arXiv subjects

Jiri Podolsky

Publications and source records attributed to Jiri Podolsky.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamics of Genuine Kerr-Bertotti-Robinson Black Holes

We propose a thermodynamic description of the genuine Kerr-Bertotti-Robinson (Kerr-BR) black hole spacetimes. Contrary to previous studies, such solutions no longer have electric charge. Consequently, the thermodynamics is governed by simple relations. Namely, upon introducing a suitable normalization factor for the timelike Killing vector, these spacetimes are characterized by the standard Hawking temperature, Bekenstein's entropy, Komar mass and angular momentum, and horizon angular velocity. The corresponding mass is shown to obey the standard Christodoulou-Ruffini formula, along with the standard first law and Smarr relations. In fact, by a proper rescaling of coordinates and solution parameters, and up to a non-trivial parameter space constraint, we formally recover the thermodynamic quantities of the vacuum Kerr solution. This is used to bring the genuine Kerr-BR spacetime into a Kerr-like form.

gr-qc↗

arXiv2026

Kerr-Newman and genuine Kerr black holes in the Bertotti-Robinson magnetic field

We present a spacetime that describes a rotating and charged black hole immersed in an external magnetic field. This exact solution to the Einstein-Maxwell equations has a surprisingly simple form which reduces to standard Kerr-Newman metric, and to the uniform Bertotti-Robinson magnetic universe. We show that the Kerr-BR solution presented in [Phys. Rev. Lett. {\bf 135}, 181401 (2025)] has a special charge, and we identify a genuine Kerr black hole without any charge, in the magnetic field. In the weak-field limit it gives the Wald solution. We analyze main physical properties of the new family, namely singularities, horizons, regularity of axes, charges, entropy and temperature.

gr-qc↗

arXiv2026

New metric useful for studies of gravitational radiation from accelerating black holes of type D with any cosmological constant

We apply a convenient parametrization of all Plebanski-Demianski black holes of algebraic type D with the Kerr rotation, NUT twist, acceleration, electric and magnetic charges, and any value of the cosmological constant $Λ$, recently found by Astorino. This represents a complete class of exact solutions to the Einstein-Maxwell-$Λ$ equations such that the (non-null) electromagnetic field is aligned with both the (geodesic, shear-free, double) principal null directions of the Weyl tensor. We derive a novel appropriate metric form and the corresponding canonical frames naturally adapted to both the de~Sitter-like ($Λ>0$) and the anti-de~Sitter-like ($Λ<0$) conformal infinity, and we demonstrate that these geometric objects are useful for investigation of radiation properties. In particular, using the Fernandez-Alvarez-Senovilla criterion, it confirms that the gravitational radiation is present if, and only if, these black holes are accelerating.

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arXiv2026

Uniqueness of stationary axisymmetric type D black holes with non-aligned electromagnetic field

We demonstrate the uniqueness of the spacetimes recently found by us in [H. Ovcharenko and J. Podolsky, Phys. Rev. D 112 (2025) 064076]. First, we prove that the conformal-to-Carter metric ansatz we used therein is the only possible for stationary axisymmetric geometries that are of Weyl type D, with geodesic and shear-free principal null directions (PNDs) which are orthogonal to polar directions, and whose specific 1-form $θ$ is closed. Because this result is general, without employing any field equations, such conformal-to-Carter metric may find interesting applications also in various alternative theories of gravity. Then, we show that in the Einstein-Maxwell theory the only non-trivial electrovacuum solution for the conformal-to-Carter metric with the fully non-aligned and non-null electromagnetic field is the Ovcharenko-Podolsky class found in 2025. Complementarily, the only solution with the double-aligned and non-null electromagnetic field is the Plebański-Demiański class found in 1976.

gr-qc↗

arXiv2026

Static black holes in an external uniform electromagnetic field: Reissner-Nordstrom accelerating in Bertotti-Robinson

