We employ the Poincaré section, fast Lyapunov indicator, recurrence analysis, bifurcation diagram and basins of attraction to investigate the dynamical behaviors of the motion of particles around a new dyonic Kerr–Newman black hole immersed in the Melvin-swirling universe presented in (Di Pinto et al. in J High Energy Phys 06:150, 2025). We note that the swirling parameter $\textit{j}$ and magnetic field strength $\textit{B}$ make the equations of motion for particles nonseparable, and confirm the presence of chaotic behavior in the motion in this dyonic Kerr–Newman–Melvin-swirling spacetime and its sub-cases by removing the conical singularities and removing both the conical singularities and the Dirac strings. We observe that both the number of chaotic orbits and the chaotic region increase with the increase of the parameters $\textit{j}$ and $\textit{B}$, but decrease as the electric charge $\textit{Q}$, magnetic charge $\textit{H}$ or spin parameter $\textit{a}$ increases. Moreover, we find that the presence of $\textit{j}$ changes the ranges of $\textit{B}$, $\textit{Q}$, $\textit{H}$ and $\textit{a}$ where the chaotic motion appears for particles. The swirling parameter together with the magnetic field strength, electric charge, magnetic charge and spin parameter yields richer physics in the motion of particles for the spacetime of a dyonic Kerr–Newman black hole immersed in the Melvin-swirling universe.

China

Deshui Cao

Lina Zhang

Songbai Chen

Qiyuan Pan

Jiliang Jing

Chaotic motion of particles around a dyonic Kerr–Newman black hole immersed in the Melvin-swirling universe

We investigate superradiant bound states of a charged, massive scalar in the Melvin-Kerr spacetime, a rotating black hole immersed in an external magnetic field, working in the weak-field regime <math altimg='si8.svg'><mrow><mi>b</mi><mi>M</mi><mo>&#8810;</mo><mn>1</mn></mrow></math>. We adopt a gauge with <math altimg='si9.svg'><mrow><msub><mi>A</mi><mi>t</mi></msub><mspace width='-0.16em' /><mo>&#8594;</mo><mspace width='-0.16em' /><mn>0</mn></mrow></math> at spatial infinity, thereby removing spurious <math altimg='si10.svg'><mrow><mn>1</mn><mo linebreak='goodbreak'>/</mo><mi>a</mi></mrow></math> artifacts in the <math altimg='si11.svg'><mrow><mi>a</mi><mspace width='-0.16em' /><mo>&#8594;</mo><mspace width='-0.16em' /><mn>0</mn></mrow></math> limit, and show that the Klein&#8211;Gordon equation separates so that the radial dynamics can be cast in Schr&#246;dinger-like form. The effective potential exhibits a universal large- <math altimg='si12.svg'><mi>r</mi></math> tail with both <math altimg='si13.svg'><mrow><mn>1</mn><mo linebreak='goodbreak'>/</mo><mi>r</mi></mrow></math> and <math altimg='si14.svg'><mrow><mn>1</mn><mo linebreak='goodbreak'>/</mo><msup><mi>r</mi><mn>2</mn></msup></mrow></math> corrections controlled by the magnetic coupling <math altimg='si15.svg'><mrow><mi>b</mi><mi>m</mi><mi>q</mi></mrow></math>. Using a far-zone Whittaker reduction we derive a simple trapping criterion that captures when a potential well forms outside the horizon. Combining this with the magnetically shifted superradiant band at the horizon and with the decay requirement at infinity yields an instability window in which superradiantly amplified quasi-bound states exist. The criterion reduces continuously to the standard Kerr bound in the limit <math altimg='si16.svg'><mrow><mi>b</mi><mo>&#8594;</mo><mn>0</mn></mrow></math>, which provides a nontrivial consistency check. Numerical profiles of the effective potential illustrate parameter sets with and without trapping, clarifying how the magnetic field and the azimuthal number compete to enhance or to quench the instability.

