# Black Holes and Curved Spacetime

## Gravitational Wave Astronomy


### Learning Objectives

By the end of this section, you will be able to:
1. Describe what a gravitational wave is, what can produce it, and how fast it propagates
2. Understand the basic mechanisms used to detect gravitational waves
Another part of Einstein’s ideas about gravity can be tested as a way of checking the theory that underlies black holes. According to general relativity, the geometry of spacetime depends on where matter is located. Any rearrangement of matter—say, from a sphere to a sausage shape—creates a disturbance in spacetime. This disturbance is called a gravitational wave, and relativity predicts that it should spread outward at the speed of light. The big problem with trying to study such waves is that they are tremendously weaker than electromagnetic waves and correspondingly difficult to detect.

### Proof from a Pulsar

We’ve had indirect evidence for some time that gravitational waves exist. In 1974, astronomers Joseph Taylor and Russell Hulse discovered a pulsar (with the designation PSR1913+16) orbiting another neutron star. Pulled by the powerful gravity of its companion, the pulsar is moving at about one-tenth the speed of light in its orbit.
According to general relativity, this system of stellar corpses should be radiating energy in the form of gravitational waves at a high enough rate to cause the pulsar and its companion to spiral closer together. If this is correct, then the orbital period should decrease (according to Kepler’s third law) by one ten-millionth of a second per orbit. Continuing observations showed that the period is decreasing by precisely this amount. Such a loss of energy in the system can be due only to the radiation of gravitational waves, thus confirming their existence. Taylor and Hulse shared the 1993 Nobel Prize in physics for this work.

### Direct Observations

Although such an indirect proof convinced physicists that gravitational waves exist, it is even more satisfying to detect the waves directly. What we need are phenomena that are powerful enough to produce gravitational waves with amplitudes large enough that we can measure them. Theoretical calculations suggest some of the most likely events that would give a burst of gravitational waves strong enough that our equipment on Earth could measure it:
1. the coalescence of two neutron stars in a binary system that spiral together until they merge
2. the swallowing of a neutron star by a black hole
3. the coalescence (merger) of two black holes
4. the implosion of a really massive star to form a neutron star or a black hole
5. the first “shudder” when space and time came into existence and the universe began
For the last four decades, scientists have been developing an audacious experiment to try to detect gravitational waves from a source on this list. The US experiment, which was built with collaborators from the UK, Germany, Australia and other countries, is named LIGO (Laser Interferometer Gravitational-Wave Observatory). LIGO currently has two observing stations, one in Louisiana and the other in the state of Washington. The effects of gravitational waves are so small that confirmation of their detection will require simultaneous measurements by two widely separated facilities. Local events that might cause small motions within the observing stations and mimic gravitational waves—such as small earthquakes, ocean tides, and even traffic—should affect the two sites differently.
Each of the LIGO stations consists of two 4-kilometer-long, 1.2-meter-diameter vacuum pipes arranged in an L-shape. A test mass with a mirror on it is suspended by wire at each of the four ends of the pipes. Ultra-stable laser light is reflected from the mirrors and travels back and forth along the vacuum pipes (). If gravitational waves pass through the LIGO instrument, then, according to Einstein’s theory, the waves will affect local spacetime—they will alternately stretch and shrink the distance the laser light must travel between the mirrors ever so slightly. When one arm of the instrument gets longer, the other will get shorter, and vice versa.
The challenge of this experiment lies in that phrase “ever so slightly.” In fact, to detect a gravitational wave, the change in the distance to the mirror must be measured with an accuracy of one ten-thousandth the diameter of a proton. In 1972, Rainer Weiss of MIT wrote a paper suggesting how this seemingly impossible task might be accomplished.
A great deal of new technology had to be developed, and work on the laboratory, with funding from the National Science Foundation, began in 1979. A full-scale prototype to demonstrate the technology was built and operated from 2002 to 2010, but the prototype was not expected to have the sensitivity required to actually detect gravitational waves from an astronomical source. Advanced LIGO, built to be more precise with the improved technology developed in the prototype, went into operation in 2015—and almost immediately detected gravitational waves.
What LIGO found was gravitational waves produced in the final fraction of a second of the merger of two black holes (). The black holes had masses of 20 and 36 times the mass of the Sun, and the merger took place 1.3 billion years ago—the gravitational waves occurred so far away that it has taken that long for them, traveling at the speed of light, to reach us.
In the cataclysm of the merger, about three times the mass of the Sun was converted to energy (recall E = mc2). During the tiny fraction of a second for the merger to take place, this event produced power about 10 times the power produced by all the stars in the entire visible universe—but the power was all in the form of gravitational waves and hence was invisible to our instruments, except to LIGO. The event was recorded in Louisiana about 7 milliseconds before the detection in Washington—just the right distance given the speed at which gravitational waves travel—and indicates that the source was located somewhere in the southern hemisphere sky. Unfortunately, the merger of two black holes is not expected to produce any light, so this is the only observation we have of the event.
This detection by LIGO (and another one of a different black hole merger a few months later) opened a whole new window on the universe. One of the experimenters compared the beginning of gravitational wave astronomy to the era when silent films were replaced by movies with sound (comparing the vibration of spacetime during the passing of a gravitational wave to the vibrations that sound makes).
By the end of 2021, the LIGO-Virgo collaboration (Virgo is a gravitational wave detector operated by the European Gravitational Observatory in Italy) published a catalog that now included some 90 events. Most were mergers of two black holes, and most involved black holes with a range of masses detected only by gravitational waves (see ). In the most extreme merger, black holes with masses of 86 and 65 times the mass of the Sun merged to form a black hole with a mass of about 142 times the mass the Sun, and released energy equivalent to 9 times the mass of our Sun (remember E= mc2)—an enormous amount.