We provide a detailed analysis of the non-twisting subcase of the large class of type D black holes with a non-aligned electromagnetic field, presented recently in [H. Ovcharenko and J. Podolsky, Phys. Rev. D 112 (2025) 064076]. We show that such exact solutions split into two main subclasses that (after a suitable re-parametrization) can be interpreted as either the uncharged Schwarzschild or C-metric in the external Bertotti-Robinson (BR) spacetime with geometry ${\mathrm{AdS}_2\times\mathrm{S}_2}$, or as the charged Reissner-Nordstrom black hole accelerating in the external BR electromagnetic field. The distinction between these two subclasses is determined by the parameter $r_0$ that encodes relations between the external Maxwell field (given by the non-aligned components of the Faraday tensor ${Φ_0=Φ_2}$) and the Maxwell field created by the charge of the black hole (given by the aligned component $Φ_1$). Namely, if ${r_0=0}$ then the electromagnetic field is fully determined by ${Φ_0=Φ_2}$, and one gets the C-metric in the BR universe (including also the non-accelerating Schwarzschild-BR black hole). But if ${r_0\neq 0}$ then the electromagnetic field is independently determined by both the external BR field and the field of a black hole itself, and this can be interpreted as the Reissner-Nordstrom black hole accelerating in the Bertotti-Robinson spacetime. Even though such an interpretation of the spacetime family is quite simple, it contains a lot of subtleties (e.g. the no-charge limit of the RN-BR spacetime, the non-trivial dependence on the signs of the mass and charge of a black hole, extreme black holes, and others) which we carefully investigate in this work. We also show the explicit relation to solutions previously found by Van den Bergh and Carminati, and we discuss the connection to the Alekseev-Garcia and Alexeev solutions.

gr-qc↗

arXiv2025

Hidden symmetries and separability structures of Ovcharenko-Podolský and conformal-to-Carter spacetimes

Recently, a remarkable new class of spacetimes describing black holes immersed in a non-aligned electromagnetic field has been found. While still of type D, this class goes beyond the famous Plebański--Demiański family. Here we demonstrate that the whole class admits a hidden symmetry encoded in the non-degenerate conformal Killing--Yano 2-form. Interestingly, as a direct consequence of non-alignment of the electromagnetic field and contrary to the Plebański--Demiański class (where the field is aligned), such a symmetry no longer generates the full "tower of symmetries". Despite this, it enables one to separate variables in massless Hamilton--Jacobi, conformal wave, and massless Dirac equations, as well as allows one to tackle massless vector and tensor perturbations. These results provide a useful mathematical tool for discussing numerous (astrophysical) applications to be described by these metrics. Moreover, as we shall show, the novel spacetimes provide an interesting test-ground for studying the recently defined Penrose charges whose existence is intrinsically related to hidden rather than explicit symmetries.

gr-qc↗

arXiv2025

Algebraic classification of 2+1 geometries

We present a new effective method of algebraic classification of 2+1 geometries. Our approach simply classifies spacetimes using five real scalars, defined as specific projections of the Cotton tensor onto a suitable null basis. The algebraic type of a spacetime is determined by gradual vanishing of these scalars. We derive the Bel-Debever criteria, together with the multiplicity of the Cotton aligned null directions (CANDs). Additionally, we provide a frame-independent algorithm for classification based on the polynomial curvature invariants and show the equivalence to previous methods of classification.

gr-qc↗

arXiv2025

A novel class of rotating black holes with non-aligned electromagnetic field

We present a new class of expanding and twisting solutions to the Einstein-Maxwell equations of algebraic type D, where the null eigendirections of the Faraday tensor are not aligned with PNDs of the Weyl tensor. After deriving this novel solution, we explore its various metric forms and parameterizations. In suitable coordinates, the solution depends on six physical parameters, namely mass $m$, Kerr and NUT twist parameters $a$ and $l$, complex charge $c$, acceleration $α$, and parameter $β$ that governs the interplay between electric and magnetic charges in the aligned part of the Faraday tensor. This parameterization, as the Griffiths-Podolský form of the Plebański-Demiański solution, facilitates explicit special subcases, such as Kerr-Newman black holes, and a deeper physical interpretation. Additionally, in the static limit, our solution reduces to previously known cases.

