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We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of…
Ghost neutrinos in radiative Kerr spacetime endowed with totally skew-symmetric Cartan contortion is presented. The computations are made by using the Newman-Penrose (NP) calculus. The model discussed here maybe useful in several…
We start with formulation of the generalized Fermat's principle for light propagation in a curved spacetime. We apply Pontryagin's minimum principle of the optimal control theory and obtain an effective Hamiltonian for null geodesics in a…
Compton scattering is involved in many astrophysical situations. It is well known and has been studied in detail for the past fifty years. Exact formulae for the different cross sections are often complex, and essentially asymptotic…
Radiative transfer plays a major role in high-energy astrophysics. In multiple scenarios and in a broad range of energy scales, the coupling between matter and radiation is essential to understand the interplay between theory, observations…
We consider the high spin expansion for the null geodesics in the Kerr spacetime. We expand the null geodesic equation successively to higher orders in deviation from extremity. Via the method of matched asymptotic expansion, the radial…
This paper presents two new direct symbolic-numerical algorithms for the transformation of Cartesian coordinates into geodetic coordinates considering the general case of a triaxial reference ellipsoid. The problem in both algorithms is…
We present a novel formulation of the Kerr spacetime solution, based on the Lema\^itre coordinates. Such an approach allows one to avoid the coordinate singularities of the Boyer-Lindquist metric, thus offering the possibility to explore in…
Johannsen metric is a natural and significant generalization of the Kerr metric, representing the most general stationary, axisymmetric spacetime that preserves the Carter constant of motion. The theoretical status furnishes a powerful,…
We describe a Monte Carlo radiative transport code intended for calculating spectra of hot, optically thin plasmas in full general relativity. The version we describe here is designed to model hot accretion flows in the Kerr metric and…
In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles.…
Recently, the current authors have formulated and extensively explored a rather novel Painleve-Gullstrand variant of the slow-rotation Lense-Thirring spacetime, a variant which has particularly elegant features -- including unit lapse,…
It is not currently known how to put the Kerr spacetime metric into the so-called Gordon form, although the closely related Kerr-Schild form of the Kerr metric is well known. A Gordon form for the Kerr geometry, if it could be found, would…
Hamilton-Jacobi theory for general relativity provides an elegant covariant formulation of the gravitational field. A general `coordinate-free' method of integrating the functional Hamilton-Jacobi equation for gravity and matter is…
We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit…
We demonstrate the separability of the Hamilton-Jacobi and scalar field equations in general higher dimensional Kerr-NUT-AdS spacetimes. No restriction on the parameters characterizing these metrics is imposed.
An study of the equatorial circular motion of photons and massive particles around a rotating compact body like a neutron star is presented. For this goal, we use an approximate Kerr-like metric with mass quadrupole as perturbation. The…
We study spacetimes that lead to a separable Klein-Gordon equation in a general dimension. We introduce an ansatz for the metric in higher dimensions motivated by analogical work by Carter in four dimensions and find solutions of the…
We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation and it is accurate for optically thin, thick, and intermediate…
In the square root velocity framework, the computation of shape space distances and the registration of curves requires solution of a non-convex variational problem. In this paper, we present a new PDE-based method for solving this problem…