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We analyze the scalar radiation emitted by a source in a circular geodesic orbit around a spherically symmetric black hole. The black hole spacetime considered is quite general, in the sense that it encompasses the solutions of…
The stationary gravitational field of two identical counter-moving beams of pure radiation is found in full generality. The solution depends on an arbitrary function and a parameter which sets the scale of the energy density. Some of its…
We derive exact analytical solutions describing multi-soliton complexes and their interactions on top of a multi-component background in media with self-focusing or self-defocusing Kerr-like nonlinearities. These results are illustrated by…
The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…
Under certain conditions the number of photons radiated classically by a charged particle following a prescribed trajectory can be finite. An interesting formula for this number is presented and discussed.
The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is…
We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…
We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion…
For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the…
We studied the shock propagation and its stability with the causal dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence of the usual viscosity is not enough to stabilize the solution. This problem is solved by…
In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of…
We present a few subjects from physics that have one in common: the spectral resolution of the Laplacian.
We present an analytic solution to diffusion equation for high energy cosmic rays in the expanding universe. The particles are assumed to be ultra-relativistic and they can have energy losses arbitrarily dependent on energy and time. The…
The nuclei fraction in cosmic rays (CR) far exceeds the fraction of other CR species, such as antiprotons, electrons, and positrons. Thus the majority of information obtained from CR studies is based on interpretation of isotopic abundances…
Spirals shocks have been widely studied in the context of galactic dynamics and protostellar discs. They may however also play an important role in some classes of close binary stars, and more particularly in cataclysmic variables. In this…
We show that dispersive shock waves resulting from the nonlinearity overbalancing a weak leading-order dispersion can emit resonant radiation owing to higher-order dispersive contributions. We analyze such phenomenon for the defocusing…
In this paper, we provide a systematic way of finding explicit solutions for a class of continuous fragmentation equations with growth or decay in the state space and derive explicit solutions in the cases of constant and linear…
Patterns in the scientific developments of Relativistic Astrophysics are analyzed with special attention to the physics and astrophysics of Black Holes and Gamma Ray Bursts.
Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can…
We consider the structure of mildly relativistic shocks in dense media, taking into account the radiation and pair loading, and diffusive radiation energy transfer within the flow. For increasing shock velocity (increasing post-shock…