Recent zbMATH articles in MSC 70E05https://zbmath.org/atom/cc/70E052024-03-13T18:33:02.981707ZWerkzeugGyrostatic Suslov problemhttps://zbmath.org/1528.700042024-03-13T18:33:02.981707Z"Maciejewski, Andrzej J."https://zbmath.org/authors/?q=ai:maciejewski.andrzej-j"Przybylska, Maria"https://zbmath.org/authors/?q=ai:przybylska.mariaSummary: In this paper, we investigate the gyrostat under influence of an external potential force with the Suslov nonholonomic constraint: the projection of the total angular velocity onto a vector fixed in the body vanishes. We investigate cases of free gyrostat, the heavy gyrostat in the constant gravity field, and we discuss certain properties for general potential forces. In all these cases, the system has two first integrals: the energy and the geometric first integral. For its integrability, either two additional first integrals or one additional first integral and an invariant \(n\)-form are necessary. For the free gyrostat we identify three cases integrable in the Jacobi sense. In the case of heavy gyrostat three cases with one additional first integral are identified. Among them, one case is integrable and the non-integrability of the remaining cases is proved by means of the differential Galois methods. Moreover, for a distinguished case of the heavy gyrostat a co-dimension one invariant subspace is identified. It was shown that the system restricted to this subspace is super-integrable, and solvable in elliptic functions. For the gyrostat in general potential force field conditions of the existence of an invariant \(n\)-form defined by a special form of the Jacobi last multiplier are derived. The class of potentials satisfying them is identified, and then the system restricted to the corresponding invariant subspace of co-dimension one appears to be integrable in the Jacobi sense.Geodesic structure of a rotating regular black holehttps://zbmath.org/1528.830682024-03-13T18:33:02.981707Z"Bautista-Olvera, Brandon"https://zbmath.org/authors/?q=ai:bautista-olvera.brandon"Degollado, Juan Carlos"https://zbmath.org/authors/?q=ai:degollado.juan-carlos"German, Gabriel"https://zbmath.org/authors/?q=ai:german.gabrielSummary: We examine the dynamics of particles around a rotating regular black hole. In particular we focus on the effects of the characteristic length parameter of the spinning black hole on the motion of the particles by solving the equation of orbital motion. We have found that there is a fourth constant of motion that determines the dynamics of orbits out the equatorial plane similar as in the Kerr black hole. Through detailed analyses of the corresponding effective potentials for massive particles the possible orbits are numerically simulated. A comparison with the trajectories in a Kerr spacetime shows that the differences appear when the black holes rotate slowly for large values of the characteristic length parameter.Gyroscopic precession in the vicinity of a static blackhole's event horizonhttps://zbmath.org/1528.830802024-03-13T18:33:02.981707Z"Majumder, Paulami"https://zbmath.org/authors/?q=ai:majumder.paulami"Nayak, K. Rajesh"https://zbmath.org/authors/?q=ai:nayak.k-rajeshSummary: In this article, we investigate gyroscopic precession in the vicinity of a spherically symmetric static event horizon. Our goal is to address whether the gyroscopic precession frequency diverges when approaching an event horizon. To do so, we employ the Frenet-Serret formalism of gyroscopic precession, which provides a complete covariant formalism, and extend it to include arbitrary timelike curves. We analyze the precession frequency near the Schwarzschild and Schwarzschild-anti-de-Sitter black holes, using horizon-penetrating Kerr-Schild coordinates to eliminate coordinate singularities near the horizon. Our study shows that a diverging gyroscopic precession frequency is not a universal feature for a trajectory crossing an event horizon. As a counter-example, we construct a timelike curve passing through the event horizon along which the gyroscopic precession frequency remains finite at the horizon.Impact of multiple modes on the evolution of self-interacting axion condensate around rotating black holeshttps://zbmath.org/1528.830812024-03-13T18:33:02.981707Z"Omiya, Hidetoshi"https://zbmath.org/authors/?q=ai:omiya.hidetoshi"Takahashi, Takuya"https://zbmath.org/authors/?q=ai:takahashi.takuya"Tanaka, Takahiro"https://zbmath.org/authors/?q=ai:tanaka.takahiro"Yoshino, Hirotaka"https://zbmath.org/authors/?q=ai:yoshino.hirotaka(no abstract)Energy formula, surface geometry and energy extraction for Kerr-Sen black holehttps://zbmath.org/1528.830822024-03-13T18:33:02.981707Z"Pradhan, Parthapratim"https://zbmath.org/authors/?q=ai:pradhan.parthapratimSummary: We evaluate the \textit{surface energy \((\mathcal{E}_s^\pm)\), rotational energy} \((\mathcal{E}_r^\pm)\) \textit{and electromagnetic energy} \((\mathcal{E}_{em}^\pm)\) for a \textit{Kerr-Sen black hole (BH)} having the event horizon \((\mathcal{H}^+)\) and the Cauchy horizon \((\mathcal{H}^-)\). Interestingly, we find that the \textit{sum of these three energies is equal to the mass parameter i.e.}\(\mathcal{E}_s^\pm +\mathcal{E}_r^\pm +\mathcal{E}_{em}^\pm =\mathcal{M}\) . Moreover in terms of the \textit{ scale parameter} \((\zeta_\pm)\), \textit{the distortion parameter} \((\xi_\pm)\) \textit{and a new parameter} \((\sigma_\pm)\) which corresponds to the area \((\mathcal{A}_\pm)\), the angular momentum \((J)\) and the charge parameter \((Q)\), we find that the \textit{mass parameter in a compact form} \(\mathcal{E}_s^\pm +\mathcal{E}_r^\pm +\mathcal{E}_{em}^\pm =\mathcal{M} =\frac{\zeta_\pm}{2} \sqrt{\frac{1+2 \sigma_\pm^2}{1-\xi_\pm^2}}\) which is valid through all the horizons \(( \mathcal{H}^\pm)\). We also compute the \textit{equatorial circumference and polar circumference} which is a gross measure of the BH surface deformation. It is shown that when the spinning rate of the BH increases, the \textit{equatorial circumference increases} while the \textit{polar circumference decreases}. We show that there exist two classes of geometry separated by \(\xi_\pm =\frac{1}{2}\) in Kerr-Sen BH. In the regime \(\frac{1}{2}<\xi_\pm \leq \frac{1}{\sqrt{2}}\), the Gaussian curvature is negative and there exist \textit{two polar caps} on the surface. While for \(\xi_\pm <\frac{1}{2}\), the Gaussian curvature is positive and the surface will be an oblate deformed sphere. Furthermore, we compute the exact expression of \textit{rotational energy that should be extracted from the BH via Penrose process}. The maximum value of rotational energy which is extractable should occur for \textit{extremal Kerr-Sen BH} i.e. \(\mathcal{ E}_r^+ =\left( \sqrt{2}-1\right) \sqrt{\frac{J}{2}}\).Spins of primordial black holes formed with a soft equation of statehttps://zbmath.org/1528.830842024-03-13T18:33:02.981707Z"Saito, Daiki"https://zbmath.org/authors/?q=ai:saito.daiki"Harada, Tomohiro"https://zbmath.org/authors/?q=ai:harada.tomohiro"Koga, Yasutaka"https://zbmath.org/authors/?q=ai:koga.yasutaka"Yoo, Chul-Moon"https://zbmath.org/authors/?q=ai:yoo.chul-moon(no abstract)