Albert Einstein Center
for Gravitation and Astrophysics

Overview of our research activities in 2017

• Introduction
• Mathematical Relativity
• Cosmology and Theoretical Relativistic Astrophysics
• Astrophysical Processes and Compact Objects
• Gravitational lensing
• Outreach
• References

Introduction

There was no major conference on general relativity and gravitation organized in 2017, however, the European Week of Astronomy and Space Science (EWASS), the annual meeting of the European Astronomical Society (EAS) took place during the week June 26-30, 2017 at the Faculty of Law, Charles University in Prague. It was visited by over 1200 participants from Europe and other continents. On Monday, June 26, Petr Hadrava (member of the Center) and his wife gave a plenary talk “History of Astronomy in the Czech Lands”; on Wednesday, June 28, at the “Relativity at 100” symposium, J. Bičák gave an invited review talk “Classical General Relativity: Light and Gravity” in which, among other topics, he reviewed in detail the work of two members of the Center, M. Scholtz on isolated horizons and D. Heyrovský on gravitational lensing of accretion disks around black holes. A number of members of the Center, in particular from the Astronomical Institute and from the relativistic astrophysics group at the Silesian University, participated actively in various Sections organized within EWASS.

The Astronomical Institute of Charles University organized a major international conference on astrophysics of dense stellar systems, MODEST17 (https://modest17.cuni.cz), with several sessions dedicated to astrophysics of black holes and their stellar environment. Another small, yet very fruitful international meeting was held in December. L. Šubr, member of the Center from AI, Charles University, was the main organizer involved in these meetings. A number of talks at various conferences abroad were given by the members of the Center or their students. Some of them are referred to in this report at other places.

As we shall see below, there exist not only mutual interactions and contacts within seminars or conferences between the groups from different institutions participating in the Center but new direct collaborations on papers have now also arisen between (I) members of the group of the Astronomical Institute (AI) CAS in Prague and the group of relativistic astrophysics of the Silesian University (SU) in Opava, and (ii) members of the group at the Mathematical Institute (MI) of CAS in Prague and mathematical relativists at the Institute of Theoretical Physics (ITP) of Charles University. As in the previous years we divide our report into several subsections.

Mathematical Relativity

J. Bičák and his PhD student J. Schmidt from the Faculty of Nuclear Sciences and Physical Engineering published in 2016 a comprehensive work on uniqueness of the energy-momentum tensors in linearized Einstein’s theory and in massive gravity. J. Schmidt acquired a great experience in working with the software system CADABRA for tensor manipulations. In the end of 2016 and during 2017 we analyzed conserved currents and related conservation laws in Horndeski’s generalizations of general relativity. These, in addition to the metric, consider also scalar fields of various characters as description of gravity and have become of interest in connection with a possible explanation of dark energy. The calculations become unmanageable without using CADABRA. The work is finished and has been submitted for publication in Journal of Mathematical Physics [1].

We employed a special sector of Horndeski’s theories in our work on perturbations of black holes with scalar hair some time ago, more recent results appeared in [2].

In [3] and [4], J. Bičák and his PhD student F. Hejda continued their investigation of near extremal black holes. In the first paper our previous work (published in Phys. Rev. in 2015) has been summarized, slightly generalized and presented in one of the most important conferences on general relativity in Rome. In the second work particle collisions near the horizons of extremal black holes which can lead, at special limiting points, to unbounded energies have been studied together with kinematical restrictions that may prevent the particles from reaching the limiting collision point.

In collaboration with Prof. Lynden-Bell, FRS, from Cambridge, J. Bičák studied circularly polarized light beams in general relativity and investigated the energy, momentum, angular momentum and their fluxes for these beams and in general for cylindrical systems. They elucidated Komar’s mysterious factor 2 by evaluating Komar integral expressions for systems that have no trace in their stress tensors. For details, see [5].

