

Static spherically symmetric Kundt vacuum solutions of higher-derivative gravities

We study static spherically symmetric Kundt solutions to the vacuum field equations of quadratic gravity with a cosmological constant, as well as specific models of six-derivative gravity. In quadratic gravity, we identify all solutions for coupling constants satisfying ${α\neq3β}$, while the case ${α=3β}$ is studied using the Frobenius method, where we derive the recurrence relations for the power series. In contrast, in six-derivative gravity, we focus on selected models to illustrate the variety of closed-form solutions; we also analyze possible indicial families of Frobenius solutions. For all solutions, we analyze curvature singularities and their accessibility to geodesic observers. We then construct exact gravitational-wave solutions propagating on some of these backgrounds in quadratic and six-derivative gravity. It is known that in Einstein gravity, gravitational waves on the Nariai background unavoidably contain singularities, which are interpreted as physical sources generating these gravitational waves. In contrast, in addition to singular solutions, for appropriate values of the coupling constants, higher-order gravities allow for globally smooth solutions representing gravitational waves.

gr-qc↗

arXiv2026

Canonical quantization of all minisuperspaces with consistent symmetry reductions

We present the quantization of all symmetry reductions of the Einstein--Hilbert Lagrangian that correctly reproduce the reduced Einstein's field equations -- i.e., characterized by the infinitesimal group actions obeying the principle of symmetric criticality. These correspond to the spacetime symmetries of spherical/hyperbolic/planar Schwarzschild/Taub--NUT, BI/BII/BIII-metrics, near-horizon extreme Kerr geometry, swirling universe, closed/open/flat FLRW cosmologies, other FLRW-type metrics, and Bianchi type I, II, VIII, and IX spacetimes. We derive the Hamiltonian and the conformal symmetries of the superspace metrics (the conditional symmetries), promote them to operators, and solve the Wheeler--DeWitt equation with and without imposing these symmetries.

gr-qc↗

arXiv2026

Conical singularity in spacetimes with NUT is observer-dependent

We discuss the issue of defining and measuring conical deficits (conicity) in spacetimes with the torsion singularity such as the Misner string in Taub--NUT spacetime. We propose a geometric definition that generalizes the standard notion of conicity to stationary axially symmetric spacetimes with torsion singularity, where the conical deficit becomes observer-dependent -- it depends on the choice of a timelike Killing vector. This implies the existence of observers who perceive no conical singularity along the symmetry axis. As a result, in any spacetime with a non-vanishing NUT parameter, there are observers for whom the conicity has the same value on both semi-axes. This challenges the usual interpretation of conicity differences as indicators of string/rod-induced acceleration along the axis. We illustrate our definition across the full Plebański--Demiański class, including the recently identified accelerated Taub--NUT solution. Our attempts in determining a canonical observer lead to even less desirable definitions of conicity.

gr-qc↗

arXiv2026

Neglected solutions in quadratic gravity

We report on several previously overlooked families of static spherically symmetric solutions in quadratic gravity. Our main result concerns the existence of solutions whose leading exponents depend on the ratio ${ω=α/(3β)}$ of the four-derivative couplings. We demonstrate that the space of models with ${ω>1}$ contains a dense set that admits non-Frobenius solutions ${(s_*, 2 - 3 s_*)_0}$ (in standard Schwarzschild coordinates), with certain rational numbers $s_*(ω)$. These solutions correspond to a singular core at ${\bar{r}=0}$. Another related non-Frobenius family, $(s_*, 2 - 3 s_*)_\infty$, exists for a dense set of models with ${1/4 < ω< 1}$, describing a singular boundary at ${\bar{r}\to\infty}$. Both families are uncovered by recasting the metric into special coordinates in which the solutions become Frobenius. Additionally, for models with real ratios ${ω\neq 1}$ we identify six novel families of non-Frobenius solutions around points ${\bar{r}=\bar{r}_0} \neq 0$, describing horizons and wormhole throats. Finally, we re-derive and summarize all known families of solutions in modified as well as in the standard Schwarzschild coordinates.