Indonesia

Haryanto M. Siahaan

Superradiant bound states of charged scalars around Melvin-Kerr black holes

In this paper, we investigate the existence of stationary scalar clouds in the magnetized Kerr black hole background within the framework of Einstein–Maxwell theory. We consider the dynamics of a massive, charged test scalar field governed by the Klein–Gordon equation. Under the assumption of a weak magnetic field, we demonstrate that the Klein–Gordon equation admits separable solutions in radial and angular variables. The angular equation reduces to a generalized spheroidal harmonic form, while the radial equation can be expressed in terms of the double confluent Heun function. By analyzing the asymptotic behavior of the radial solution, we establish the existence of bound-state scalar clouds characterized by a discrete mass spectrum. We further outline how the (quasi)bound spectrum can be extracted using the continued-fraction method of Vieira–Bezerra–Kokkotas (VBK).

Haryanto Siahaan

Scalar clouds around Melvin–Kerr black holes

We investigate the effect of rainbow gravity on Klein-Gordon (KG) bosons in a quantized nonuniform magnetic field in the background of Bonnor-Melvin (BM) spacetime with a cosmological constant. In the process, we show that the BM spacetime introduces domain walls (i.e., infinitely impenetrable hard walls) at <math altimg='si1.svg'><mi>r</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0</mn></math> and <math altimg='si2.svg'><mi>r</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>&#960;</mi><mo stretchy='false'>/</mo><msqrt><mrow><mn>2</mn><mi mathvariant='normal'>&#923;</mi></mrow></msqrt></math>, as a consequence of the effective gravitational potential field generated by such a magnetized BM spacetime. As a result, the motion of KG particles/antiparticles is restricted indefinitely within the range <math altimg='si3.svg'><mi>r</mi><mo>&#8712;</mo><mo stretchy='false'>[</mo><mn>0</mn><mo>,</mo><mi>&#960;</mi><mo stretchy='false'>/</mo><msqrt><mrow><mn>2</mn><mi mathvariant='normal'>&#923;</mi></mrow></msqrt><mo stretchy='false'>]</mo></math>, and the particles and antiparticles cannot be found elsewhere. Next, we provide a conditionally exact solution in the form of the general Heun function <math altimg='si118.svg'><msub><mrow><mi>H</mi></mrow><mrow><mi>G</mi></mrow></msub><mo stretchy='false'>(</mo><mi>a</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>&#945;</mi><mo>,</mo><mi>&#946;</mi><mo>,</mo><mi>&#947;</mi><mo>,</mo><mi>&#948;</mi><mo>,</mo><mi>z</mi><mo stretchy='false'>)</mo></math>. Within the BM domain walls and under the condition of exact solvability, we study the effects of rainbow gravity on KG bosonic fields in a quantized nonuniform external magnetic field in the BM spacetime background. We use three pairs of rainbow functions: <math altimg='si5.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msup><mrow><mo stretchy='false'>(</mo><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mover accent='true'><mrow><mi>&#946;</mi></mrow><mrow><mo stretchy='false'>&#732;</mo></mrow></mover><mo stretchy='false'>|</mo><mi>E</mi><mo stretchy='false'>|</mo><mo stretchy='false'>)</mo></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>1</mn></mrow></msup><mo>,</mo><mspace width='0.2em' /><mi>h</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1</mn></math>; and <math altimg='si6.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1</mn><mo>,</mo><mspace width='0.2em' /><mi>h</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msqrt><mrow><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mover accent='true'><mrow><mi>&#946;</mi></mrow><mrow><mo stretchy='false'>&#732;</mo></mrow></mover><mo stretchy='false'>|</mo><mi>E</mi><msup><mrow><mo stretchy='false'>|</mo></mrow><mrow><mi>&#965;</mi></mrow></msup></mrow></msqrt></math>, with <math altimg='si145.svg'><mi>&#965;</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math>, where <math altimg='si23.svg'><mi>u</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo stretchy='false'>|</mo><mi>E</mi><mo stretchy='false'>|</mo><mo stretchy='false'>/</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, <math altimg='si123.svg'><mover accent='true'><mrow><mi>&#946;</mi></mrow><mrow><mo stretchy='false'>&#732;</mo></mrow></mover><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>&#946;</mi><mo stretchy='false'>/</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, and <italic>&#946;</italic> is the rainbow parameter. We find that such pairs of rainbow functions, <math altimg='si10.svg'><mo stretchy='false'>(</mo><mi>f</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo>,</mo><mi>h</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo stretchy='false'>)</mo></math>, fully comply with the theory of rainbow gravity, ensuring that <math altimg='si11.svg'><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub></math> is the maximum possible energy for particles and antiparticles alike. Moreover, we show that the corresponding bosonic states form magnetized, rotating vortices, as intriguing consequences of such a magnetized BM spacetime background.