In [6], P. Krtouš and his PhD student I. Kolář studied Taub-like and near-horizon limits of the Kerr-NUT-(A)dS solution. They reparametrized the metric in terms of critical values of metric polynomials and analyzed a general limiting procedure, which generalizes the limit to the Taub-NUT solution known in four dimensions. As a special case, they have recovered the “nutty” spacetimes discovered in [7]. An analogous procedure in the Lorentzian sector leads to the near-horizon limit. We have discussed three possible ways of performing the limit, generalizing thus the discussion in [8] from four dimensions. In [9], P. Krtouš, together with V. Frolov and D. Kubizňák from Canada studied a test electromagnetic field on the background of the off-shell Kerr-NUT-(A)dS geometry. They constructed the field as a linear combination of the closed conformal Killing–Yano tensor, which is present in such a spacetime, and a derivative of its primary Killing vector. For the vanishing cosmological constant such an electromagnetic field reduces to the Wald’s ansatz for the primary Killing vector. The relation to the fields [10, 11] aligned to the principal tensor has been discussed. Collaboration between Center members from MI and ITP produced a paper on quadratic gravity [12]—a generalization of Einstein gravity stemming from additional quadratic correction terms in curvature added to the Einstein-Hilbert action. Vacuum solutions to Einstein gravity also solve vacuum equations to quadratic gravity, however, this theory also admits non-Einstein vacuum solutions. It was shown that exact solutions belong to the Kundt class. A number of such solutions is constructed explicitly using conformal method. Some explicit Kundt and Robinson-Trautman solutions to quadratic gravity are provided.

Other results from the group at MI include the construction of an exact, hairy, asymptotically locally AdS black hole solution with a flat horizon in the Einstein-nonlinear sigma model system in (3+1) dimensions [13]. The solution is characterized by a discrete parameter which has neither topological nor Noether charge associated with it and therefore represents a hair. The thermodynamics is analysed; interestingly, the hairy black hole is always thermodynamically favored with respect to the corresponding black hole with a vanishing Pionic field.

“Universal metrics” simultaneously solve vacuum field equations of a large class of modified theories of gravity; all known Lorentzian universal spacetimes belong to the Kundt class. However, in [14] four-dimensional spaces of neutral signature were considered and non-Kundt universal spaces of Walker type were found. They have no analogue in other signatures.

It is well known that genuine type II Robinson-Trautman spacetimes do not exist for dimensions n>4. In [15] it is proved that for n>4 this non-existence extends well beyond the Robinson-Trautman class. Under certain assumptions, the Goldberg-Sachs theorem in six dimensions was also discussed.

M. Žofka prepared for publication a paper on a cylindrically symmetric Bonnor-Melvin magnetic universe generalized to include a non-vanishing cosmological constant. He showed that the resulting metric has already been obtained by Plebanski and Hacyan as a direct-product spacetime without realizing that this is a generalization of the Bonnor-Melvin solution.

With his student, M. Žofka investigated the motion of extended bodies in Schwarzschild spacetime. As a model of the test body they used a dumbbell consisting of two point masses with a predefined, time-dependent separation.

T. Tahamtan and O. Svítek, together with a new postdoc A. Zampeli, investigated the nature of curvature singularity in the spherically symmetric spacetime with a scalar field using various approaches—quantum particle probes, covariant loop quantum gravity and a complete canonical quantization applying superspace symmetries. The paper is currently being finalized.

T. Ledvinka and his PhD student A. Khirnov have been investigating a hard problem of numerical relativity: gravitational collapse of gravitational waves forming a black hole starting from the so-called Brill initial data. Interestingly, critical behavior of this class of initial data is still an open problem. They constructed a new “quasi-maximal” slicing condition and demonstrated that it exhibits better behavior for such data. Using this condition, complete evolution from initial data through formation of a black hole up to its settling down was achieved. Numerical data enable to illustrate various properties of constructed spacetimes using gauge-independent quantities in the compactified spacetime diagrams. The invariants show how the black holes thus produced settle down to a Schwarzschild black hole and how the event horizon is formed during the collapse. A manuscript with these results has been submitted to Phys. Rev. D.

