Non-Linear Monte Carlo Ray Tracing for Visualizing Warped Spacetime
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Non-linear Monte Carlo Ray Tracing for Visualizing Warped Spacetime Avirup Mandal∗, Kumar Ayush∗ and Parag Chaudhuri Indian Institute of Technology Bombay, Powai, Mumbai, India Keywords: Raytracing, Non-linear Monte Carlo, Warped Spacetime, Relativity. Abstract: General relativity describes the curvature of spacetime. Rays of light follow geodesic paths in curved space- time. Visualizing scenes containing spacetime regions with pronounced curvature requires tracing of these light ray paths. We present a Monte Carlo approach for non-linear raytracing to render scenes in curved space- time. In contrast to earlier work, we can accurately resolve ray-object interactions. This allows us to create plausible visualizations of what happens when a black hole appears in a more known environment, like a room with regular specular and diffuse surfaces. We demonstrate that our solution is correct at cosmological scales by showing how spacetime warps around a stationary Schwarzschild black hole and a non-stationary Kerr black hole. We verify that the solution is consistent with the predictions of general relativity. In the absence of any curvature in spacetime, our renderer behaves like a normal linear ray tracer. Our method has the poten- tial to create rich, physically plausible visualizations of complex phenomena that can be used for a range of purposes, from creating visual effects to making pedagogical aids to understand the behaviour of spacetime as predicted by general relativity. 1 INTRODUCTION momentum is referred to as a Schwarzschild black hole (Schwarzschild, 1916). A Kerr black hole (Kerr, General relativity changed the way in which we un- 1963) on the other hand, possesses angular momen- derstand our universe. The theory presented by Ein- tum and rotates. Another related cosmological phe- stein in 1915 has been verified via multiple experi- nomenon is a wormhole, which is like a hole punched mental observations. However, the concept of curved through curved spacetime connecting two different spacetime that is central to this theory stays elusive to regions of spacetime. An example of this is the Ellis a casual reader. Even students of physics have trouble Wormhole, visualized in the movie Interstellar (Ellis, visualizing what curved spacetime looks like because 1973) (Morris and Thorne, 1988) (Thorne, 2015). it is so far removed from our daily experience. It was The curving of spacetime, however, is a fact pre- only recently that a visualization of curved spacetime dicted by the theory of general relativity and is present was created that is true as per general relativity and it in the vicinity of any object that has mass. We are in- depicted how a black hole would look to an observer terested in visualizing not only black holes, but any much closer to it (James et al., 2015a) (James et al., warped spacetime, both at cosmological and at earth- 2015b). The cosmological phenomenon visualized in like or everyday scales. We present in this paper a ray these works were a rotating black hole and a worm- tracing method that allows us to visualize any arbi- hole. trary scene in any type of spacetime. We can stochas- A black hole can be described as a region in space tically trace rays in the warped spacetime, while tak- where the gravitational field is so strong that no matter ing care of normal light-surface interactions like re- or radiation can escape. The boundary of the region flection and refraction. This allows us to visualize ev- from which no escape is possible is called the event eryday geometry in strongly curved spacetimes. We horizon. According to the general theory of relativity, believe our work is first of its kind in being able to a body of sufficient mass can deform or warp space- create such visualizations. We find the images that time around it and result in a black hole. A static black our renderer produces to be extremely useful in un- hole, which possesses no electric charge or angular derstanding the concept of curved spacetime and vi- sualizing how the universe behaves in the presence of ∗A. Mandal and K. Ayush contributed equally to this gravity. We also believe it is unique in being able to work. 76 Mandal, A., Ayush, K. and Chaudhuri, P. Non-linear Monte Carlo Ray Tracing for Visualizing Warped Spacetime. DOI: 10.5220/0010217600760087 In Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2021) - Volume 3: IVAPP, pages 76-87 ISBN: 978-989-758-488-6 Copyright c 2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved Non-linear Monte Carlo Ray Tracing for Visualizing Warped Spacetime create physics-based visualizations that are of interest specific intensity that reaches the observer by in- to generating special effects in cinema and as such, tegrating the radiative transfer equation along the it is intended to work as a proof of