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create physics-based visualizations that are of interest
to generating special effects in cinema and as such,
it is intended to work as a proof of concept that ray
tracing in curved spacetime can easily be integrated
into existing production pipelines. As a result, now
we may have more realistic wormholes opening up in
an alley in New York, which acts as a pathway for
aliens. The major contributions of our work are listed
as below
• We perform secondary ray tracing and resolve all
object-ray intersections in curved space-time.
• We render our scene using complete global illumi-
nations in warped spacetime which is essential to
produce visual phenomena like soft shadows and
caustics.
• We develop a non-linear ray tracing algorithm that
works both in cosmological as well as terrestrial
scale.
We talk about relevant current literature in the next
section. We explain light paths in curved spacetime,
and derive expressions for the geodesics that repre-
sent the light paths in Section 3. We present partic-
ular solutions for the Schwarzschild and Kerr met-
rics for non-rotating and rotating black holes respec-
tively, and for the Ellis metric for wormholes. Then
we present our simple ray integrator in Section 4. De-
tailed results and discussions of the results are pre-
sented in Section 5.
2 RELATED WORK
Astrophysical ray tracers have a long history. These
visualizations have become adept at simulating and
visualizing increasingly complex cosmological phe-
nomena. Gas, dust and other stellar debris that has
come close to a black hole but not quite fallen into
it, forms a flattened band of spinning matter around
the event horizon called the accretion disk. Thin ac-
cretion disks around black holes were visualized in
early work in the area (Luminet, 1979). Subsequent
works added color (Fukue and Yokoyama, 1988),
handled rotating black holes and thicker accretion
disks (Viergutz, 1993) and finally images produced
by a simulated camera flyby near the disk (Marck,
1996). The special relativistic visualization of 4D
space (Müller et al., 2010) and visualization of circu-
lar motion around Schwarzschild black hole (Müller
and Boblest, 2011) have been explored before. The
general relativistic ray tracer GYOTO (Vincent et al.,
2011) uses the Hamiltonian formalism to integrate
the rays backward in time. They also compute the
specific intensity that reaches the observer by in-
tegrating the radiative transfer equation along the
computed geodesic. However, they assume the ob-
jects to be emissive, as most astrophysical objects
of interest in such extreme environments are, and do
not handle reflection and refraction from those ob-
jects, specular or diffuse. Another work presented by
Müller (Müller, 2014) uses the Motion4D library to
handle spacetime metrics and ray tracing. The GPU
accelerated renderer presented in GRay (Chan et al.,
2013) (Kuchelmeister et al., 2012) further parallelizes
the work presented in earlier literature, to increase the
throughput at which rays can be traced. Another GPU
based renderer (Weiskopf et al., 2004) discusses re-
fraction through a continuous medium of varying re-
fractive index as an example on non-linear ray tracing,
but does not tackle refraction within a warped space-
time itself.
Among other work, is also the Black Hole Flight
Simulator (BHFS) (Hamilton, 2008), that shows how
it looks like to travel towards and through various
kinds of black holes. A ray tracing algorithm for
visualizing two different spinning celestial objects, a
neutron star and a quasi-Kerr black hole are described
in (Psaltis and Johannsen, 2012) and (Bauböck et al.,
2012) respectively.
It was only recently that visualizations with an
observer placed closer to the black hole were pro-
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
is unique in that it not only solves the equations for
a ray-bundle propagation near a spinning black hole,
but also produces extremely high resolution imagery
required for a cinema production. This is done by
mapping the celestial sphere around a black hole or
a wormhole to the local sky of the observing camera,
while accounting for the change in the cross-section
of the light beam and, color and intensity changes due
to Doppler shifts that occur in the process.
2.1 Comparison to State of the Art
We do not claim to present any new astrophysics
insights in our paper, nor do we claim to be bet-
ter than DNGR in all respects. We certainly do not
produce cinematic production quality images. How-
ever, we believe that to the best of our knowledge,
we present the only renderer of its kind that can vi-
sualize highly warped spacetime, both in outer space
and in everyday human-scale scenes like rooms and
buildings. None of the previous works (Müller,
2014), (Kuchelmeister et al., 2012), (James et al.,
Non-linear Monte Carlo Ray Tracing for Visualizing Warped Spacetime
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