Kerr black hole null geodesic ray tracing (part 2) скачать в хорошем качестве

Kerr black hole null geodesic ray tracing (part 2)

Simulation of lightlike particles (null-geodesics) in the proximity of an extreme Kerr black hole (a = 1). The rapid rotation of the black hole is depicted by the purple cogwheel, having one tenth of the angular frequency of the black hole. The black hole is shown as a sphere with the Schwarzschild radius in spite of the actual shape of the Kerr black hole being partially oblate as shown in the ray tracing. Illustrative objects including walls, a cylinder and accretion disks are displayed to illustrate the appearance of the black hole and its surroundings in relation to the path of the photons - the technique is generally referred to as ray tracing. :: How the ray tracing works :: The particles emitted from the same position first cross the canvas (rectangular screen) defining their observed position and afterwards interact with an object or the black hole defining the color of the canvas pixel at the observed position (gravitational redshift is not depicted). This process is repeated for batches of particles with randomized directions towards the canvas. The ray tracing in this video differs from conventional ray tracing by the observer-canvas distance and the randomized sampling / Monte-Carlo-method which are here chosen for illustrative purposes. :: Technical :: The simulation was based on Hamilton's equations for the combined Hamiltonian of the Kerr-, Kerr-Newman- and Reissner-Nordström black hole, including the (anti) de Sitter variants, where the Kerr black hole equations are simply obtained by setting Q = Λ = 0 and M = a = 1 for this case. The Hamiltonian was derived and optimized in "Cartesian" Kerr-Schild coordinates eliminating the polar singularities resulting from commonly used Boyer-Lindquist coordinates by fault of spherical coordinates. The null-geodesics for the Schwarzschild black hole are obtained from the criterion H = 0 that has a unique solution for the initial conditions of Kerr-Schild coordinates also valid when initialized in proximity of the black hole. The simulation of the particles was performed using high order symplectic integrators and the video was rendered in real time, although completion of the ray tracing canvas does require a few hours by the inefficient single-core Monte-Carlo-method approach. The technical approach for ray tracing used in this video is generally ill-advised, and is here presented only as a general Hamiltonian approach that conserves exactly the symplectic two-form and with graphics being illustrative rather than fast and detailed. 🎵 "Dead Feelings" by "Carter" | not affiliated with/endorsed by.