Astronomers are not yet sure how black holes in this unexpected mass range form. Bear in mind that the kind of black holes in binary star systems that we discussed in Evidence for Black Holes (and listed in ) have masses ranging from 4 to 15 times the mass of the Sun.

To be sure, a few mergers did involve black holes with stellar masses comparable to those of black holes in X-ray binary systems. In one case, for example, the merging black holes had masses of 14 and 8 times the mass of the Sun.  
While astronomers can learn about the masses of objects involved in gravitational wave events, the challenge is to locate the event in the sky precisely. A single gravitational wave detector cannot determine accurately the direction to a gravitational wave source. Four comparable detectors operating simultaneously are required to localize a source of gravitational waves in every location in the sky. The first observing run with four detectors, including the two LIGO detectors, Virgo, and KAGRA in Japan, is scheduled to begin in the summer of 2022. LIGO India will be a fifth, thereby enhancing the probability that at least four detectors will be operational simultaneously. Experience has shown that the LIGO and Virgo detectors are down about 25 percent of the time because these complex systems are difficult to run.  
A three-observatory network does provide a sharp location for events that occur in about half of all possible locations on the sky. 
In late 2017, data from the LIGO and Virgo detectors provided an accurate position for what analysis showed was the spiraling together of two neutron stars with masses of 1.1 to 1.6 times the mass of the Sun (see The Death of Stars).

With an accurate location known, follow up observations with ground-based telescopes detected electromagnetic emission from a gravitational wave event for the first time. The observations showed that this source was located in NGC 4993, a galaxy at a distance of about 130 million light-years in the direction of the constellation Hydra. The Fermi satellite detected a flash of gamma rays at the same time and in the same direction, which confirms the long-standing hypothesis that mergers of neutron stars are progenitors of short gamma-ray bursts  (see The Mystery of Gamma-Ray Bursts).
Spectra showed that the merger ejected material with a mass of about 6 percent of the mass of the Sun at a speed of one-tenth the speed of light.

This material is rich in heavy elements, just as the theory of kilonovas (see The Mystery of Gamma-Ray Bursts) predicted. First estimates suggest that the merger produced about 200 Earth masses of gold, and around 500 Earth masses of platinum. This makes clear that neutron star mergers are a significant source of heavy elements. More such mergers are being found (see ) and they will improve estimates of the frequency at which neutron star mergers occur; it may well turn out that the vast majority of heavy elements have been created in such cataclysms.

No electromagnetic observations have been detected from the mergers of two black holes.

In June 2021, scientists from LIGO and Virgo announced the first detection of mergers between black holes and neutron stars, another of the really energetic events that we listed as possible sources for a detectable burst of gravitational waves.  Again, no electromagnetic waves from the two events were observed or expected, demonstrating the importance of using what we are now calling “multi-messenger astronomy” to understand the universe fully.
Observing the merger of black holes via gravitational waves means that we can now test Einstein’s general theory of relativity where its effects are very strong—close to black holes—and not weak, as they are near Earth. One remarkable result from these detections is that the observed signals so closely match the theoretical predictions made using Einstein’s theory. Once again, Einstein’s revolutionary idea is found to be the correct description of nature.

Because of the scientific significance of the observations of gravitational waves, three of the LIGO project leaders—Rainer Weiss of MIT, and Kip Thorne and Barry Barish of Caltech—were awarded the Nobel Prize in 2017.

