arXiv subjects

Jiri Podolsky

Publications and source records attributed to Jiri Podolsky.

At least 37 records · Page 2Linked to original sources

arXiv2023

A novel classification method of 2+1 spacetimes based on the Cotton scalars

A new effective approach to the algebraic classification of geometries in 2+1 gravity is presented. It uses five real Cotton scalars $Ψ_A$ of distinct boost weights, which are 3D analogues of the Newman-Penrose scalars representing the Weyl tensor in 4D. The classification into types I, II, D, III, N, O is directly related to the multiplicity of the four Cotton-aligned null directions (CANDs). We derive a synoptic algorithm based on the invariants constructed from $Ψ_A$, and we show its agreement with the Petrov scheme based on eigenvalues and canonical Jordan form of the Cotton-York tensor. Our method is simpler and also general because it can be used in any 2+1 theory, such as Einstein's gravity or topologically massive gravity. As an example we analyze the algebraic structure of Robinson-Trautman spacetimes which include charged black holes with a cosmological constant.

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arXiv2022

Penrose junction conditions with $Λ$: Geometric insights into low-regularity metrics for impulsive gravitational waves

Impulsive gravitational waves in Minkowski space were introduced by Roger Penrose at the end of the 1960s, and have been widely studied over the decades. Here we focus on nonexpanding waves which later have been generalized to impulses traveling in all constant-curvature backgrounds, i.e., the (anti-)de Sitter universe. While Penrose's original construction was based on his vivid geometric "scissors-and-paste" approach in a flat background, until recently a comparably powerful visualization and understanding has been missing in the case with a cosmological constant $Λ\not=0$. Here we review the original Penrose construction and its generalization to non-vanishing $Λ$ in a pedagogical way, as well as the recently established visualization: A special family of global null geodesics defines an appropriate comoving coordinate system that allows to relate the distributional to the continuous form of the metric.

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arXiv2021

Extremal isolated horizons with $Λ$ and the related unique type D black holes

We extend our previous work in which we derived the most general form of an induced metric describing the geometry of an axially symmetric extremal isolated horizon (EIH) in asymptotically flat spacetime. Here we generalize it to EIHs in asymptotically (anti-)de Sitter spacetime. The resulting metric conveniently forms a 6-parameter family which, in addition to a cosmological constant $Λ$, depends on the area of the horizon, total electric and magnetic charges, and two deficit angles representing conical singularities at poles. Such a metric is consistent with results obtained in the context of near-horizon geometries. Moreover, we study extremal horizons of all black holes within the class of Plebanski-Demianski exact (electro)vacuum spacetimes of the algebraic type D. In an important special case of non-accelerating black holes, that is the famous Kerr-Newman-NUT-(A)dS metric, we were able to identify the corresponding extremal horizons, including their position and geometry, and find explicit relations between the physical parameters of the metric and the geometrical parameters of the EIHs.

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arXiv2021

All solutions of Einstein-Maxwell equations with a cosmological constant in 2+1 dimensions

We present a general solution of the coupled Einstein-Maxwell field equations (without the source charges and currents) in three spacetime dimensions. We also admit any value of the cosmological constant. The whole family of such $Λ$-electrovacuum local solutions splits into two distinct subclasses, namely the non-expanding Kundt class and the expanding Robinson-Trautman class. While the Kundt class only admits electromagnetic fields which are aligned along the geometrically privileged null congruence, the Robinson-Trautman class admits both aligned and also more complex non-aligned Maxwell fields. We derive all the metric and Maxwell field components, together with explicit constraints imposed by the field equations. We also identify the most important special spacetimes of this type, namely the coupled gravitational-electromagnetic waves and charged black holes.

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arXiv2021

Uniqueness of extremal isolated horizons and their identification with horizons of all type D black holes

We systematically investigate axisymmetric extremal isolated horizons (EIHs) defined by vanishing surface gravity, corresponding to zero temperature. In the first part, using the Newman-Penrose and GHP formalism we derive the most general metric function for such EIHs in the Einstein-Maxwell theory, which complements the previous result of Lewandowski and Pawlowski. We prove that it depends on 5 independent parameters, namely deficit angles on the north and south poles of a spherical-like section of the horizon, its radius (area), and total electric and magnetic charges of the black hole. The deficit angles and both charges can be separately set to zero. In the second part of our paper, we identify this general axially symmetric solution for EIH with extremal horizons in exact electrovacuum Plebanski-Demianski spacetimes, using the convenient parametrization of this family by Griffiths and Podolsky. They represent all (double aligned) black holes of algebraic type D without a cosmological constant. Apart from a conicity, they depend on 6 physical parameters (mass, Kerr-like rotation, NUT parameter, acceleration, electric and magnetic charges) constrained by the extremality condition. We were able to determine their relation to the EIH geometrical parameters. This explicit identification of type D extremal black holes with a unique form of EIH includes several interesting subclasses, such as accelerating extremely charged Reissner-Nordstrom black hole (C-metric), extremal accelerating Kerr-Newman, accelerating Kerr-NUT, or non-accelerating Kerr-Newman-NUT black holes.