Modifications of the Hamiltonian approach to General relativity based on manifestly covariant version of the classical theory of gravity were considered. The covariant quantum gravity wave equation by means of the Hamilton-Jacobi method of quantization of classical tensor field was discussed by members of the SU group in [16-18].

Cosmology and Theoretical Relativistic Astrophysics

The research project, of our new postdoc, N. Uzun, who joined the Center last year, focused mainly on statistical evolution of 3-geometries within a cosmological setting. Unlike in standard cosmology, the aim is to model a realistic, inhomogeneous universe as a collection of spatial 3-dimensional regions which differ from each other via their spatial curvature. Concepts of game theory and probability theory have been introduced to the model in order to study the evolution equations of such a construction. The problem of probabilistic light propagation has also been studied. Reciprocity relations for light propagation within multiple geometries have led to an introduction of a phase space whose symplectic transformations take one set of solutions of the null geodesic equations to another.

The postdoc supported by the Center last year was Ana Alonso-Serrano. Together with Matt Visser, she published 4 papers [19-22] in which they developed a better understanding of the interplay between entropy, coarse-graining and “hidden information”. The main goal was to apply this to Hawking evaporation and the information puzzle. Models to track the coarse-graining in Shannon and von Neumann entropies were found and corresponding processes written as super-scattering operators. They analyzed entropy, information and entanglement of multipartite systems, finding new bounds to these quantities. Finally, they have applied these results to understand the information budget when a black hole evaporates, showing a perfect transfer of information.

Our former PhD student N. Gürlebeck (now in ZARM, Bremen) and M. Scholtz (member of the Center up to the end of 2016) worked on the Meissner effect for weakly isolated horizons. Stationary, axisymmetric black hole horizons exhibit a phenomenon analogous to the Meissner effect: the horizons expel external electromagnetic fields when they become extremal. Many specific demonstrations of the Meissner effect have been found. In [23], the question whether this phenomenon is a generic property of black holes was investigated. It was shown that any extremal, axisymmetric black hole shows the Meissner effect, independently of possible deformations of black hole geometry due to the outside matter or fields. In [23], which was published at the beginning of 2017 and so was not included in the report for 2016, possible impact of the Meissner effect on the efficiency of jet production in active galactic nuclei powered by the Blandford-Znajek process was also studied

O. Semerák, together with his PhD student M. Basovník, continued their study of black holes subjected to the influence of other strong sources of gravity. In 2017 they have specifically considered a system of two black holes "held apart" by a repulsive effect of the Appell ring. They have checked, in particular, how the intrinsic geometry of the black-hole horizons is changed and how curvature is modified outside as well as inside the black holes. A paper is almost prepared for submission.

Astrophysical Processes and Compact Objects

In [24], V. Karas and collaborators studied the processes leading to thermal instability in the multiphase environment of compact galactic nuclei. They included the impact of the stellar radiation field from nuclear star cluster, which has not been previously discussed but is thought to play a significant role in galaxies containing a dense stellar cluster. In the case of Milky Way's nucleus (Sgr A*), stellar heating prevents the spontaneous formation of cold clouds, and thus it reduces the accretion efficiency. On the other hand, in the case of M60-UCD1 ultracompact dwarf galaxy, the model predicts spontaneous formation of cold clouds in the inner part of the galaxy. These cold clouds may survive since the cooling time-scale is shorter than the inflow/outflow time-scale. In the context of galactic nuclei, members of AI and SU jointly explored the role of self-gravity on the equilibrium figures of magnetized tori and polar clouds near a black hole [25]. While the central black hole dominates the gravitational field, the surrounding material has a non-negligible self-gravitational effect on the torus structure. It is influenced by the balance between the gravitational and magnetic forces.

