Relativity visualized

Space Time Travel

Four-dimensional ray tracing in a curved spacetime

Four-dimensional ray tracing in a curved spacetime

Corvin Zahn, October 14, 1990

A few movies show various objects (black holes, neutron stars, a gravitational collapse) in a Schwarzschild spacetime. This serves to illustrate the effect of gravitational light deflection on the visual appearance of these objects.

 

The movies show various objects in a Schwarzschild spacetime. This serves to illustrate the effect of gravitational light deflection on the visual appearance of these objects.

They do not show real astronomical objects, sizes and colors are chosen so that the effects of light deflection are clearly visible.

In the descriptions, the parameters are given in geometric units in dimensionless form. If the unit length is 2 km, the values are typical for a neutron star. Unit mass then corresponds to 1.5 solar masses.


Neutron star

Neutron star with radius 4. The mass is increased from M = 0 to M = 1.78. A mass of 1.78 corresponds to a ratio of radius to Schwarzschild radius of 9/8. Theory predicts that a smaller ratio is not possible for a stable star.

MPEG4 320×240 (299 kB), MPEG4 640×480 (928 kB)
Orbiting a massless sphere

A massless companion orbits a massless central star.
Mass of the central star: 0, radius of the central star: 4, radius of the companion: 8, orbital radius: 20.

MPEG4 320×240 (164 kB), MPEG4 640×480 (390 kB)
Orbiting a neutron star

A massless companion orbits a neutron star.
Mass of the neutron star: 1, radius of the neutron star: 4, radius of the companion: 8, orbital radius: 20.

MPEG4 320×240 (210 kB), MPEG4 640×480 (517 kB)
Ring around a black hole

In the center of a ring (inner radius 8, outer radius 12, height 1) a black hole forms with increasing mass.

MPEG4 320×240 (201 kB), MPEG4 640×480 (712 kB)
Rotating ring
MPEG4 320×240 (307 kB), MPEG4 640×480 (837 kB)
Rotating ring around a black hole
MPEG4 320×240 (431 kB), MPEG4 640×480 (1.2 MB)
Massless sphere with accretion column
MPEG4 320×240 (242 kB), MPEG4 640×480 (543 kB)
Massless sphere with accretion column

The position of the accretion column is different from that in the previous movie.

MPEG4 320×240 (258 kB), MPEG4 640×480 (588 kB)
Neutron star with accretion column
MPEG4 320×240 (328 kB), MPEG4 640×480 (810 kB)
Neutron star with accretion column

The position of the accretion column is different from that in the previous movie.

MPEG4 320×240 (525 kB), MPEG4 640×480 (1.3 MB)
Gravitational collapse of a neutron star

Gravitational collapse of a neutron star with mass M = 1 seen by a distant observer.

MPEG4 320×240 (217 kB), MPEG4 640×480 (690 kB)
Gravitational collapse of a neutron star

Gravitational collapse of a neutron star with mass M = 1 seen by a freely falling observer. Initially the neutron star has radius 4 M, the observer is located at 6 M. The neutron star surface and the observer start falling at the same Schwarzschild time.

MPEG4 320×240 (430 kB), MPEG4 640×480 (1.3 MB)
 
More: The simulations shown above are based on light deflection in a Schwarzschild spacetime. You can find the relevant equations in Light Deflection Near Neutron Stars.

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Authors: Corvin Zahn, Date: October 14, 1990
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