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arXiv2021

Black holes and other spherical solutions in quadratic gravity with a cosmological constant

We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant $Λ$. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant throughout a spacetime. Furthermore, we employ the conformal-to-Kundt metric ansatz that is valid for all static spherically symmetric spacetimes and leads to a considerable simplification of the field equations. We arrive at a set of two ordinary differential equations and study its solutions using the Frobenius-like approach of (infinite) power series expansions. While the indicial equations considerably restrict the set of possible leading powers, careful analysis of higher-order terms is necessary to establish the existence of the corresponding classes of solutions. We thus obtain various non-Einstein generalizations of the Schwarzschild, (anti-)de Sitter [or (A)dS for short], Nariai, and Plebański-Hacyan spacetimes. Interestingly, some classes of solutions allow for an arbitrary value of $Λ$, while other classes admit only discrete values of $Λ$. For most of these classes, we give recurrent formulas for all series coefficients. We determine which classes contain the Schwarzschild-(A)dS black hole as a special case and briefly discuss the physical interpretation of the spacetimes. In the discussion of physical properties, we naturally focus on the generalization of the Schwarzschild-(A)dS black hole, namely the Schwarzschild-Bach-(A)dS black hole, which possesses one additional Bach parameter. We also study its basic thermodynamical properties and observable effects on test particles caused by the presence of the Bach tensor. This work is a considerable extension of our letter [Phys. Rev. Lett., 121, 231104, 2018].

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arXiv2020

Kundt spacetimes in the Einstein-Gauss-Bonnet theory

We systematically investigate the complete class of vacuum solutions in the Einstein-Gauss-Bonnet gravity theory which belong to the Kundt family of non-expanding, shear-free and twist-free geometries (without gyratonic matter terms) in any dimension. The field equations are explicitly derived and simplified, and their solutions classified into three distinct subfamilies. Algebraic structures of the Weyl and Ricci curvature tensors are determined. The corresponding curvature scalars directly enter the invariant form of equation of geodesic deviation, enabling us to understand the specific local physical properties of the gravitational field constrained by the EGB theory. We also present and analyze several interesting explicit classes of such vacuum solutions, namely the Ricci type III spacetimes, all geometries with constant-curvature transverse space, and the whole pp-wave class admitting a covariantly constant null vector field. These exact Kundt EGB gravitational waves exhibit new features which are not possible in Einstein's general relativity.

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arXiv2020

Accelerating NUT black holes

We present and analyze a class of exact spacetimes which describe accelerating black holes with a NUT parameter. First, we verify that the intricate metric found by Chng, Mann and Stelea in 2006 indeed solves Einstein's vacuum field equations of General Relativity. We explicitly calculate all components of the Weyl tensor and determine its algebraic structure. As it turns out, it is actually of algebraically general type I with four distinct principal null directions. It explains why this class of solutions has not been (and could not be) found within the large Plebanski-Demianski family of type D spacetimes. Then we transform the solution into a much more convenient metric form which explicitly depends on three physical parameters: mass, acceleration, and the NUT parameter. These parameters can independently be set to zero, recovering thus the well-known spacetimes in standard coordinates, namely the C-metric, the Taub-NUT metric, the Schwarzschild metric, and flat Minkowski space. Using this new metric, we investigate physical and geometrical properties of such accelerating NUT black holes. In particular, we localize and study four Killing horizons (two black-hole plus two acceleration) and investigate the curvature. Employing the scalar invariants we prove that there are no curvature singularities whenever the NUT parameter is nonzero. We identify asymptotically flat regions and relate them to conformal infinities. This leads to a complete understanding of the global structure. The boost-rotation metric form reveals that there is actually a pair of such black holes. They uniformly accelerate in opposite directions due to the action of rotating cosmic strings or struts located along the corresponding two axes. Rotation of these sources is directly related to the NUT parameter. In their vicinity there are pathological regions with closed timelike curves.