Türkiye

Omar Mustafa

Abdullah Guvendi

Klein-Gordon particles in a nonuniform external magnetic field in Bonnor-Melvin rainbow gravity background

We present a new exact solution of Einstein-Maxwell field equations which represents a rotating black hole with both electric and magnetic charges immersed in a universe which itself is also rotating and magnetized, i.e. the dyonic Kerr-Newman black hole in a Melvin-swirling universe.

Italy

Andrea Pinto

Silke Klemm

Adriano Viganò

Kerr-Newman black hole in a Melvin-swirling universe

We investigate the effect of rainbow gravity on Klein–Gordon (KG) bosons in the background of the magnetized Bonnor–Melvin (BM) spacetime with a cosmological constant. We first show that the very existence of the sinusoidal term $$\sin ^2(\sqrt{2\Lambda }r)$$ , in the BM space-time metric, suggests that $$\sin ^2(\sqrt{2\Lambda }r) \in [0,1],$$ which consequently restricts the range of the radial coordinate $$r$$ to $$r \in [0,\pi /\sqrt{2\Lambda }]$$ . Moreover, we show that at $$r = 0$$ and $$r = \pi /\sqrt{2\Lambda }$$ , the magnetized BM-spacetime introduces domain walls (infinitely impenetrable hard walls) within which the KG bosonic fields are allowed to move. Interestingly, the magnetized BM-spacetime introduces not only two domain walls but a series of domain walls. However, we focus on the range $$r \in [0,\pi /\sqrt{2\Lambda }]$$ . A quantum particle remains indefinitely confined within this range and cannot be found elsewhere. Based on these findings, we report the effects of rainbow gravity on KG bosonic fields in BM-spacetime. We use three pairs of rainbow functions: $$ f(\chi ) = \frac{1}{1 - \tilde{\beta } |E|}, \, h(\chi ) = 1 $$ ; $$ f(\chi ) = (1 - \tilde{\beta } |E|)^{-1}, \, h(\chi ) = 1 $$ ; and $$ f(\chi ) = 1, \, h(\chi ) = \sqrt{1 - \tilde{\beta } |E|^\upsilon } $$ , with $$\upsilon = 1,2$$ . Here, $$\chi = |E| / E_p$$ , $$\tilde{\beta } = \beta / E_p$$ , and $$\beta $$ is the rainbow parameter. We found that while the pairs $$(f,h)$$ in the first and third cases fully comply with the theory of rainbow gravity and ensure that $$E_p$$ is the maximum possible energy for particles and antiparticles, the second pair does not show any response to the effects of rainbow gravity. Moreover, the fascinating properties of this magnetized spacetime background can be useful for modeling magnetic domain walls in condensed matter systems. We show that the corresponding bosonic states can form magnetized, spinning vortices in monolayer materials, and these vortices can be driven by adjusting an out-of-plane aligned magnetic field.

On the Klein–Gordon bosonic fields in the Bonnor–Melvin spacetime with a cosmological constant in rainbow gravity: Bonnor–Melvin domain walls

