The Astrophysics Spectator

March 1, 2006

This fortnight The Astrophysics Spectator turns its attention to black holes. Three pages are added to the “General Relativity” topic path that give an introduction to black holes and a description of their properties when they carry no angular momentum.

The black hole is the most exotic of all astronomical objects, and if our theory of gravity is correct, they must exist. But do they exist? Personally I doubt it. But under general relativity they must exist, and currently general relativity is the best theory—meaning the theory that matches the data most accurately and most simply—of gravity.

Black holes must exist if general relativity is valid because large stars collapse. The pressure inside a very large stars cannot support the star's weight once thermonuclear fusion ceases. This leads to a supernova explosion that leaves behind a compact object that is either a neutron star or a black hole. A neutron star, which is the most compact star found in nature, can only support itself against gravitational collapse if it is less than about two and a half times the mass of the Sun. Much larger than this, and it collapses into a black hole. This mass limit determines the kind of compact object left behind in a supernova explosion.

Where do we find black holes? A black hole floating freely in space would be difficult to discover, because its only signature is its magnification of the light from more distant stars, an ability shared with stars. We need a more visible signature. The best is the light generated by a black hole when it pulls gas onto itself; when the gas spirals into the black hole, gravitational potential energy is converted into light. This happens when a black hole orbited by a companion star can pull the star's atmosphere onto itself. Another way of finding black holes is by finding their influence on the orbits of other stars. This can be done for extremely massive stars. This method was used to show that a large black hole candidate sits at the center of our Galaxy.

Black holes have many peculiar properties. The best known is the permanent trapping of objects and light that fall into a black hole. Other properties include the absence of stable circular orbits close to the black hole, and the creation of an infinite number of images of stars far beyond the black hole.

Next Issue: The next issue is scheduled for March 15.

General Relativity

Black Holes. When the core of a massive star collapses, it may become a black hole. A black hole is the gravitational field around a point mass. Unlike a compact star, such as a neutron star, the central object of a black hole has only one role—to provide the black hole's gravitational field. Black holes, in fact, depend on only two physical quantities: mass and angular momentum. Near black holes, the passage of time appears to come to a halt. Black holes can capture anything permanently, including light. (continue)

The Schwarzschild Black Hole. A black hole has mass and angular momentum. If it's angular momentum is zero, it is called a Schwarzschild black hole. This type of black hole is a point mass surrounded by an isotropic gravitational field. The gravitational field can Doppler shift and deflect light. The black hole has an event horizon, which is a boundary that defines where objects and light become permanently trapped. Two peculiar properties of the Schwarzschild black hole are the absence of stable circular orbits near the event horizon and the ability of the black hole to split the image of a more distant star into an infinite number of images. (continue)

Fall through the Event Horizon. A black hole's event horizon is a point of no return; once an object falls through the event horizon, neither it nor any light it emits can escape the black hole. For the object, this passage through the event horizon is unremarkable—the local physical conditions do not change and starlight from outside the event horizon still reaches the object. To those outside the event horizon, however, the object never reaches the event horizon; instead it appears to sink more and more slowly towards the event horizon, becoming dimmer as it sinks. (continue) Erratum (3/4/06): The original version of this page incorrectly stated that starlight has no Doppler shift when seen by an object falling through the event horizon. In fact, assuming the object is falling radially into the black hole, starlight that comes from directly above the object is redshifted, and starlight that comes from the side is blueshifted. In contrast, a hovering observer sees starlight blueshifted by an amount that depends only on the distance of the hovering observer from the black hole's center. The current version of this page makes this point.