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Alena Pravdová

Publications and source records attributed to Alena Pravdová.

9 recordsLinked to original sources
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↗
arXiv2025

On vacuum and charged asymptotically (A)dS black holes in quadratic gravity

In this paper, we study asymptotic properties of static spherically symmetric black holes in quadratic gravity with a cosmological constant $Λ$. We find that for sufficiently large values of $|Λ|$ these black holes are generically asymptotically (A)dS and form a three-parameter family of black holes, with free parameters being the horizon radius, $Λ$, and Bach parameter $b$. For smaller values of $|Λ|$, fine-tuning of the Bach parameter is necessary to recover asymptotically (A)dS behaviour, resulting in two distinct two-parameter families of spherically symmetric black holes with (A)dS asymptotics. One family is the (A)dS-Schwarzschild solution, the other is a fine-tuned asymtotically (A)dS-Schwarzschild-Bach solution. We also generalise the above solutions to electrically charged black holes, obtaining qualitatively similar asymptotic behaviour. This adds the electric charge as an additional free parameter of these black holes. Both fine-tuned three-parameter families are distinct from Reissner-Nordström black holes.

gr-qc↗
arXiv2019

Almost universal spacetimes in higher-order gravity theories

We study almost universal spacetimes - spacetimes for which the field equations of any generalized gravity with the Lagrangian constructed from the metric, the Riemann tensor and its covariant derivatives of arbitrary order reduce to one single differential equation and one algebraic condition for the Ricci scalar. We prove that all d-dimensional Kundt spacetimes of Weyl type III and traceless Ricci type N are almost universal. Explicit examples of Weyl type II almost universal Kundt metrics are also given. The considerable simplification of the field equations of higher-order gravity theories for almost universal spacetimes is then employed to study new Weyl type II, III, and N vacuum solutions to quadratic gravity in arbitrary dimension and six-dimensional conformal gravity. Necessary conditions for almost universal metrics are also studied.

gr-qc↗
arXiv2018

On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction

We prove that higher dimensional Einstein spacetimes which possess a geodesic, non-degenerate double Weyl aligned null direction (WAND) $\ell$ must additionally possess a second double WAND (thus being of type D) if either: (a) the Weyl tensor obeys $C_{abc[d}\ell_{e]}\ell^c=0$ ($\LeftrightarrowΦ_{ij}=0$, i.e., the Weyl type is II(abd)); (b) $\ell$ is twistfree. Some comments about an extension of the Goldberg-Sachs theorem to six dimensions are also made.

gr-qc↗
arXiv2017

Universal spacetimes in four dimensions

Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except of type II. We show that all universal spacetimes in four dimensions are algebraically special and Kundt. Petrov type D universal spacetimes are necessarily direct products of two 2-spaces of constant and equal curvature. Furthermore, type II universal spacetimes necessarily possess a null recurrent direction and they admit the above type D direct product metrics as a limit. Such spacetimes represent gravitational waves propagating on these backgrounds. Type III universal spacetimes are also investigated. We determine necessary and sufficient conditions for universality and present an explicit example of a type III universal Kundt non-recurrent metric.

gr-qc↗
arXiv2016

Type II universal spacetimes

We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selected classes of gravitational theories, such as Lovelock, quadratic and L(Riemann) gravities.

gr-qc↗
arXiv2014

Asymptotic behaviour of the Weyl tensor in higher dimensions

We determine the leading order fall-off behaviour of the Weyl tensor in higher dimensional Einstein spacetimes (with and without a cosmological constant) as one approaches infinity along a congruence of null geodesics. The null congruence is assumed to "expand" in all directions near infinity (but it is otherwise generic), which includes in particular asymptotically flat spacetimes. In contrast to the well-known four-dimensional peeling property, the fall-off rate of various Weyl components depends substantially on the chosen boundary conditions, and is also influenced by the presence of a cosmological constant. The leading component is always algebraically special, but in various cases it can be of type N, III or II.

gr-qc↗
arXiv2012

On the Goldberg-Sachs theorem in higher dimensions in the non-twisting case

We study a generalization of the "shear-free part" of the Goldberg-Sachs theorem for Einstein spacetimes admitting a non-twisting multiple Weyl Aligned Null Direction (WAND) l in n>=6 spacetime dimensions. The form of the corresponding optical matrix $ρ$ is restricted by the algebraically special property in terms of the degeneracy of its eigenvalues. In particular, there necessarily exists at least one multiple eigenvalue and further constraints arise in various special cases. For example, when $ρ$ is non-degenerate and the Weyl components $Φ_{ij}$ are non-zero, all eigenvalues of $ρ$ coincide and such spacetimes thus correspond to the Robinson-Trautman (RT) class. On the other hand, in certain degenerate cases all non-zero eigenvalues can be distinct. We also present explicit examples of Einstein spacetimes admitting some of the permitted forms of $ρ$, including examples violating the "optical constraint". The obtained restrictions on $ρ$ are, however, in general not sufficient for l to be a multiple WAND, as demonstrated by a few "counterexamples". We also discuss the geometrical meaning of these restrictions in terms of integrability properties of certain null distributions. Finally, we specialize our analysis to the six-dimensional case, where all the permitted forms of $ρ$ are given in terms of just two parameters. In the appendices some examples are given and certain results pertaining to (possibly) twisting mWANDs of Einstein spacetimes are presented.

gr-qc↗