In this study, we examine the propagation of light rays and wave dynamics within the <math altimg='si1.svg'><mo stretchy='false'>(</mo><mn>2</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>1</mn><mo stretchy='false'>)</mo></math>-dimensional analogue of the Bonnor-Melvin magnetic (BMM) spacetime, which incorporates a nonzero cosmological constant. The BMM spacetime, characterized by cylindrical symmetry, maintains Lorentz invariance along the axial direction, facilitating a systematic investigation of ray trajectories and wave behavior in the corresponding <math altimg='si1.svg'><mo stretchy='false'>(</mo><mn>2</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>1</mn><mo stretchy='false'>)</mo></math>-dimensional magnetic background. This three-dimensional spacetime can be derived as a <math altimg='si2.svg'><mo stretchy='false'>(</mo><mn>2</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>0</mn><mo stretchy='false'>)</mo></math>-brane solution within the context of gravity coupled to nonlinear electrodynamics. Initially, we analyze general ray trajectories and derive exact solutions for the angular motion of light rays. Our findings reveal that light is confined to circular paths within a specific radial region, indicating the formation of light rings governed by the magnetic background. Extending this analysis to wave dynamics, we solve the Helmholtz equation analytically, identifying discrete wave modes with quantized frequencies. The background gravitational field induces oscillatory wave behavior, resulting in well-defined photonic states. These states are notably ring-shaped and rotate, resembling magnetic vortices.

Semra Gurtas Dogan

Ray and wave optics in Bonnor-Melvin domain walls: Photon rings

In this paper, we explore the relativistic quantum motion of spin-zero scalar charge-free particles influenced by rainbow gravity’s (RG’s) in Bonnor–Melvin magnetic space-time, a four-dimensional solution featuring a positive cosmological constant. We solve the Klein–Gordon equation in this scenario by using two sets of rainbow function: (i) $$f(\chi )=\frac{1}{(1-\beta \,\chi )}$$ , $$h(\chi )=1$$ and (ii) $$f(\chi )=\frac{1}{(1-\beta \,\chi )}=h(\chi )$$ , where $$0 < \chi \left( =\frac{|E|}{E_p}\right) \le 1$$ with $$E_p$$ being the Planck’s energy, is the particle’s energy, and $$\beta $$ is the rainbow parameter. Furthermore, we study the relativistic quantum oscillator through the Klein–Gordon oscillator equation in the same Bonnor–Melvin magnetic space-time under RG effects. Employing the first pair of rainbow function, we obtain an approximate eigenvalue solution of the quantum oscillator fields. Notably, we demonstrate that the relativistic energy profile of scalar and oscillator particles are influenced by the topology of the geometry and the cosmological constant which is related with the magnetic field strength lies along the symmetry axis. Additionally, we see the impact of rainbow parameter on these approximate relativistic energy profiles in both quantum systems.

India

Faizuddin Ahmed

Algeria

Abdelmalek Bouzenada

Effects of gravity rainbow on scalar bosonic and oscillator fields in Bonnor–Melvin space-time with a cosmological constant

In this paper, we employ the Generalized Feshbach-Villars transformation (GFVT) to investigate the relativistic quantum dynamics of spin-0 scalar particles within the backdrop of a magnetic universe characterized by the Bonnor-Melvin cosmological space-time, which exhibits a geometrical topology resulting in an angular deficit. We derive the radial equation of the Klein-Gordon equation using this FV representation and obtain analytical solutions utilizing special functions. Our analysis demonstrates that various parameters associated with the space-time geometry exert significant influence on the eigenvalue solutions within this novel representation.

Abdelmalek Boumali

Dynamics of spin-0 (particles-antiparticles) in Bonnor-Melvin cosmological space-time using the Generalized Feshbach-Villars transformation

Nuclear physical inputs are critical for predicting the abundance of r-process elements. Extensive sensitivity studies have recently been performed to gauge the impact of the individual properties of nuclei on the r-process. In this work, we investigate the impact of the large uncertainties in the theoretical predictions of the masses of neutron-rich Sn isotopes and the location of the neutron drip line on the abundance of r-process abundances. The uncertainties in the predicted r-process abundances are obtained through large-scale network calculations by simultaneously varying the masses and reaction rates of Sn within the predicted mass uncertainties. The calculations use a generally indicative astrophysical trajectory of neutron-star mergers and are based on three different mass models. The results indicate that the large uncertainty in the location of the neutron drip line for Sn can significantly and asymmetrically affect the predicted abundances of nuclei after the second peak, in particular around <math><mi>A</mi><mo>=</mo><mn>140</mn><mo>−</mo><mn>155</mn></math>, sometimes accompanied by a delayed freeze-out.