# Do shapes of matter affect space-time distortion?

We know heavy objects bend space-time, but does the curvature only depends on the mass? Or different shapes bend space time differently?

Spacetime is curved by the presence of mass in a perticular point and not by the body's center of mass... so the shape of the body affects the overall curvature because it affects the distribution of mass in the spacetime... the magnitude of the curvature is porpotional to the mass present in a point and the overall "shape" of the curvature is related to the mass distribution on the body...

• What would happen in a scenario where a large 5 point star (for example) is orbited by a small sphere? The pointy ends of the star would distort the space time "shape" from the tips to the center with increasing "magnitude of disturbance". How would this affect the orbit? Perhaps it would create a rounded pentagon type orbit? Classical mechanics (or that part which im familiar with) doesn't account for the shape, merely the center of mass. Is my interpretation of this wrong? – 22134484 Jun 20 '18 at 10:41
• @22134484: Classical mechanics does account for the shape of an extended object, it's just that these effects aren't usually considered in intro courses. For example, the gravitational field of a star-shaped object differs from that of a point mass. Usually we can get away with this approximation, though, because of the fact that the gravitational field outside a uniform sphere is the same as that of a point mass. Many celestial objects are pretty close to spherical, so we can get away with considering them as point masses. – Michael Seifert Jun 20 '18 at 18:07

$$R_{\mu\nu}-\frac12 g_{\mu\nu}R = 8\pi G\, T_{\mu\nu}$$
where $T_{\mu\nu}$ is the stress-energy-momentum tensor. This is not a constant matrix, it is a tensor field which can depend on space-time.
As such, how the matter is distributed will influence the curvature of space-time and hence ultimately the resultant metric. As a particular example, $T_{\mu\nu}$ with a delta function like distribution often give rise to brane line geometries.