gr-qc↗

arXiv2026

Carrollian limit of quadratic gravity

We study the Carrollian limit of the (general) quadratic gravity in four dimensions. We find that in order for the Carrollian theory to be a modification of the Carrollian limit of general relativity, the parameters in the action must depend on the speed of light in a specific way. By focusing on the leading and the next-to-leading orders in the Carrollian expansion, we show that there are four such non equivalent Carrollian theories. Imposing conditions to remove tachyons (from the linearized theory), we end up with a classification of Carrollian theories according to the leading-order and next-to-leading-order actions. All modify the Carrollian limit of general relativity with quartic terms of the extrinsic curvature. To the leading order, we show that two theories are equivalent to general relativity, one to $R+R^2$ theory, and one to the general quadratic gravity. To the next-to-leading order, two are equivalent to $R+R^2$ while the other two to the general quadratic gravity. We study the two theories that are equivalent to $R+R^2$ to the leading order and write their magnetic limit actions.

gr-qc↗

arXiv2026

Uniqueness of Galilean and Carrollian limits of gravitational theories and application to higher derivative gravity

We show that the seemingly different methods used to derive non-Lorentzian (Galilean and Carrollian) gravitational theories from Lorentzian ones are equivalent. Specifically, the pre-nonrelativistic and the pre-ultralocal parametrizations can be constructed from the gauging of the Galilei and Carroll algebras, respectively. Also, the pre-ultralocal approach of taking the Carrollian limit is equivalent to performing the ADM decomposition and then setting the signature of the Lorentzian manifold to zero. We use this uniqueness to write a generic expansion for the curvature tensors and construct Galilean and Carrollian limits of all metric theories of gravity of finite order ranging from the $f(R)$ gravity to a completely generic higher derivative theory, the $f(g_{μν},R_{μνσρ},\nabla_μ)$ gravity. We present an algorithm for calculation of the $n$-th order of the Galilean and Carrollian expansions that transforms this problem into a constrained optimization problem. We also derive the condition under which a gravitational theory becomes a modification of general relativity in both limits simultaneously.

gr-qc↗

arXiv2026

Carroll black holes in (A)dS and their higher-derivative modifications

We define the Carrollian black holes corresponding to the limit of Schwarzschild-(A)dS spacetime and its higher-derivative counterpart known as Schwarzschild-Bach-(A)dS spacetime, which is also a static spherically symmetric vacuum solution of quadratic gravity. By analyzing motion of massive particles in these geometries, we found that: In the case of Schwarzschild-(A)dS, a (nearly) tangential particle from infinity will wind around the extremal surface with a finite number of windings depending on the impact parameter and the cosmological constant. In Schwarzschild-Bach-(A)dS, a particle passing close enough to the extremal surface will have an infinite number of windings; hence, it will not escape to asymptotic infinity as in Schwarzschild-(A)dS. We also calculate the thermodynamical quantities for such black holes and argue that it is analogous to an incompressible thermodynamical system with divergent entropy when the temperature goes to zero (in the strict Carroll limit). We then define a divergent specific heat that can be positive, negative, or zero.

gr-qc↗

arXiv2025

Double Wick rotations between symmetries of Taub-NUT, near-horizon extreme Kerr, and swirling spacetimes

We explicitly show that certain 4-dimensional infinitesimal group actions with 3-dimensional orbits are related by double Wick rotations. In particular, starting with the symmetries of the spherical/hyperbolic/planar Taub-NUT spacetimes, one can obtain symmetries of the near-horizon extreme Kerr (NHEK) geometry or swirling universe by complex analytic continuations of coordinates. Similarly, the static spherical/hyperbolic/planar symmetries (i.e., symmetries of the Schwarzschild spacetime and other A-metrics) are mapped to symmetries of the B-metrics (or Melvin spacetime). All these mappings are theory-independent -- they constitute relations among symmetries themselves, and, hence among the classes of symmetry-invariant metrics and electromagnetic field strengths, rather than among specific solutions. Consequently, finding, e.g., vacuum Taub-NUT-type solutions in a given gravitational theory automatically yields vacuum NHEK- or swirling-type solutions of that theory, with a possible extension to the electromagnetic case.

