We investigate the dynamics of a neutral and a charged particle around a black hole in modified gravity immersed in a magnetic field. Our focus is on the scalar-tensor-vector theory as modified gravity. We are interested in exploring the conditions on the energy of the particle under which it can escape to infinity after collision with another neutral particle in the vicinity of the black hole. We calculate the escape velocity of particle orbiting in the innermost stable circular orbit (ISCO) after the collision. We study the effects of modified gravity on the dynamics of particles. Further, we discuss how the presence of a magnetic field in the vicinity of a black hole affects the motion of the orbiting particle. We show that the stability of ISCO increases due to the presence of a magnetic field. It is observed that a particle can go arbitrarily close to the black hole due to the presence of a magnetic field. Furthermore, ISCO for a black hole is more stable as compared with a Schwarzschild black hole. We also discuss the Lyapunov exponent and the effective force acting on the particle in the presence of a magnetic field.

The dynamics of a charged particle moving around a slowly rotating Kerr black hole in the presence of an external magnetic field is investigated. We are interested in exploring the conditions under which the charged particle can escape from the gravitational field of the black hole after colliding with another particle. The escape velocity of the charged particle in the innermost stable circular orbit is calculated. The effective potential and escape velocity of the charged particle with angular momentum in the presence of the magnetic field is analyzed. This work serves as an extension of a preceding paper dealing with the Schwarzschild black hole (Zahrani et al., Phys Rev D 87:084043, 2013).

Clusters of galaxies can potentially produce cosmic rays (CRs) up to very high energies via large-scale shocks and turbulent acceleration. Due to their unique magnetic-field configuration, CRs with energy ≤10¹⁷ eV can be trapped within these structures over cosmological time-scales, and generate secondary particles, including neutrinos and gamma rays, through interactions with the background gas and photons. In this work, we compute the contribution from clusters of galaxies to the diffuse neutrino background. We employ 3D cosmological magnetohydrodynamical simulations of structure formation to model the turbulent intergalactic medium. We use the distribution of clusters within this cosmological volume to extract the properties of this population, including mass, magnetic field, temperature, and density. We propagate CRs in this environment using multidimensional Monte Carlo simulations across different redshifts (from z ∼ 5 to z = 0), considering all relevant photohadronic, photonuclear, and hadronuclear interaction processes. We find that, for CRs injected with a spectral index α = 1.5–2.7 and cutoff energy E_max = 10¹⁶–5 × 10¹⁷ eV, clusters contribute to a sizeable fraction to the diffuse flux observed by the IceCube Neutrino Observatory, but most of the contribution comes from clusters with M ≳ 10¹⁴ M_⊙ and redshift z ≲ 0.3. If we include the cosmological evolution of the CR sources, this flux can be even higher.

The origin of the diffuse gamma-ray background (DGRB), the one that remains after subtracting all individual sources from observed gamma-ray sky, is unknown. The DGRB possibly encompasses contributions from different source populations such as star-forming galaxies, starburst galaxies, active galactic nuclei, gamma-ray bursts, or galaxy clusters. Here, we combine cosmological magnetohydrodynamical simulations of clusters of galaxies with the propagation of cosmic rays (CRs) using Monte Carlo simulations, in the redshift range z ≤ 5.0, and show that the integrated gamma-ray flux from clusters can contribute up to 100% of the DGRB flux observed by Fermi-LAT above 100 GeV, for CRs spectral indices α = 1.5 − 2.5 and energy cutoffs $${E}_{\max }=1{0}^{16}-1{0}^{17}$$E max = 1 0 16 − 1 0 17 eV. The flux is dominated by clusters with masses 10¹³ ≲ M/M_⊙ ≲ 10¹⁵ and redshift z ≲ 0.3. Our results also predict the potential observation of high-energy gamma rays from clusters by experiments like the High Altitude Water Cherenkov (HAWC), the Large High Altitude Air Shower Observatory (LHAASO), and potentially the upcoming Cherenkov Telescope Array (CTA).

In this paper, geodesic motion of the charged particles in the vicinity of event horizon of Schwarzschild anti-de-Sitter black hole (BH) with topological defects has been investigated. Weakly magnetized environment is considered in the surrounding of BH which only effects the motion of the particles and doesn’t effect the geometry of the BH. Hence, particles are under the influence of gravity and electromagnetic forces. We have explored the effect of magnetic field on the trajectories of the particles and more importantly on the position of the innermost stable circular orbit. It is observed that the trajectories of the particles in the surrounding of BH are chaotic. Escape conditions of the particles under the influence of gravitomagnetic force are also discussed. Moreover, the escape velocity of particles and its different features have been investigated in the presence and absence of magnetic field. Effect of dark energy on the size of event horizon, mass of the BH and stability of the orbits of the particles have also been explored in detail. These studies can be used to estimate the power of relativistic jets originated from the vicinity of BH.

Clusters of galaxies possess the capability to accelerate cosmic rays (CRs) to very high energy up to ∼10¹⁸ eV due to their large size and magnetic field strength, which favor CR confinement for cosmological times. During their confinement, they can produce neutrinos and γ-rays out of interactions with the background gas and photon fields. In recent work, Hussain et al. have conducted three-dimensional cosmological magnetohydrodynamical simulations of the turbulent intracluster medium combined with multidimensional Monte Carlo simulations of CR propagation for redshifts ranging from z ∼ 5 to z = 0 to study the multimessenger emission from these sources. They found that when CRs with a spectral index in the range 1.5–2.5 and cutoff energy E max = 10 16 – 10 17 eV are injected into the system, they make significant contributions to the diffuse background emission of both neutrinos and γ-rays. In this work, we have revisited this model and undertaken further constraints on the parametric space. This was achieved by incorporating the recently established upper limits on neutrino emission from galaxy clusters, as obtained by the IceCube experiment. We find that for CRs injected with spectral indices in the range 2.0–2.5, cutoff energy E max = 10 16 – 10 17 eV, and power corresponding to (0.1–1)% of the cluster luminosity, our neutrino flux aligns with the upper limits estimated by IceCube. Additionally, the resulting contribution from clusters to the diffuse γ-ray background remains significant with values of the order of ∼10⁻⁵ MeV cm⁻² s⁻¹ sr⁻¹ at energies above 500 GeV.