concept that ray computed geodesic. However, they assume the ob- tracing in curved spacetime can easily be integrated jects to be emissive, as most astrophysical objects into existing production pipelines. As a result, now of interest in such extreme environments are, and do we may have more realistic wormholes opening up in not handle reflection and refraction from those ob- an alley in New York, which acts as a pathway for jects, specular or diffuse. Another work presented by aliens. The major contributions of our work are listed Müller (Müller, 2014) uses the Motion4D library to as below handle spacetime metrics and ray tracing. The GPU • We perform secondary ray tracing and resolve all accelerated renderer presented in GRay (Chan et al., object-ray intersections in curved space-time. 2013) (Kuchelmeister et al., 2012) further parallelizes the work presented in earlier literature, to increase the • We render our scene using complete global illumi- throughput at which rays can be traced. Another GPU nations in warped spacetime which is essential to based renderer (Weiskopf et al., 2004) discusses re- produce visual phenomena like soft shadows and fraction through a continuous medium of varying re- caustics. fractive index as an example on non-linear ray tracing, • We develop a non-linear ray tracing algorithm that but does not tackle refraction within a warped space- works both in cosmological as well as terrestrial time itself. scale. Among other work, is also the Black Hole Flight We talk about relevant current literature in the next Simulator (BHFS) (Hamilton, 2008), that shows how section. We explain light paths in curved spacetime, it looks like to travel towards and through various and derive expressions for the geodesics that repre- kinds of black holes. A ray tracing algorithm for sent the light paths in Section 3. We present partic- visualizing two different spinning celestial objects, a ular solutions for the Schwarzschild and Kerr met- neutron star and a quasi-Kerr black hole are described rics for non-rotating and rotating black holes respec- in (Psaltis and Johannsen, 2012) and (Bauböck et al., tively, and for the Ellis metric for wormholes. Then 2012) respectively. we present our simple ray integrator in Section 4. De- It was only recently that visualizations with an tailed results and discussions of the results are pre- observer placed closer to the black hole were pro- sented in Section 5. duced. The Double Negative Gravitational Renderer (DNGR) was used to produce the imagery for the acclaimed movie Interstellar (Thorne, 2015) (James et al., 2015a) (James et al., 2015b). The renderer 2 RELATED WORK is unique in that it not only solves the equations for a ray-bundle propagation near a spinning black hole, Astrophysical ray tracers have a long history. These but also produces extremely high resolution imagery visualizations have become adept at simulating and required for a cinema production. This is done by visualizing increasingly complex cosmological phe- mapping the celestial sphere around a black hole or nomena. Gas, dust and other stellar debris that has a wormhole to the local sky of the observing camera, come close to a black hole but not quite fallen into while accounting for the change in the cross-section it, forms a flattened band of spinning matter around of the light beam and, color and intensity changes due the event horizon called the accretion disk. Thin ac- to Doppler shifts that occur in the process. cretion disks around black holes were visualized in early work in the area (Luminet, 1979). Subsequent 2.1 Comparison to State of the Art works added color (Fukue and Yokoyama, 1988), handled rotating black holes and thicker accretion We do not claim to present any new astrophysics disks (Viergutz, 1993) and finally images produced insights in our paper, nor do we claim to be bet- by a simulated camera flyby near the disk (Marck, ter than DNGR in all respects. We certainly do not 1996). The special relativistic visualization of 4D produce cinematic production quality images. How- space (Müller et al., 2010) and visualization of circu- ever, we believe that to the best of our knowledge, lar motion around Schwarzschild black hole (Müller we present the only renderer of its kind that can vi- and Boblest, 2011) have been explored before. The sualize highly warped spacetime, both in outer space general relativistic ray tracer GYOTO (Vincent et al., and in everyday human-scale scenes like rooms and 2011) uses the Hamiltonian formalism to integrate buildings. None of the previous works (Müller, the rays backward in time. They also compute the 2014), (Kuchelmeister et al., 2012), (James et al., 77 IVAPP 2021 - 12th International Conference on Information Visualization Theory and Applications 2015a), (James et al., 2015b) deal with simulating ing of spacetime. This will happen to all the stars on complete global illumination in curved spacetime.