Ground-based gravitational-wave detectors can detect mergers of black holes with masses up to about 100 times the mass of the Sun. Astronomers would now like to look for the merger of distant supermassive black holes (see Supermassive Black Holes: What Quasars Really Are) with masses of thousands to millions of times larger, which might have occurred when the first generation of stars formed, only a few hundred million years after the Big Bang.  The gravitational waves emitted by mergers of supermassive black holes are so long that it is necessary to go to space to build an observatory large enough to detect them.  
ESA (the European Space Agency), with contributions from NASA, is planning to launch a facility named LISA (Laser Interferometer Space Antenna) in 2034 to search for mergers of black holes with masses thousands to millions of times larger than the mass of the Sun. The experiment will consist of three spacecraft arranged in an equilateral triangle with sides 2.5 million km long, flying along an Earth-like heliocentric orbit. A test mass floats free inside each spacecraft, effectively in free-fall, while the spacecraft around it absorbs the effects of light pressure, solar wind particles, and anything that might perturb its orbit. Lasers will be used to measure very accurately the distances between the test masses. Changes in distance will then signal the passing of gravitational waves.  
We should end by acknowledging that the ideas discussed in this chapter may seem strange and overwhelming, especially the first time you read them. The consequences of the general theory of relatively take some getting used to. But they make the universe more bizarre—and interesting—than you probably thought before you took this course.


### Key Concepts and Summary

General relativity predicts that the rearrangement of matter in space should produce gravitational waves. The existence of such waves was first confirmed in observations of a pulsar in orbit around another neutron star whose orbits were spiraling closer and losing energy in the form of gravitational waves. In 2015, LIGO found gravitational waves directly by detecting the signal produced by the merger of two stellar-mass black holes, opening a new window on the universe. Since then, many other gravitational wave signals have been found, signaling the mergers of both black holes and neutron stars.

### For Further Exploration


### Articles


### Black Holes

Charles, P. & Wagner, R. “Black Holes in Binary Stars: Weighing the Evidence.” Sky & Telescope (May 1996): 38. Excellent review of how we find stellar-mass black holes.
Gezari, S. “Star-Shredding Black Holes.” Sky & Telescope (June 2013): 16. When black holes and stars collide.
Jayawardhana, R. “Beyond Black.” Astronomy (June 2002): 28. On finding evidence of the existence of event horizons and thus black holes.
Nadis, S. “Black Holes: Seeing the Unseeable.” Astronomy (April 2007): 26. A brief history of the black hole idea and an introduction to potential new ways to observe them.
Psallis, D. & Sheperd, D. “The Black Hole Test.” Scientific American (September 2015): 74–79. The Event Horizon Telescope (a network of radio telescopes) will test some of the stranger predictions of general relativity for the regions near black holes. The September 2015 issue of Scientific American was devoted to a celebration of the 100th anniversary of the general theory of relativity.
Rees, M. “To the Edge of Space and Time.” Astronomy (July 1998): 48. Good, quick overview.
Talcott, R. “Black Holes in our Backyard.” Astronomy (September 2012): 44. Discussion of different kinds of black holes in the Milky Way and the 19 objects known to be black holes.

### Gravitational Waves

Bartusiak, M. “Catch a Gravity Wave.” Astronomy (October 2000): 54.
Gibbs, W. “Ripples in Spacetime.” Scientific American (April 2002): 62.
Haynes, K., & Betz, E. “A Wrinkle in Spacetime Confirms Einstein’s Gravitation.” Astronomy (May 2016): 22. On the direct detection of gravity waves.
Sanders, G., and Beckett, D. “LIGO: An Antenna Tuned to the Songs of Gravity.” Sky & Telescope (October 2000): 41.

### Websites


### Black Holes

Black Hole Encyclopedia: http://blackholes.stardate.org. From StarDate at the University of Texas McDonald Observatory.
Black Holes: http://science.nasa.gov/astrophysics/focus-areas/black-holes. NASA overview of black holes, along with links to the most recent news and discoveries.
Introduction to Black Holes: https://www.newscientist.com/article/dn18348-introduction-black-holes/. Basic information from New Scientist magazine.
Virtual Trips into Black Holes and Neutron Stars: http://antwrp.gsfc.nasa.gov/htmltest/rjn_bht.html. By Robert Nemiroff at Michigan Technological University.

