Sphere, doughnut, double ring

Black holes in higher dimensions

May 30, 2010

All black holes have a spherical shape - but must this also hold true in higher dimensions? Dr. Maria Rodriguez from the Max Planck Institute for Gravitational Physics (Albert Einstein Institute/AEI) recently published an entire catalogue of “permissible” forms of black holes including, for instance, black rings, black double rings and ‘black Saturns’, namely a sphere encircled by a ring. To do this, she analysed the solutions of Einstein equations for black holes in higher dimensions.

We perceive and describe our world and what happens in it in three spatial dimensions and a single time dimension. In this four-dimensional universe, all black holes are spherical. Einstein’s general theory of relativity of space-time, however, does not indicate how many dimensions the world actually has - Einstein’s equations also provide solutions for more than four dimensions. It is therefore possible to reflect on a world with five, six, seven or more dimensions and to describe them mathematically. In these higher dimensional worlds, black holes do not necessarily have to be spherical, they can also look like e.g. doughnuts or double rings.

Maria Rodriguez explains: “The cases that, in higher dimensions, black holes no longer look like spheres, is already amazing in itself. The catalogue that I compiled is somewhat reminiscent of a family gathering where you suddenly discover a bunch of exotic looking relatives who you didn’t even know existed.” Professor Hermann Nicolai, Director of the Quantum Gravity and Unified Theories Department adds: “Research into the higher dimensions is very important, especially when searching for a unified theory of all physical interactions. Maria Rodriguez’ results provide brand new insights into how gravity ‘functions’ in higher dimensions.”

A unified theory should combine general relativity with quantum theory. String theory plays an important role in the search for a consistent quantum theory of gravity. This theory forces us to rethink familiar concepts of space and time, as here, the cosmos not only has the already-known three, but nine or even ten spatial dimensions.

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