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General Relativity

Black Holes

Most people are familiar with the name “black hole.” After years of portrayal in movies and on television, the image that people most likely have is of multicolored gas flowing into a drain. Black holes, however, are much more exotic than this.

Before thinking about a black hole's actual appearance, let's first think about what a black hole is: the black hole is an object of our imagination, driven by the mathematics of general relativity, our current best theory of gravity. To this point, there is no evidence that they exist. On the observational side, we know that very massive and compact objects exist. Many compact objects of several times the Sun's mass are found in binary star systems, where the compact object generates tremendous power by pulling onto itself the atmosphere from an orbiting star. The orbits of stars at the center of our Galaxy suggest that an extremely massive compact object sits there. Black holes are thought to power the active galactic nuclei found in some distant galaxies. Where we falter is in evidence that proves these compact objects are black holes. Under our theories, they can only be black holes, but if general relativity is not valid, then these compact objects may be something else. In this absence of evidence, astrophysicists assume the existence of black holes, which allows them to model the effect of a massive compact object on its surroundings.

We can ask of general relativity the question that we ask of Newtonian gravity: what is the gravitational field in the vacuum surrounding a point of mass? In Newtonian gravity, the answer is the inverse-square law; in general relativity, the answer is the black-hole. As with Newtonian gravity, where the inverse-square law describes the gravitational field outside of all spherically-symmetric masses such as the Sun, the stars, and the planets, the black-hole solution describes the gravitational field around a spherically-symmetric mass under general relativity. This solution is used to calculate both the bending of light as it passes by the Sun and the deviation of Mercury's orbit from a closed ellipse. For very weak gravitational fields, the equation for the black hole's gravitational field becomes identical to the inverse-square law of Newtonian gravity. For very strong gravitational fields, such as those found around neutron stars, the black hole solution of the gravitational field strongly Doppler shifts to lower frequencies the radiation from the star's surface, and it bends the path of the light from the star so strongly that a large fraction of the star's back side is visible to us.

The most peculiar properties of strong gravitational fields appear in the black hole. The best known property is the black hole's event horizon. It is a spherical boundary that completely surrounds the point mass that generates the black hole. An object that fall through the event horizon become dark to those remaining outside; once it has fallen inside, neither the object nor light from it can ever escape back to the outside. This effect is the reason that the black hole has its name. But the event horizon is not the only peculiar effect seen in black holes. Circular orbits are not possible close to the black hole's event horizon. The circular orbit closest to the event horizon is called the last stable orbit of the black hole, and at this orbit light can orbit the black hole in a circle indefinitely. Related to the last stable orbit is the ability of a black hole to create an infinite number of images of a background star.

While the Newtonian gravitational field is proportional to a single constant—the mass of the gravitating body—the black hole's gravitational field is set by two constants—a mass and an angular momentum. A black hole with zero angular momentum, called a Schwarzschild black hole, is spherically symmetric. A black hole with non-zero angular momentum, called a Kerr black hole, is axisymmetric about the axis of rotation. All objects in space carry some angular momentum, and if we are seeing black holes in our universe, they are inevitably Kerr black holes. But the Schwarzschild black hole is simpler than the Kerr black hole, and its principal features are shared with the Kerr black hole, so it is described next.

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