gr-qc↗

arXiv2025

Black holes and other exact solutions in six-derivative gravity

We study exact static spherically symmetric vacuum solutions in generic six-derivative gravity (i.e., without assuming specific relations between the coupling constants). Using modified Schwarzschild coordinates, we systematically classify solutions through Frobenius expansions, determining their number of free parameters and confirming previously known cases, such as the regular solutions at the origin. Importantly, we identify novel solutions absent in four-derivative gravity, including those with (double-degenerate) extreme horizons (and their near-horizon limits) that exist without matter sources, which may indicate the existence of regular black holes. We also find asymptotically (anti-)de Sitter spacetimes, giving rise to an effective cosmological constant. The solutions can be classified into six main classes, and, when possible, we provide the description in standard Schwarzschild coordinates, in which they split into thirteen main solution classes.

gr-qc↗

arXiv2025

Rotating Carroll Black Holes: A No Go Theorem

Recently, there has been a lot of interest in Carroll black holes and in particular whether or not one could find a Carrollian analogue of a rotating black hole spacetime. Here we show that every stationary and axisymmetric solution (and thence also a black hole) of Carrollian general relativity in any number of $d>3$ dimensions is necessarily also static (up to a "topological rotation"). The case of $d=3$ dimensions is special. There, the topological rotation is important and one can have a rotating Carroll BTZ black hole, obtained from a static one by the Carroll boost accompanied by the re-identification of the angular coordinate, similar to what happens in the Lorentzian case. We also find a Carrollian analogue of an accelerating black hole, showing that Schwarzschild is not the only possible stationary and axisymmetric Carroll black hole in four dimensions. A generalization of the no go theorem to include Maxwell, dilatonic, and axionic matter fields is also discussed.

hep-th↗

arXiv2025

Symmetry reduction of gravitational Lagrangians

We analyze all possible symmetry reductions of Lagrangians that yield fully equivalent field equations for any 4-dimensional metric theory of gravity. Specifically, we present a complete list of infinitesimal group actions obeying the principle of symmetric criticality, identify the corresponding invariant metrics (and $l$-chains), discuss relations among them, and analyze simplifications allowed by the residual diffeomorphism group and Noether identities before and after variation of the reduced Lagrangian. We employ rigorous treatment of the symmetry reduction by Fels and Torre and use the Hicks classification of infinitesimal group actions by means of Lie algebras pairs of isometries and their isotropy subalgebras. The classification is recast in the coordinates in which the well-known symmetries and geometries are easily recognizable and relatable to each other. The paper is accompanied by a code for the symmetry reduction of Lagrangians that we developed in \texttt{xAct} package of \textsc{Mathematica}.

gr-qc↗

arXiv2025

Inner-extremal regular black holes from pure gravity

Recently it was shown that essentially all regular black hole models constructed so far can be obtained as solutions of vacuum gravity equations, upon considering an infinite series of quasi-topological higher curvature corrections. Here we show that such a construction can be upgraded to yield regular black holes with vanishing inner horizon surface gravity. In four dimensions, such a condition is necessary for the absence of classical instabilities associated with mass inflation on the inner horizon.