gr-qc↗

arXiv2025

Various metric forms of all type D black holes and their application

Several recent results concerning the complete class of exact solutions to the Einstein-Maxwell-$Λ$ equations of type D with a double-aligned electromagnetic field are summarized. This large class of spacetimes includes charged black holes with rotation, NUT parameter, and acceleration. In particular, we present their Plebanski-Demianski, Griffiths-Podolsky-Vratny, and Astorino metric representations, we discuss mutual relations between them, and demonstrate their usefulness for investigation of physical and geometrical properties (singularities, horizons, conformal diagrams, ergoregions, rotating strings causing the acceleration, thermodynamics). It includes the proof that such black holes emit gravitational radiation if, and only if, they accelerate. Very recent extension to type D black holes with non-aligned Maxwell field is also mentioned.

gr-qc↗

arXiv2025

Kerr black hole in a uniform Bertotti-Robinson magnetic field: An exact solution

A new class of exact spacetimes in Einstein's gravity, which are Kerr black holes immersed in an external magnetic (or electric) field that is asymptotically uniform and oriented along the rotational axis, is presented. These are axisymmetric stationary solutions to the Einstein-Maxwell equations such that (unlike in the Plebanski-Demianski spacetime) the null directions of the Faraday tensor are not aligned with neither of the two principal null directions of the Weyl tensor of algebraic type D (unlike the Kerr-Melvin spacetime). Three physical parameters are the black hole mass $m$, its rotation $a$, and the external field value $B$. For vanishing $B$ the metric directly reduces to standard Boyer-Lindquist form of the Kerr black hole, while for zero $m$ we recover conformally flat Bertotti-Robinson universe with a uniform Maxwell field. For zero $a$ the spacetime is contained in the Van den Bergh-Carminati solutions which can be understood as the Schwarzschild black hole in a magnetic field. Our family of black holes with non-aligned Maxwell hair - that can be called the Kerr-Bertotti-Robinson (Kerr-BR) black holes - may find application in various studies ranging from mathematical relativity to relativistic astrophysics.

gr-qc↗

arXiv2025

Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation

We study relative motion of nearby test particles in Topologically Massive Gravity (TMG) in three spacetime dimensions, using the equation of geodesic deviation. We show that, in a suitable reference frame, the influence of any gravitational field can be decomposed into transverse, longitudinal, and Newtonian components, which are directly related to the Cotton scalars of the Newman-Penrose-type. In particular, we prove that Cotton type N spacetimes exhibit a purely transverse gravitational effect on test particles, and can thus be reasonably interpreted as specific gravitational waves with a single polarization mode in TMG. The influence of the cosmological constant manifests itself as an isotropic effect. We also discuss the physical interpretation of spacetimes of specific algebraic types, as well as the influence of various matter fields, namely pure radiation, perfect fluid, and electromagnetic field. As an example, we provide an explicit analysis of TN-waves and pp-waves in three-dimensional TMG.

gr-qc↗

arXiv2025

Revisiting black holes of algebraic type D with a cosmological constant

As an extension of our previous work [1] (arXiv:2409.02308), we study a complete family of type D black holes with Kerr-like rotation, NUT twist, acceleration, electric and magnetic charges, and any value of the cosmological constant $Λ$. We relate various metric forms of these spacetimes, namely those found by Plebanski-Demianski (PD), Griffiths-Podolsky (GP), and most recently Astorino (A). By explicit coordinate transformations and proper identification of the physical parameters we show that these representations are locally equivalent, and cover the entire class of type D solutions of the Einstein-Maxwell-$Λ$ equations, such that the (non-null) electromagnetic field is aligned with both the (double-degenerate) principal null directions of the Weyl tensor. In particular, we concentrate on the subclass which describes accelerating NUT black holes without the Kerr-like rotation.

