Related papers: A Fast New Public Code for Computing Photon Orbits…
Following \cite{dexagol2009} we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass' and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical…
In this paper we present a new public code, named $ynogkm$, for the fast calculation of time-like geodesics in the Kerr-Newmann (K-N) spacetime, which is a direct extension of $ynogk$ calculating null geodesics in a Kerr spacetime.…
The null geodesic equation in the Kerr spacetime can be expressed as a set of integral equations involving certain potentials. We classify the roots of these potentials and express the integrals in manifestly real Legendre elliptic form. We…
The equations of general relativity in the form of timelike and null geodesics that describe motion of test particles and photons in Kerr spacetime are solved exactly including the contribution from the cosmological constant. We then…
In this paper we study the motion of photons or massless particles in the C-metric with cosmological constant. The Hamilton--Jacobi equations are known to be completely separable, giving a Carter-like quantity $Q$ which is a constant of…
The timelike geodesic equations resulting from the Kerr gravitational metric element are derived and solved exactly including the contribution from the cosmological constant. The geodesic equations are derived, by solving the…
We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parameterized explicitly by constants of motion -- the energy, the angular momentum, and the Carter constant -- and initial…
We analyze the transformation of the polarization of a photon propagating along an arbitrary null geodesic in Kerr geometry. The motivation comes from the problem of an observer trying to communicate quantum information to another observer…
In this article, we describe and numerically implement a method for relativistic location in slightly curved but otherwise generic spacetimes. For terrestrial positioning in the context of Global Navigation Satellite Systems, our algorithm…
It has now become possible to study directly, via numerical simulation, the evolution of relativistic, radiation-dominated flows around compact objects. With this in mind we set out explicitly covariant forms of the radiative transfer…
Ray tracing radiative transfer is a powerful method for comparing theoretical models of black hole accretion flows and jets with observations. We present a public code, grtrans, for carrying out such calculations in the Kerr metric,…
A new form of the Kerr solution is presented. The solution involves a time coordinate which represents the local proper time for free-falling observers on a set of simple trajectories. Many physical phenomena are particularly clear when…
We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black hole's exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is…
We present an invariant characterization of the Kerr spacetime, and utilize the invariant structure of the spacetime to derive a function whose zeros identify a special family of null geodesics. Each member of this family is tangent to…
We develop the 3-dimensional general relativistic radiative transfer code: CARTOON (Calculation code of Authentic Radiative Transfer based On phOton Number conservation in curved space-time) which is improved from the 2-dimensional code:…
The Kerr spacetime is one of the most widely known solutions to Einstein's vacuum field equations and is commonly used to describe a black hole with mass $m$ and spin $a$. Astrophysical observations in the electromagnetic spectrum as well…
We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games. We overcome the curse-of-infinite-dimensionality nature of HJD by proposing a generalized Hopf…
We present a new code for radiation transport around Kerr black holes, including arbitrary emission and absorption terms, as well as electron scattering and polarization. The code is particularly useful for analyzing accretion flows made up…
We develop a neutrino transfer code for core-collapse simulations, that directly solves the multidimensional Boltzmann equations in full general relativity. We employ the discrete ordinate method, which discretizes the six dimensional phase…
In this paper, we deal with the null geodesics extending from the near-horizon region out to a distant observatory in an extremal Kerr-Newman black hole background. In particular, using the matched asymptotic expansion method, we…