Relativity visualized

# 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.

 Movie: 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)
 Movie: 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)
 Movie: 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)
 Movie: 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)
 Movie: Rotating ring MPEG1 320×240 (915 kB), MPEG1 640×480 (10.3 MB)
 Movie: Rotating ring around a black hole MPEG1 320×240 (935 kB), MPEG1 640×480 (13.5 MB)
 Movie: Massless sphere with accretion column MPEG1 320×240 (937 kB), MPEG1 640×480 (6.1 MB)
 Movie: 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)
 Movie: Neutron star with accretion column MPEG1 320×240 (929 kB), MPEG1 640×480 (9.0 MB)
 Movie: 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)
 Movie: 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)
 Movie: 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.