$$\require{cancel}$$

13.30 Black Holes

Black holes can only be described and understood using Einstein’s theory of relativity, but their existence was hypothesized over 200 years ago. The Reverend John Mitchell, an English amateur astronomer, knew that Newton’s law of gravity predicted that massive and dense objects would have high escape velocities. In 1784, he pointed out that a sufficiently dense object might have an escape velocity faster than light. Since all electromagnetic radiation travels at the speed of light, such an object would be completely dark.

The nature of a black hole can be understood in terms of the idea of escape velocity. Imagine that the Sun has somehow been compressed into a black hole of 1 solar mass. A rocket passing at a great distance would experience the same gravity field as a rocket at a great distance from the Sun. At 1 A.U. from the black hole, for example, the velocity needed to escape into interstellar space would be 42 kilometers per second, the same as the speed needed to leave the Earth's orbit. You can see that the gravity far from a black hole is not very severe. It is not true that a black hole acts like a cosmic "vacuum cleaner," sucking up everything around it. But as we get much closer to the black hole, the escape velocity increases. Larger speeds are needed to escape the stronger and stronger gravity. At a distance of 3 kilometers, the speed needed to escape would be the speed of light. Since we know of nothing that can travel faster than light, nothing can escape this region.

Crush a star like the Sun down to a radius of 3 kilometers and you have a black hole. The imaginary sphere with a radius of 3 kilometers is called the event horizon. Inside this surface, no object, no particle, no information, not even light can escape. Any star that collapses within its event horizon disappears from the universe, betraying its presence only by its gravity.

Simulated view of a black hole in front of the Large Magellanic Cloud. The ratio between the black hole Schwarzschild radius and the observer distance to it is 1:9. Of note is the gravitational lensing effect known as an Einstein ring, which produces a set of two fairly bright and large but highly distorted images of the Cloud as compared to its actual angular size. Click here for original source URL.

The radius corresponding to the event horizon is called the Schwarzschild radius, after the astronomer who was the first to solve Einstein's equations of general relativity for a collapsed object. How is a black hole produced? An object of any mass can become a black hole if it is sufficiently compressed. However, black holes were predicted to exist as a consequence of stellar evolution. Any star that ends its life with a core mass of 3 solar masses or more will become a black hole, because no known force in nature can prevent its collapse within its event horizon.

The theory of general relativity can be used to calculate the effect of the gravity on light rays at different distances from the event horizon. At a large distance from a black hole, light travels away from a light source uniformly in all directions. As the black hole is approached, light passing near the hole will be slightly deflected. Closer to the event horizon, some light rays are deflected by the strong gravity and are captured by the black hole. At a distance of 1.5 times the Schwarzschild radius, half the light escapes. Photons emitted at right angles to the black hole are trapped in circular orbits. These orbits define the photon sphere. At the Schwarzschild radius, the deflection of light is so severe that no light can escape. This defines the event horizon.

Another analogy can be used to convey the extreme space-time curvature caused by black holes. General relativity predicts that any mass will distort the space and time around it. A good analogy for the space curvature in two dimensions is the distortion in a thin rubber sheet. In the absence of any matter, space will be flat and have no curvature. With a mass placed on the sheet, the distortion is large enough to clearly deflect matter and radiation that pass near it. In the extreme case of a black hole, the curvature is complete. We can imagine a piece of space and time being "pinched off" and permanently removed from communication with the rest of the universe.

If you were unfortunate enough to fall into a 1 solar mass black hole, you would be killed by tidal forces long before you reached the event horizon. (Essentially, the difference between the gravity force on your head and that on your feet would rip you apart!) Assuming that somehow you could survive the descent, you would see clocks far from the black hole keeping slower and slower time, until as you neared the event horizon they appeared to stop altogether. Seen from the outside, your clock would appear to slow down as you took an infinite time to reach the event horizon! If you carried a light source with you as you fell into the black hole, a distant observer would see the photons suffer a larger and larger gravitational red shift (to you, the light would stay the same color). The redshift occurs because light loses energy escaping from the intense gravity. Seen from the outside, the photons would be infinitely redshifted to zero energy as you reached the event horizon.

What lies within the event horizon of a black hole? Nobody really knows. The event horizon is not a physical barrier, just an information barrier. Einstein's theory predicts that matter will keep collapsing gravitationally until it has shrunk to a point of zero volume and infinite density! This endpoint is called a singularity and it cannot be adequately described using general relativity. Black holes are not entirely black. In the 1970s, English physicist Stephen Hawking calculated that black holes could create subatomic particles near their event horizons and slowly radiate away their energy, or "evaporate." This so-called Hawking radiation is expected to be dramatic for microscopic black holes, but barely noticeable for solar-sized black holes. Far more important is the fact that any material falling toward the event horizon will be subject to enormous gravitational forces. The friction and heating of material that falls in will be released in the form of X-rays. Therefore, a black hole may be a source of energy due to the death spasms of matter falling into it.

Can we ever hope to detect a black hole? Yes. Outside their event horizons, black holes have gravity fields indistinguishable from those of ordinary stars of the same mass. Thus they can orbit around stars just like planets or binary star companions. If we observed such a star from a distance, we would not see the black hole, but we could see the star's orbital motion and calculate the mass of the unseen companion, just as astronomers routinely do in the case of ordinary faint companions. The result would indicate an unusually high-mass companion for an X-ray source — maybe 5 or 10 solar masses — which is a sign that we are dealing with a black hole candidate.

Artist impression of a binary system with an accretion disk around a black hole being fed by material from the companion star. Click here for original source URL.

Suppose a black hole is orbiting around an evolved star that has expanded into the giant state and is shedding mass. Some of the expanding gas would fall toward the black hole at relativistic speeds. Because this gas would, on the average, have some angular momentum around the star, rather than falling directly toward it, it would form a disk of gas spiraling inward toward the black hole. This disk is called an accretion disk. Its gas would be extremely hot, because it would be constantly hit by new gas streaming in from the other star. Because of the high temperature, the disk would radiate at short ultraviolet or X-ray wavelengths.

Chandra image of Cygnus X-1. Click here for original source URL.

The best evidence for a black hole would be a massive, high-temperature X-ray source orbiting another normal star. There are currently about a dozen excellent candidates, and another dozen or so plausible candidates. One such object is Cygnus X-1, a binary system composed of a super giant star we can see orbiting an unseen companion. The companion object has been calculated to have a mass of at least 5 solar masses, and the system is one of the brightest X-ray sources in the sky. It's one of the strongest candidates for a black hole among several dozen binary system with good orbital mass constraints. The argument for a black hole in these systems has three steps. First, the X-ray emission must be consistent with accretion onto a compact object. Second, the calculation of the orbit of the binary system must lead to a mass for the compact object that exceeds 3 solar masses. Third, it is assumed that general relativity is the correct theory of gravitation and that neutron stars with masses above 3 solar masses cannot exist. Is the evidence convincing? All of the observations have uncertainties attached and the interpretation is indirect and circumstantial. Whereas the evidence for the existence of neutron stars is convincing, the evidence for stellar black holes is strong but not overwhelming. Black holes are the most exotic member of the stellar "zoo," and astronomers continue to work to prove their existence beyond doubt.