gr-qc↗

arXiv2024

Black holes of type D revisited: relating their various metric forms

We investigate a complete family of spacetimes which represent black holes with rotation, NUT twist, acceleration, electric and magnetic charges. These are exact solutions of the Einstein-Maxwell equations with any cosmological constant, such that the (non-null) electromagnetic field is aligned with both the double-degenerate principal null directions of the Weyl tensor. In particular, we explicitly relate various coordinates and the corresponding physical parameters of such solutions, namely the original Plebanski-Demianski (PD) form, the convenient Astorino (A) form which was found recently, and formally improved here (A+), the Griffiths-Podolsky (GP), and Podolsky-Vratny (PV) form of the metric. It is demonstrated that, if properly mapped and physically interpreted, all these representations cover the complete class of type D black holes. Using the new A-parameters, the two main PD quartic metric functions are factorized into the product of quadratic expressions, enabling thus an explicit analysis. Moreover, we clarify the role of the twist parameter $ω$, related to both the Kerr-like rotation and the NUT parameters $a$ and $l$, respectively. Special attention is payed to the elusive subclass of accelerating NUT black holes with $a=0$.

gr-qc↗

arXiv2024

Extremal rotating BTZ black holes cannot be dressed in (anti-)self-dual Maxwell field

Under the (anti-)self-dual condition for orthonormal components of the Faraday tensor, the 3D Einstein-Maxwell system with a negative cosmological constant $Λ$ admits a solution obtained by Kamata and Koikawa and later by Cataldo and Salgado in the most general form. Actually, Clement first obtained this solution and interpreted it as a regular particle-like solution without horizon. Nevertheless, it has been erroneously stated in some literature that this Clement-Cataldo-Salgado (CCS) solution, locally characterized by a single parameter, describes a black hole even in the charged case as it reduces to the extremal rotating Banados-Teitelboim-Zanelli (BTZ) solution in the vacuum limit and its curvature invariants are constant. In this paper, we supplement Clement's interpretation by showing that there appears a parallelly propagated curvature singularity corresponding to an infinite affine parameter along spacelike geodesics at the location of the Killing horizon in the extremal rotating BTZ solution when the (anti-)self-dual Maxwell field is added. If the spatial coordinate $θ$ is periodic, closed timelike curves exist near the singularity. It is also shown that the CCS solution is of the Cotton type N (in contrast to charged rotating BTZ black holes which are of type I away from the horizon), and the energy-momentum tensor of the Maxwell field is of the Hawking-Ellis type II. The metric solves the Einstein-$Λ$ equations also with a massless scalar field or a null dust fluid. We demonstrate that it belongs to the Kundt shear-free, non-twisting, non-expanding class of geometries, whereas extremal rotating BTZ black holes have expanding principal null directions. It means that the CCS metric represents the specific null ("radiative") Maxwell field generated by a singular source, rather than an extremal rotating BTZ black hole dressed in an (anti-)self-dual Maxwell field.

hep-th↗

arXiv2024

Charged rotating BTZ solution revisited: New coordinates and algebraic classifications

We revisit the charged rotating Bañados-Teitelboim-Zanelli (BTZ) solution in the three-dimensional Einstein-Maxwell-$Λ$ system. After the erroneous announcement of its discovery at the end of the original BTZ paper in 1992, the solution was first obtained by Clément in the paper published in 1996 by coordinate transformations from the charged non-rotating BTZ solution. While Clément's form of the solution is valid only for ${Λ<0}$, we present a new form for a wider range of $Λ$ by uniform scaling transformations and a reparametrization. We also introduce new coordinates corresponding to the Doran coordinates in the Kerr spacetime, in which the metric and also its inverse are regular at the Killing horizon, and described by elementary functions. Lastly, we show that (i) the algebraic Cotton type of the spacetime is type III on the Killing horizon and type I away from the horizon, and (ii) the energy-momentum tensor for the Maxwell field is of the Hawking-Ellis type I everywhere.

