Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar

Interstellar is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by somebody nearby. For this we developed a code called DNGR (Double Negative Gravitational Renderer) to solve the equations for ray-bundle (light-beam) propagation through the curved spacetime of a spinning (Kerr) black hole, and to render IMAX-quality, rapidly changing images. Our ray-bundle techniques were crucial for achieving IMAX-quality smoothness without flickering. This paper has four purposes: (i) To describe DNGR for physicists and CGI practitioners . (ii) To present the equations we use, when the camera is in arbitrary motion at an arbitrary location near a Kerr black hole, for mapping light sources to camera images via elliptical ray bundles. (iii) To describe new insights, from DNGR, into gravitational lensing when the camera is near the spinning black hole, rather than far away as in almost all prior studies. (iv) To describe how the images of the black hole Gargantua and its accretion disk, in the movie \emph{Interstellar}, were generated with DNGR. There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of Interstellar interesting.Comment: 46 pages, 17 figure

Geometry of a Black Hole Collision

The Binary Black Hole Alliance was formed to study the collision of black holes and the resulting gravitational radiation by computationally solving Einstein's equations for general relativity. The location of the black hole surface in a head-on collision has been determined in detail and is described here. The geometrical features that emerge are presented along with an analysis and explanation in terms of the spacetime curvature inherent in the strongly gravitating black hole region. This curvature plays a direct, important, and analytically explicable role in the formation and evolution of the event horizon associated with the surfaces of the black holes

Extending backward polygon beam tracing of glossy scattering surfaces

Backward polygon beam tracing methods, that is beam tracing from the light source (L), are well suited to gather path coherency from specular (S) scattering surfaces. These methods are useful for modelling and efficiently simulating caustics on diffuse (D) surfaces; an effect due to LS+D transport paths. This paper generalizes backward polygon beam tracing to include a glossy (G) scattering surface. To this end the details of a beam tracing lumped model and implementation of L (S\G) D transport paths are presented. Although we limit the discussion to short transport paths, we show that backward beam tracing is faster than photon mapping by an order of magnitude for rendering caustics from glossy and specular surfaces.http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-8659

Visualizing Interstellar's Wormhole

Christopher Nolan's science fiction movie Interstellar offers a variety of opportunities for students in elementary courses on general relativity theory. This paper describes such opportunities, including: (i) At the motivational level, the manner in which elementary relativity concepts underlie the wormhole visualizations seen in the movie. (ii) At the briefest computational level, instructive calculations with simple but intriguing wormhole metrics, including, e.g., constructing embedding diagrams for the three-parameter wormhole that was used by our visual effects team and Christopher Nolan in scoping out possible wormhole geometries for the movie. (iii) Combining the proper reference frame of a camera with solutions of the geodesic equation, to construct a light-ray-tracing map backward in time from a camera's local sky to a wormhole's two celestial spheres. (iv) Implementing this map, for example in Mathematica, Maple or Matlab, and using that implementation to construct images of what a camera sees when near or inside a wormhole. (v) With the student's implementation, exploring how the wormhole's three parameters influence what the camera sees---which is precisely how Christopher Nolan, using our implementation, chose the parameters for \emph{Interstellar}'s wormhole. (vi) Using the student's implementation, exploring the wormhole's Einstein ring, and particularly the peculiar motions of star images near the ring; and exploring what it looks like to travel through a wormhole.Comment: 14 pages and 13 figures. In press at American Journal of Physics. Minor revisions; primarily insertion of a new, long reference 15 at the end of Section II.

Trade-off between angular resolution and straylight contamination in CMB anisotropy experiments. I. Pattern simulations

The study of Cosmic Microwave Background (CMB) anisotropies represents one of the most powerful Cosmological tools. After the great success of the two NASA's satellite missions COBE and WMAP, Planck represents the third generation of mm-wave instruments designed for space observations of CMB anisotropies within the new Cosmic Vision 2020 ESA Science Programme. The Planck survey will cover the whole sky with unprecedented sensitivity, angular resolution and frequency coverage, using two instruments that share the focal region of a 1.5 m off-axis dual reflector telescope: the Low Frequency Instrument (LFI) and the High Frequency Instrument (HFI). Within the LFI optical interfaces optimisation activity, two concurrent demands have to be satisfied: the best angular resolution (which impacts the ability to reconstruct the anisotropy power spectrum of the CMB anisotropies at high multipoles) and the lowest level of straylight contamination (that may be one of the most critical sources of systematic effects). We present the results of the optical simulations aimed to establish the trade-off between angular resolution and straylight rejection, carried out for the 100 GHz channel of Planck Low Frequency Instrument. Antenna pattern of different models of dual profiled corrugated conical feed horns have been simulated using advanced simulation techniques, considering the whole spacecraft geometry in order to obtain truthful sidelobe predictions. Optical computation accuracy necessary to provide strong straylight evaluation in reasonable computational time is shown and the inadequacy of a Gaussian feed model in realistic far pattern predictions is demonstrated. This paper is based on LFI activities.Comment: 23 pages, 19 figures (quality of the figures was degraded for size-related reasons). Submitted to A&

Photo-Realistic Rendering of Fiber Assemblies

In this thesis we introduce a novel uniform formalism for light scattering from filaments, the Bidirectional Fiber Scattering Distribution Function (BFSDF). Similar to the role of the Bidirectional Surface Scattering Reflectance Distribution Function (BSSRDF) for surfaces, the BFSDF can be seen as a general approach for describing light scattering from filaments. Based on this theoretical foundation, approximations for various levels of abstraction are derived allowing for efficient and accurate rendering of fiber assemblies, such as hair or fur. In this context novel rendering techniques accounting for all prominent effects of local and global illumination are presented. Moreover, physically-based analytical BFSDF models for human hair and other kinds of fibers are derived. Finally, using the model for human hair we make a first step towards image-based BFSDF reconstruction, where optical properties of a single strand are estimated from "synthetic photographs" (renderings) a full hairstyle