In a published conference contribution, [26] explored the bow-shock size evolution, the emergence of shocked layers, the surface density, and the emission-measure maps close to the peribothron passage of a supersonic star near a supermassive black hole. The large body of evidence continues to identify SgrA* as a supermassive black hole, it is, however, unclear when there will be a fully convincing proof available, as discussed in [27]. Two doctoral students from AI CAS, M. Zajaček [28] and F. Dinnbier [29], completed and defended their Ph.D. theses successfully (supervisors V. Karas and R. Wunsch in Prague). Both students continue at postdoctoral positions in the same research field in Germany (M.Z. at Max Planck Institute in Bonn and F.D. at University of Cologne).

L. Šubr from AI of the Charles University started time-intensive numerical modelling of star clusters hosting intermediate-mass black holes with focus on slingshot events that may be observable markers of presence of this class of black holes. The work on formation of hard binaries during the core collapse of self-gravitating star clusters was finalized and submitted to MNRAS in late 2017.

Research continued in all the relevant fields planned in the project proposal by members of the relativistic astrophysics group in SU in Opava, The topics included the following themes.

A) Optical and physical effects in alternate black holes and related spacetimes

Physical properties of a newly discovered special extraordinary class of the so-called “mining” Kerr-Newman naked singularity spacetimes demonstrating a “perpetuum mobile”-like behaviour due to (formally) unlimited accretion efficiency were studied. The results obtained for the braneworld Kerr-Newman spacetimes with positive tidal charges hold equally for the standard Kerr-Newman spacetimes. Optical phenomena and ultra-high energy collisions were considered [30]. Next, non-singular black hole spacetimes in conformal gravity and rotating black holes immersed in quintessential fields were studied as well as generic regular black holes within non-linear electrodynamics. The shadow of a rotating black hole with the quintessential energy in the presence of plasma was investigated. (See [31], [32], [33], [34], [35].)

Some interesting new results on long-lived modes in the Schwarzschild-de Sitter black hole spacetimes were presented, and the validity of the theorem on relation of the circular null geodesics to the quasi-normal modes in the eikonal limit was tested, demonstrating that the theorem is not valid generally, outside of general relativity [36], [37]. Short notes on the Casimir effect in the field of quintessential black holes and on the black hole entropy in d-dimensions—proposing a non-standard correction to the paradox of negative entropy that occurs for low mass black holes—were given in [38] and in [39], [40], respectively.

B) Structures encircling compact objects

Investigation of electrically charged toroidal structures has been continued. A general transformation leading to an integral form of pressure equations for equilibrium of charged perfect fluid circling in strong gravitational and combined electromagnetic fields was introduced. It generalizes our analytical treatment. As an example, a particular solution for a fluid circling close to a charged rotating black hole immersed in an asymptotically uniform magnetic field was found. The publication is under preparation, the proceedings contribution is in press.

Complex multi-ring structures that could represent a remnant of several accretion regimes on a supermassive black hole were studied and possible evolution schemes of basic double toroidal structures analyzed [41,42].

C) General relativistic polytropic configurations

Trapping polytropes containing a region of trapped null geodesics were analyzed. The trapping zone of the trapping polytropes is shown to be gravitationally unstable and can collapse while forming a central black hole. If such a collapse occurs inside of an extremely extended polytrope that could model a dark matter halo, one can have an explanation of the existence of supermassive black holes observed in galaxies with very large redshifts (z>6). [43, 44]

D) Charged particles and string loops dynamics

Circular orbits and related quasi-harmonic oscillatory motion of charged particles around a weakly magnetized rotating black hole were studied. Different ratios of particle fundamental frequencies were used to explain different shapes of perturbed circular orbit. The oscillatory motion around magnetized Kerr black holes can give correct explanation of the observed HF QPOs in microquasars [45].

E) Kinetic theory of collisional processes and variational principles in kinetic theory in GR

Non-interacting particles were studied in the Kerr spacetime within the kinetic theory approach in relation to the Carter’s constant of motion reflecting the hidden symmetry of the spacetime, with the possible consequences being discussed [46].

