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

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.

MPEG1 320×240 (1.2 MB), MPEG1 640×480 (10.9 MB)
Orbiting a massless sphere
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.

MPEG1 320×240 (929 kB), MPEG1 640×480 (4.7 MB)
Orbiting a neutron star
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.

MPEG1 320×240 (929 kB), MPEG1 640×480 (6.2 MB)
Ring around a black hole
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.

MPEG1 320×240 (1.3 MB), MPEG1 640×480 (10.0 MB)
Rotating ring
Rotating ring
MPEG1 320×240 (915 kB), MPEG1 640×480 (10.3 MB)
Rotating ring around a black hole
Rotating ring around a black hole
MPEG1 320×240 (935 kB), MPEG1 640×480 (13.5 MB)
Massless sphere with accretion column
Massless sphere with accretion column
MPEG1 320×240 (937 kB), MPEG1 640×480 (6.1 MB)
Massless sphere with accretion column
Massless sphere with accretion column

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

MPEG1 320×240 (669 kB), MPEG1 640×480 (6.0 MB)
Neutron star with accretion column
Neutron star with accretion column
MPEG1 320×240 (929 kB), MPEG1 640×480 (9.0 MB)
Neutron star with accretion column
Neutron star with accretion column

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

MPEG1 320×240 (917 kB), MPEG1 640×480 (12.8 MB)
Gravitational collapse of a neutron star
Gravitational collapse of a neutron star

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

MPEG1 320×240 (782 kB), MPEG1 640×480 (7.1 MB)
Gravitational collapse of a neutron star
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.

MPEG1 320×240 (1.1 MB), MPEG1 640×480 (12.0 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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All contents copyright (C) 2001-2016 Ute Kraus, Corvin Zahn. All rights reserved. For more information see Copyright.