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arXiv2019

Black holes and other exact spherical solutions in Quadratic Gravity

We study static, spherically symmetric vacuum solutions to Quadratic Gravity, extending considerably our previous Rapid Communication [Phys. Rev. D 98, 021502(R) (2018)] on this topic. Using a conformal-to-Kundt metric ansatz, we arrive at a much simpler form of the field equations in comparison with their expression in the standard spherically symmetric coordinates. We present details of the derivation of this compact form of two ordinary differential field equations for two metric functions. Next, we apply analytical methods and express their solutions as infinite power series expansions. We systematically derive all possible cases admitted by such an ansatz, arriving at six main classes of solutions, and provide recurrent formulas for all the series coefficients. These results allow us to identify the classes containing the Schwarzschild black hole as a special case. It turns out that one class contains only the Schwarzschild black hole, three classes admit the Schwarzschild solution as a special subcase, and two classes are not compatible with the Schwarzschild solution at all since they have strictly nonzero Bach tensor. In our analysis, we naturally focus on the classes containing the Schwarzschild spacetime, in particular on a new family of the Schwarzschild-Bach black holes which possesses one additional non-Schwarzschild parameter corresponding to the value of the Bach tensor invariant on the horizon. We study its geometrical and physical properties, such as basic thermodynamical quantities and tidal effects on free test particles induced by the presence of the Bach tensor. We also compare our results with previous findings in the literature obtained using the standard spherically symmetric coordinates.

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arXiv2019

Cut-and-paste for impulsive gravitational waves with $Λ$: The geometric picture

Impulsive gravitational waves in Minkowski space were introduced by Roger Penrose at the end of the 1960s, and have been widely studied over the decades. Here we focus on non-expanding waves which later have been generalised to impulses travelling in all constant-curvature backgrounds, that is also the (anti-)de Sitter universe. While Penrose's original construction was based on his vivid geometric `scissors-and-paste' approach in a flat background, until now a comparably powerful visualisation and understanding have been missing in the ${Λ\not=0}$ case. In this work we provide such a picture: The (anti-)de Sitter hyperboloid is cut along the null wave surface, and the `halves' are then re-attached with a suitable shift of their null generators across the wave surface. This special family of global null geodesics defines an appropriate comoving coordinate system, leading to the continuous form of the metric. Moreover, it provides a complete understanding of the nature of the Penrose junction conditions and their specific form. These findings shed light on recent discussions of the memory effect in impulsive waves.

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arXiv2019

Absence of gyratons in the Robinson-Trautman class

We present the Riemann and Ricci tensors for a fully general non-twisting and shear-free geometry in arbitrary dimension D. This includes both the non-expanding Kundt and expanding Robinson-Trautman family of spacetimes. As an interesting application of these explicit expressions we then integrate the Einstein equations and prove a surprising fact that in any D the Robinson-Trautman class does not admit solutions representing gyratonic sources, i.e., matter field in the form of a null fluid (or particles propagating with the speed of light) with an additional internal spin. Contrary to the closely related Kundt class and pp-waves, the corresponding off-diagonal metric components thus do not encode the angular momentum of some gyraton. Instead, we demonstrate that in standard D=4 general relativity they directly determine two independent amplitudes of the Robinson-Trautman exact gravitational waves.

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arXiv2019

Gyratons in the Robinson-Trautman and Kundt classes

In our previous paper [Phys. Rev. D 89 (2014) 124029], cited as [1], we attempted to find Robinson-Trautman-type solutions of Einstein's equations representing gyratonic sources (matter field in the form of an aligned null fluid, or particles propagating with the speed of light, with an additional internal spin). Unfortunately, by making a mistake in our calculations, we came to the wrong conclusion that such solutions do not exist. We are now correcting this mistake. In fact, this allows us to explicitly find a new large family of gyratonic solutions in the Robinson-Trautman class of spacetimes in any dimension greater than (or equal to) three. Gyratons thus exist in all twist-free and shear-free geometries, that is both in the expanding Robinson-Trautman and in the non-expanding Kundt classes of spacetimes. We derive, summarize and compare explicit canonical metrics for all such spacetimes in arbitrary dimension.

