Spin foam theory is a concrete framework for quantum gravity where numerical calculations of transition amplitudes are possible. Recently, the field became very active, but entry barrier steep, mainly because its unusual language and notions scattered around literature. This paper pedagogical guide to spin amplitude calculations. We show how write an EPRL-FK amplitude, from definition 2-complex...

We study density cusps in the center of clusters of galaxies to reconcile X-ray mass estimates with gravitational lensing masses. For various mass density models with cusps we compute X-ray surface brightness distribution, and fit them to observations to measure the range of parameters in the density models. The Einstein radii estimated from these density models are compared with Einstein radii...

Observations show that accretion discs in many X-ray binaries are flared. An outer edge of the disc intercepts radiation from the central X-ray source. Part of that radiation is absorbed and reemitted in the optical/UV spectral ranges. However, a large fraction of that radiation is reflected and appears in the broad-band X-ray spectrum as a Compton reflection bump. This radiation is delayed and...

To render an object by ray tracing, one or more rays are shot from the viewpoint through every pixel of the image plane. For reflective and refractive objects, especially for multiple levels of reflections and/or refractions, this requires many expensive intersection calculations. This paper presents a new method for accelerating ray-tracing of reflective and refractive objects by substituting ...