F) High frequency QPOs in accretion discs around compact objects

Frequencies of the quasi-periodic oscillations observed in three microquasars were modelled in the framework of forced resonances for Keplerian orbital motion in the field of Kerr naked singularities. It was shown that in slightly superspinning geometries, the HF QPO data can be explained for all the considered microquasars by the epicyclic model.

Oscillations of Keplerian discs in the field of superspinning quark stars were studied by putting limits on the parameters of such quark stars implied by the twin HF QPOs observed in atoll sources [47, 48].

G) Cosmological black holes

Cosmological black holes in the Lemaître-Tolman-Bondi-model, representing a black hole enclosed in dust, were studied in the simplest case of flat space sections of the model [49].

Gravitational lensing

D. Heyrovský with his PhD student L. Ledvina continued in their research on quasar microlensing, concentrating on variations in X-ray line profiles, to reveal the structure of the innermost region of the accretion disk. The previously obtained model of the microlensing-generated peaks and edges that traced their origin to points on the disk was now corroborated by adding an analytical expansion for an arbitrary caustic orientation, which shows the link between the observed line feature and the local properties of the disk. A full paper on a thin disk around an extreme Kerr black hole, was submitted to The Astrophysical Journal.

As a generalization, the same approach to non-extremely rotating Kerr black holes with a geometrically thin / optically thick accretion disk was studied next. New features appearing in the iron K-alpha line profile, generated by a microlensing caustic crossing at the innermost stable circular orbit (ISCO), were analyzed.

To speed up the required simulations, L. Ledvina wrote a new code in CUDA for computing the spectrum of a micro-lensed accretion disk. The code, which is fully parallelizable on graphics processing units (GPUs), was debugged, tested, and then used for all subsequent spectral calculations.

Outreach

Most of the Center members have been involved in conveying our results to general public. A number of popular talks on themes studied by the Center were given at schools, universities, Science Cafés, etc.; examples of three articles are those quoted in [50-52].