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arXiv2018

All solutions of Einstein's equations in 2+1 dimensions: $Λ$-vacuum, pure radiation, or gyratons

Under a weak assumption of the existence of a geodesic null congruence, we present the general solution of the Einstein field equations in three dimensions with any value of the cosmological constant, admitting an aligned null matter field, and also gyratons (a matter field in the form of a null dust with an additional internal spin). The general local solution consists of the expanding Robinson-Trautman class and the non-expanding Kundt class. The gyratonic solutions reduce to spacetimes with a pure radiation matter field when the spin is set to zero. Without matter fields, we obtain new forms of the maximally symmetric vacuum solutions. We discuss these complete classes of solutions and their various subclasses. In particular, we identify the gravitational field of an arbitrarily accelerating source (the Kinnersley photon rocket, which reduces to a Vaidya-type non-moving object) in the Robinson-Trautman class, and pp-waves, vanishing scalar invariants (VSI) spacetimes, and constant scalar invariants (CSI) spacetimes in the Kundt class.

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arXiv2018

Exact black holes in quadratic gravity with any cosmological constant

We present a new explicit class of black holes in general quadratic gravity with a cosmological constant. These spherically symmetric Schwarzschild-Bach-(anti-)de Sitter geometries (Schwa-Bach-(A)dS), derived under the assumption of constant scalar curvature, form a three-parameter family determined by the black-hole horizon position, the value of Bach invariant on the horizon, and the cosmological constant. Using a conformal to Kundt metric ansatz, the fourth-order field equations simplify to a compact autonomous system. Its solutions are found as power series, enabling us to directly set the Bach parameter and/or cosmological constant equal to zero. To interpret these spacetimes, we analyse the metric functions. In particular, we demonstrate that for a certain range of positive cosmological constant there are both black-hole and cosmological horizons, with a static region between them. The tidal effects on free test particles and basic thermodynamic quantities are also determined.

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arXiv2018

Interpreting A and B-metrics with $Λ$ as gravitational field of a tachyon in (anti-)de Sitter universe

We investigate main properties and mutual relations of the so-called A and B-metrics with any value of the cosmological constant. In particular, we explicitly show that both the AII and BI-metrics are, in fact, the famous Schwarzschild-(anti-)de Sitter spacetime (that is the AI-metric) boosted to superluminal speed. Together they form the complete gravitational field of a tachyon in Minkowski or (anti-)de Sitter universe. The boundary separating the AII and BI regions is the Mach-Cherenkov shockwave on which the curvature is unbounded. We analyze various geometric features of such spacetimes, we provide their natural physical interpretation, and we visualize them using convenient background coordinates and embeddings.

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arXiv2018

Decreasing entropy of dynamical black holes in critical gravity

Critical gravity is a quadratic curvature gravity in four dimensions which is ghost-free around the AdS background. Constructing a Vaidya-type exact solution, we show that the area of a black hole defined by a future outer trapping horizon can shrink by injecting a charged null fluid with positive energy density, so that a black hole is no more a one-way membrane even under the null energy condition. In addition, the solution shows that the Wald-Kodama dynamical entropy of a black hole is negative and can decrease. These properties expose the pathological aspects of critical gravity at the non-perturbative level.

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arXiv2018

Explicit black hole solutions in higher-derivative gravity

We present, in an explicit form, the metric for all spherically symmetric Schwarzschild-Bach black holes in Einstein-Weyl theory. In addition to the black hole mass, this complete family of spacetimes involves a parameter that encodes the value of the Bach tensor on the horizon. When this additional "non-Schwarzschild parameter" is set to zero the Bach tensor vanishes everywhere and the "Schwa-Bach" solution reduces to the standard Schwarzschild metric of general relativity. Compared with previous studies, which were mainly based on numerical integration of a complicated form of field equations, the new form of the metric enables us to easily investigate geometrical and physical properties of these black holes, such as specific tidal effects on test particles, caused by the presence of the Bach tensor, as well as fundamental thermodynamical quantities.

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arXiv2018

Non-expanding Plebanski-Demianski space-times

The aim of this work is to describe the complete family of non-expanding Plebanski-Demianski type D space-times and to present their possible interpretation. We explicitly express the most general form of such (electro)vacuum solutions with any cosmological constant, and we investigate the geometrical and physical meaning of the seven parameters they contain. We present various metric forms, and by analyzing the corresponding coordinates in the weak-field limit we elucidate the global structure of these space-times, such as the character of possible singularities. We also demonstrate that members of this family can be understood as generalizations of classic B-metrics. In particular, the BI-metric represents an external gravitational field of a tachyonic (superluminal) source, complementary to the AI-metric which is the well-known Schwarzschild solution for exact gravitational field of a static (standing) source.

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