### Gravitational Waves

Advanced LIGO: https://www.advancedligo.mit.edu. The full story on this gravitational wave observatory.
eLISA: https://www.elisascience.org.
Gravitational Waves Detected, Confirming Einstein’s Theory: http://www.nytimes.com/2016/02/12/science/ligo-gravitational-waves-black-holes-einstein.html. New York Times article and videos on the discovery of gravitational waves.
Gravitational Waves Discovered from Colliding Black Holes: http://www.scientificamerican.com/article/gravitational-waves-discovered-from-colliding-black-holes1. Scientific American coverage of the discovery of gravitational waves (note the additional materials available in the menu at the right).
LIGO Caltech: https://www.ligo.caltech.edu.

### Videos


### Black Holes

Black Holes: The End of Time or a New Beginning?: https://www.youtube.com/watch?v=mgtJRsdKe6Q. 2012 Silicon Valley Astronomy Lecture by Roger Blandford (1:29:52).
Death by Black Hole: https://www.youtube.com/watch?v=h1iJXOUMJpg. Neil deGrasse Tyson explains spaghettification with only his hands (5:34).
Hearts of Darkness: Black Holes in Space: https://www.youtube.com/watch?v=4tiAOldypLk. 2010 Silicon Valley Astronomy Lecture by Alex Filippenko (1:56:11).

### Gravitational Waves

Journey of a Gravitational Wave: https://www.youtube.com/watch?v=FlDtXIBrAYE. Introduction from LIGO Caltech (2:55).
LIGO’s First Detection of Gravitational Waves: https://www.youtube.com/watch?v=gw-i_VKd6Wo. Explanation and animations from PBS Digital Studio (9:31).
Two Black Holes Merge into One: https://www.youtube.com/watch?v=I_88S8DWbcU. Simulation from LIGO Caltech (0:35).
What the Discovery of Gravitational Waves Means: https://www.youtube.com/watch?v=jMVAgCPYYHY. TED Talk by Allan Adams (10:58).

### Collaborative Group Activities

1. A computer science major takes an astronomy course like the one you are taking and becomes fascinated with black holes. Later in life, he founds his own internet company and becomes very wealthy when it goes public. He sets up a foundation to support the search for black holes in our Galaxy. Your group is the allocation committee of this foundation. How would you distribute money each year to increase the chances that more black holes will be found?
2. Suppose for a minute that stars evolve without losing any mass at any stage of their lives. Your group is given a list of binary star systems. Each binary contains one main-sequence star and one invisible companion. The spectral types of the main-sequence stars range from spectral type O to M. Your job is to determine whether any of the invisible companions might be black holes. Which ones are worth observing? Why? (Hint: Remember that in a binary star system, the two stars form at the same time, but the pace of their evolution depends on the mass of each star.)
3. You live in the far future, and the members of your group have been convicted (falsely) of high treason. The method of execution is to send everyone into a black hole, but you get to pick which one. Since you are doomed to die, you would at least like to see what the inside of a black hole is like—even if you can’t tell anyone outside about it. Would you choose a black hole with a mass equal to that of Jupiter or one with a mass equal to that of an entire galaxy? Why? What would happen to you as you approached the event horizon in each case? (Hint: Consider the difference in force on your feet and your head as you cross over the event horizon.)
4. General relativity is one of the areas of modern astrophysics where we can clearly see the frontiers of human knowledge. We have begun to learn about black holes and warped spacetime recently and are humbled by how much we still don’t know. Research in this field is supported mostly by grants from government agencies. Have your group discuss what reasons there are for our tax dollars to support such “far out” (seemingly impractical) work. Can you make a list of “far out” areas of research in past centuries that later led to practical applications? What if general relativity does not have many practical applications? Do you think a small part of society’s funds should still go to exploring theories about the nature of space and time?
5. Once you all have read this chapter, work with your group to come up with a plot for a science fiction story that uses the properties of black holes.
6. Black holes seem to be fascinating not just to astronomers but to the public, and they have become part of popular culture. Searching online, have group members research examples of black holes in music, advertising, cartoons, and the movies, and then make a presentation to share the examples you found with the whole class.
7. As mentioned in the Gravity and Time Machines feature box in this chapter, the film Interstellar has a lot of black hole science in its plot and scenery. That’s because astrophysicist Kip Thorne at Caltech had a big hand in writing the initial treatment for the movie, and later producing it. Get your group members together (be sure you have popcorn) for a viewing of the movie and then try to use your knowledge of black holes from this chapter to explain the plot. (Note that the film also uses the concept of a wormhole, which we don’t discuss in this chapter. A wormhole is a theoretically possible way to use a large, spinning black hole to find a way to travel from one place in the universe to another without having to go through regular spacetime to get there.)

### Review Questions


### Thought Questions


### Figuring for Yourself