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References

1. Schmidt J. and Bičák J.: Covariant conserved currents for scalar-tensor Horndeski theory, Journal of Mathematical Physics, submitted in September 2017
2. Anabalon A., Bičák J.: Aspects of Stability of Hairy Black Holes, in The Fourteenth Marcel Grossmann Meeting (2017) 1805-1809
3. Hejda F., Bičák J.: Extremal black holes in strong magnetic fields: Near-horizon geometries and Meissner effect, in The Fourteenth Marcel Grossmann Meeting (2017) 2732-2737
4. Hejda F. and Bičák J.: Kinematic restrictions on particle collisions near extremal black holes: A unified picture, Phys. Rev. D 95 (2017) 084055
5. Lynden-Bell D. and Bičák J.: Komar fluxes of circularly polarized light beams and cylindrical metrics, Phys. Rev. D 96 (2017) 104053
6. Kolář I., Krtouš P.: NUT-like and near-horizon limits of Kerr-NUT-(A)dS spacetimes, Phys. Rev. D 95 (2017) 124044, arXiv:1701.03950
7. Mann R.B., Stelea C.: New multiply nutty spacetimes, Phys. Lett. B634, 448–455 (2006)
8. Hejda F.: Particles and fields in curved spacetimes (selected problems), Master’s thesis, Charles University, Prague, Czech Republic (2013)
9. Frolov V. P., Krtouš P., Kubizňák D.: Weakly charged generalized Kerr-NUT-(A)dS spacetimes, Phys. Lett. B 771 (2017) 254, arXiv:1705.00943
10. Krtouš P.: Electromagnetic Field in Higher-Dimensional Black-Hole Spacetimes, Phys. Rev. D 76 (2007) 084035, arXiv:0707.0002
11. Kolář I., Krtouš P.: Weak electromagnetic field admitting integrability in Kerr-NUT-(A)dS spacetimes, Phys. Rev. D 91 (2015) 124045, arXiv:1504.00524
12. Pravda V., Pravdová A., Podolský J., Švarc R.: Exact solutions to quadratic gravity, Phys. Rev. D 95 (2017) 084025
13. Astorino M., Canfora F., Giacomini A., Ortaggio M.: Hairy AdS black holes with a toroidal horizon in 4D Einstein-nonlinear σ-model system, Phys. Lett. B776 (2018) 236-241
14. Hervik S., Málek T.: Universal Walker metrics, Class. Quantum Grav., accepted, arXiv:1710.02164
15. Ortaggio M., Pravda V., Pravdová A.: On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction, Class. Quantum Grav., submitted., arXiv:1711.04160
16. Cremaschini C., Tessarotto M.: Hamiltonian approach to GR – Part 1: covariant theory of classical gravity, European Physical Journal C 77 (2017) 329
17. Cremaschini C., Tessarotto M.: Hamiltonian approach to GR – Part 2: covariant theory of quantum gravity, European Physical Journal C 77 (2017) 330
18. Cremaschini C., Tessarotto M.: Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity, Entropy 19 (2017) 339
19. Alonso-Serrano A, Visser M.: Entropy/information flux in Hawking radiation, Phys. Lett. B 776 (2018) 10-16
20. Alonso-Serrano A., Visser M.: Multi-partite analysis of average-subsystem entropies, Phys. Rev. A 96 (2017) 052302
21. Alonso-Serrano A., Visser M.: Entropy Budget for Hawking Evaporation”, Universe 3(3) (2017) 58, Special Issue ”Varying Constants and Fundamental Cosmology”
22. Alonso-Serrano A., Visser M.: Coarse graining Shannon and von Neumann entropies”, Entropy 19(5) (2017) 207, Invited contribution for the Special Issue Black Hole Thermodynamics II.
23. Gürlebeck N., Scholtz M.: Meissner effect for weakly isolated horizons, Phys. Rev. D 95 (2017) 064010
24. Rozanska A., Kunneriath D., Czerny B., Adhikari T. P., & Karas V.: Multiphase environment of compact galactic nuclei: the role of the nuclear star cluster, MNRAS 464 (2017) 2090–2102
25. Trova A., Karas V., Slaný P. & Kovář J.: “Influence of self-gravity on the equilibrium structures of magnetized tori”, in New Frontiers in Black Hole Astrophysics, Proceedings IAU Symposium No. 324, ed. A. Gomboc (Cambridge Univ. Press, 2017), 253-254
26. Štofanová L., Zajaček M., Kunneriath D., Eckart A., Karas V.: Modelling the bow–shock evolution along the DSO/G2 orbit in the Galactic centre, Proceedings of RAGtime 17–19, Z. Stuchlík et al, editors (Silesian University in Opava, 2017), 153 (9 pp)