gr-qc↗

arXiv2025

Dust collapse and horizon formation in Quadratic Gravity

Quadratic Gravity supplements the Einstein-Hilbert action by terms quadratic in the spacetime curvature. This leads to a rich phase space of static, compact gravitating objects including the Schwarzschild black hole, wormholes, and naked singularities. For the first time, we study the collapse of a spherically symmetric star with uniform dust density in this setting. We assume that the interior geometry respects the symmetries of the matter configuration, i.e., homogeneity and isotropy, thus it is insensitive to the Weyl-squared term and the interior dynamics is fully determined by $R$ and $R^2$. As our main result, we find that the collapse leads to the formation of a horizon, implying that the endpoint of a uniform dust collapse with a homogeneous and isotropic interior is not a horizonless spacetime. We also show that the curvature-squared contribution is responsible for making the collapse into a singularity faster than the standard Oppenheimer-Snyder scenario. Furthermore, the junction conditions connecting spacetime inside and outside the matter distribution are found to be significantly more constraining than their counterparts in General Relativity and we discuss key properties of any exterior solution matching to the spacetime inside the collapsing star. Finally, we comment on the potentially non-generic behavior entailed by our assumptions.

gr-qc↗

arXiv2025

Intrinsically-defined higher-derivative Carrollian scalar field theories without Ostrogradsky instability

We derive the most generic Carrollian higher derivative free scalar field theory intrinsically on a Carrollian manifold. The solutions to these theories are massless free particles propagating with speeds depending on the coupling constants in the Lagrangian, thus, allowing interference solutions which are not allowed on a Lorentzian manifold. This demonstrates that the set of solutions to the Carrollian theories is much larger than that of their Lorentzian counterparts. We also show that Carrollian higher derivative theories are more resistant to Ostrogradsky's instabilities. These instabilities can be resolved by choosing the coupling constants appropriately in the Carrollian Lagrangian, something that was proven to be impossible in Lorentzian theories.

hep-th↗

arXiv2024

Toward regular black holes in sixth-derivative gravity

We study spherically symmetric static solutions of the most general sixth-derivative gravity using series expansions. Specifically, we prove that the only solutions of the complete theory (i.e., with generic coupling constants) that possess a Frobenius expansion around the origin, $r=0$, are necessarily regular. When restricted to specific branches of theories (i.e., imposing particular constraints on the coupling constants), families of potentially singular solutions emerge. By expanding around $r=r_0 \neq 0$, we identify solutions with black hole horizons. Finally, we argue that, unlike in fourth-derivative gravity, the conditions $R=0$ and $g_{tt}g_{rr}=-1$ are too restrictive for sixth-derivative gravity solutions.

gr-qc↗

arXiv2024

Mixing "Magnetic'' and "Electric'' Ehlers--Harrison transformations: The Electromagnetic Swirling Spacetime and Novel Type I Backgrounds

In this paper, we obtain a complete list of stationary and axisymmetric spacetimes, generated from a Minkowski spacetime using the Ernst technique. We do so by operating on the associated seed potentials with a composition of Ehlers and Harrison transformations. In particular, assigning an additional ``electric'' or ``magnetic'' tag to the transformations, we investigate the new spacetimes obtained either via a composition of magnetic Ehlers and Harrison transformations (first part) or via a magnetic-electric combination (second part). In the first part, the resulting type D spacetime, dubbed electromagnetic swirling universe, features key properties, separately found in swirling and (Bonnor--)Melvin spacetimes, the latter recovered in appropriate limits. A detailed analysis of the geometry is included, and subtle issues are addressed. A detailed proof that the spacetime belongs to the Kundt family, is included, and a notable relation to the planar-Reissner-Nordström-NUT black hole is also meticulously worked out. This relation is further exploited to reverse-engineer the form of the solution in the presence of a nontrivial cosmological constant. A Schwarzschild black hole embedded into the new background is also discussed. In the second part, we present four novel stationary and axisymmetric asymptotically nonflat type I spacetimes, which are naively expected to be extensions of the Melvin or swirling solution including a NUT parameter or electromagnetic charges. We actually find that they are, under conditions, free of curvature and topological singularities, with the physical meaning of the electric transformation parameters in these backgrounds requiring further investigation.

gr-qc↗