gr-qc↗

arXiv2024

Algebraic classification of 2+1 geometries: a new approach

We present a convenient method of algebraic classification of 2+1 spacetimes into the types I, II, D, III, N and O, without using any field equations. It is based on the 2+1 analogue of the Newman-Penrose curvature scalars $Ψ_A$ of distinct boost weights, which are specific projections of the Cotton tensor onto a suitable null triad. The algebraic types are then simply determined by the gradual vanishing of such Cotton scalars, starting with those of the highest boost weight. This classification is directly related to the specific multiplicity of the Cotton-aligned null directions (CANDs) and to the corresponding Bel-Debever criteria. Using a bivector (that is 2-form) decomposition, we demonstrate that our method is fully equivalent to the usual Petrov-type classification of 2+1 spacetimes based on the eigenvalue problem and determining the respective canonical Jordan form of the Cotton-York tensor. We also derive a simple synoptic algorithm of algebraic classification based on the key polynomial curvature invariants. To show the practical usefulness of our approach, we perform the classification of several explicit examples, namely the general class of Robinson-Trautman spacetimes with an aligned electromagnetic field and a cosmological constant, and other metrics of various algebraic types.

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arXiv2023

New improved form of black holes of type D

We derive a new metric form of the complete family of black hole spacetimes (without a cosmological constant) presented by Plebanski and Demianski in 1976. It further improves the convenient representation of this large family of exact black holes found in 2005 by Griffiths and Podolsky. The main advantage of the new metric is that the key functions are considerably simplified, fully explicit, and factorized. All four horizons are thus clearly identified, and degenerate cases with extreme horizons can easily be discussed. Moreover, the new metric depends only on six parameters with direct geometrical and physical meaning, namely m, a, l, alpha, e, g which characterize mass, Kerr-like rotation, NUT parameter, acceleration, electric and magnetic charges of the black hole, respectively. This general metric reduces directly to the familiar forms of either (possibly accelerating) Kerr-Newman, charged Taub-NUT solution, or (possibly rotating and charged) C-metric by simply setting the corresponding parameters to zero, without the need of any further transformations. In addition, it shows that the Plebanski-Demianski family does not involve accelerating black holes with just the NUT parameter, which were discovered by Chng, Mann and Stelea in 2006. It also enables us to investigate various physical properties, such as the character of singularities, horizons, ergoregions, global conformal structure including the Penrose diagrams, cosmic strings causing the acceleration of the black holes, their rotation, pathological regions with closed timelike curves, or explicit thermodynamic properties. It thus seems that our new metric is a useful representation of this important family of black hole spacetimes of algebraic type D in the asymptotically flat settings.

gr-qc↗

arXiv2023

New form of all black holes of type D with a cosmological constant

We present an improved metric form of the complete family of exact black hole spacetimes of algebraic type D, including any cosmological constant. This class was found by Debever in 1971, Plebanski and Demianski in 1976, and conveniently reformulated by Griffiths and Podolsky in 2005. In our new form of this metric the key functions are simplified, partially factorized, and fully explicit. They depend on seven parameters with direct physical meanings, namely m, a, l, alpha, e, g, Lambda which characterize mass, Kerr-like rotation, NUT parameter, acceleration, electric and magnetic charges of the black hole, and the cosmological constant, respectively. Moreover, this general metric reduces directly to the familiar forms of (possibly accelerating) Kerr-Newman-(anti-)de Sitter spacetime, charged Taub-NUT-(anti-)de Sitter solution, or (possibly rotating and charged) C-metric with a cosmological constant by simply setting the corresponding parameters to zero. In addition, it shows that the Plebanski-Demianski family does not involve accelerating NUT black holes without the Kerr-like rotation. The new improved metric also enables us to study various physical and geometrical properties, namely the character of singularities, two black-hole and two cosmo-acceleration horizons (in a generic situation), the related ergoregions, global structure including the Penrose conformal diagrams, parameters of cosmic strings causing the acceleration of the black holes, their rotation, pathological regions with closed timelike curves, or thermodynamic quantities.

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