27. Eckart A., Hüttemann A. Kiefer C. Britzen Z., Zajacek M., Lämmerzahl C. Stöckler M., Valencia-S M., Karas V., García-Marín M.: The Milky Way’s Supermassive Black Hole: How Good a Case Is It? A Challenge for Astrophysics & Philosophy of Science, Foundations of Physics 47 (2017) 553-624
28. Zajaček M.: Interaction between interstellar medium and black hole environment, Doctoral Thesis (Universität zu Köln, 1. Physikalisches Institut, 2017) (189 pp)
29. Dinnbier F.: Propagating Star Formation, Doctoral Thesis (Charles University in Prague, Faculty of Mathematics and Physics, 2017) (160 pp)
30. Stuchlík Z., Blaschke M., Schee J.:Particle collisions and optical effects in the mining Kerr-Newman spacetimes, Phys. Rev. D 96 (2017) 104050
31. Toshmatov B., Bambi C., Ahmedov B., Stuchlík Z., Schee J.: Scalar perturbations of nonsingular nonrotating black holes in conformal gravity, Phys. Rev. D 96 (2017) 064028
32. Toshmatov B., Bambi C., Ahmedov B., Abdujabbarov A., Stuchlík Z.: Energy conditions of non-singular black hole spacetimes in conformal gravity, European Phys. Journal C 77 (2017) 542
33. Abdujabbarov A., Toshmatov B., Stuchlík Z., Ahmedov B.: Shadow of the rotating black hole with quintessential energy in the presence of plasma, D 26 (2017) 1750051
34. Toshmatov B., Stuchlík Z., Ahmedov B.: Generic rotating regular black holes in general relativity coupled to nonlinear electrodynamics, Phys. Rev. D 95 (2017) 084037
35. Abdujabbarov A., Toshmatov B., Schee J., Stuchlík Z., Ahmedov B.:Gravitational lensing by regular black holes surrounded by plasma, Int. J. Mod. Phys. D 26 (2017) 1741011
36. Konoplya R. A., Stuchlík Z.: Are eikonal quasinormal modes linked to the unstable circular null geodesics?, Phys. Lett. B 771 (2017) 597
37. Toshmatov B., Stuchlík Z.: Slowly decaying resonances of massive scalar fields around Schwarzschild-de Sitter black holes, European Physical Journal Plus 132 (2017) 324
38. Toshmatov B., Stuchlík Z., Ahmedov B.: Comments on “Casimir effect in the Kerr spacetime with quintessence”, Mod. Phys. Lett. A 32 (2017) 1775001
39. Toshmatov B., Stuchlík Z., Ahmedov B.: Rotating black hole solutions with quintessential energy, European Physical Journal Plus 132 (2017) 98
40. Blaschke M., Stuchlík Z., Blaschke F., Blaschke P.: Classical corrections to black hole entropy in d dimensions: A rear window to quantum gravity?, Phys. Rev. D 96 (2017) 104012
41. Pugliese D., Stuchlík Z.: Ringed Accretion Disks: Evolution of Double Toroidal Configurations, Astrophys. J. Supplement Series 229 (2017) 40
42. Pugliese D., Stuchlík Z.: Tori sequences as remnants of multiple accreting periods of Kerr SMBHs, Journal of High Energy Astrophysics 17 (2018) 1
43. Novotný J., Hladík J., Stuchlík Z.: Polytropic spheres containing regions of trapped null geodesics, Phys. Rev. D 95 (2017) 043009
44. Stuchlík Z., Schee J., Toshmatov B., Hladík J. & Novotný J.: Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos, Jour. Of Cosmol. And Astropart. Phys. 06 (2017) 056
45. Kološ M., Tursunov A., Stuchlík Z.: Possible signature of the magnetic fields related to quasi-periodic oscillations observed in microquasars, European Physical Journal C 77 (2017) 860
46. Cremaschini C., Stuchlík Z.: Carter constant induced mechanism for generation of anisotropic kinetic equilibria in collisionless N-body systems, Int. J. Mod. Phys. D 26 (2017) 1750001
47. Kotrlová A., Šrámková E., Török G., Stuchlík Z., Goluchová K.: Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars II. Forced resonances, Astronomy & Astrophysics 607 (2017) A69
48. Stuchlík Z., Schee J., Šrámková E., Török G.: Superspinning Quark Stars Limited by Twin High-Frequency Quasiperiodic Oscillations, Acta Astronomica 67 (2017) 181
49. Jalůvková P., Kopteva E., Stuchlík Z.: The model of the black hole enclosed in dust: the flat space case, Gen. Relat. Grav. 49 (2017) 80
50. Bičák J.: Umění a věda, Universum XXVII, č. 1, 20 (2017)
51. Podolský J.: Nobelova cena 2017 udělena za objev gravitačních vln, Astropis č. 4, 12 (2017)
52. Švarc R.:Miliardu let staré poselství , Universum XXVII, č. 1, 14 (2017)