Jan 20

Complete history of black holes. From Schwarzschild’s calculations to the discovery of gravitational waves

Complete history of black holes. From Schwarzschild's calculations to the discovery of gravitational waves
Complete history of black holes. From Schwarzschild’s calculations to the discovery of gravitational waves

Black hole devouring a partner star

The universe is a mysterious place. Planets, stars, galaxies – they all have their mysteries, still unexplained by science. But nothing is stranger and more amazing than black holes. They were first “formulated” in a hurried way, without much detail, but Einstein himself did not believe in such things, even though they were predicted by his theories. Many physicists have expressed skepticism about the reality of black holes. Here’s the incredible story behind the discovery of black holes; the incredible story of how the understanding and interpretation of black holes improved and how black holes affect the fundamental structure of the universe.

Nowadays, most of us have heard of black holes. We are talking about cosmic objects which are billions of times as massive as the Sun, with masses billions of times that of the sun. They are physical objects that have infinite density. They attract the matter around them and have the power to bend the light. Time itself changes near a black hole, time slowing down when gravity is strong.

Today we know more than ever about the black holes, although there is still much to learn. They are the most exotic objects in the universe, but we still don’t have the theoretical device to describe them. Although black holes are referred to as “cosmic objects”, they are in fact true holes in the space-time fabric, a place in the universe where a tremendous gravity is all we have.

  1. Gravity

The most important thing we need to know when talking about black holes is that they are related to gravity. But what is gravity?

Newton was fascinated by gravity. He invented the laws of motion, applied even today, precisely explaining the movement of the celestial bodies but also the movement of planets in the solar system. But although Newton’s laws describe the effects of gravitational force, they don’t explain gravity. Here comes Einstein, with his contributions.

Einstein was also fascinated by gravity. Imagine the following scenario: take an apple and let it fall. There’s no mystery… if you are on Earth, it will fall on the ground.

But what if we move the earth apart from the fall of the apple, when we let the apple fall, so that the apple doesn’t touch the ground? Einstein realized that gravity was related to the fall.


But what if, instead of letting the apple fall, we throw it to the horizon, with 27,358 km/h? The apple will move into the Earth’s orbit, as does the International Space Station, for example.

According to Einstein’s Theory of General Relativity, the apple and the International Space Station are in a free fall along a curved trajectory in space. What caused this curve trajectory? Earth mass.

So Einstein came up with this simple idea: space and time are curved by the masses in the Universe, the Earth, the Sun, and all celestial bodies that have a mass. Gravity is no longer a force, as in Newton’s conception, but it’s the incarnation of how the masses of the universe curve space-time. Cosmic objects moving through the Universe follow the shortest path in this warped space-time distorted by the masses.

universe curve space-time

Graphical representation of space curved by gravity

  1. Papers on black holes. Karl Schwarzschild’s idea

The idea that objects bend space-time leads directly to black holes. It’s not Einstein, but a German astronomer who makes the first link between gravity and black holes. This is Karl Schwarzschild, director of the Astrophysical Observatory Potsdam (AOP), Germany.

Karl Schwarzschild

Karl Schwarzschild

He was preoccupied with planetary orbits. When Einstein presented his theory of general relativity, in 1915, Schwarzschild was in the German army, calculating artillery trajectories during World War I. A few weeks after the publication of Einstein’s theory, the German astronomer also receives the work, somewhere on the Russian front. He starts drawing the map of the gravitational field around a star.

Schwarzschild identifies exact solutions to the Einstein’s equations and sent Einstein a manuscript, in which he derived his exact solution of Einstein’s field equations. Einstein was astonished because he hadn’t imagined his equations could be solved so precisely (he only had made some approximations).

Einstein was astonished

In his calculations, Schwarzschild discovers something Einstein didn’t anticipate. He concentrated the whole mass of a star in a single point (mathematically, of course). Then he calculated how the mass will curve the space-time as well as the nearby light rays. Schwarzschild identified a border area (nowadays referred to as an event horizon) around the point where the light particles will disappear. Time stops.

Schwarzschild found that a mass concentrated in a single point will curve the space-time so dramatically, that a region would be created around that point; a region from which the return outside of it is impossible. Nothing, not even light, can escape from inside this area. Although his own theory predicted this phenomenon, Einstein did not believe that such strange manifestations are taking place in nature. He didn’t like the idea.

In 1916, Schwarzschild became ill and died. His ideas on the effects of an enormous gravity seem destined to be forgotten.

  1. From the birth of a star to the appearance of a black hole

In the coming decades after Schwarzschild’s death, physicists improve their understanding of the atom as well as how the atomic or nuclear fusion is the energy fuel of a star.

Stars are born of cosmic gas; they come in many different sizes. They have a lifecycle, which is different depending on the mass of the star. Stars primarily fuse hydrogen atoms (the simplest and lightest of all the elements) together in a series of stages to form helium. More-massive stars can fuse heavier atoms. The more massive the star, the hotter its core, so it can create heavier elements by fusion.

Gravity inside the star tends to collapse the star itself, but the energy generated by fusion processes counterbalances this tendency.

Small stars can’t fusion elements heavier than helium, but very massive stars are able to fuse all the way to iron. The iron is such a massive element, that after its formation the energy to counterbalance the force of gravity is no longer generated. So from a certain perspective, iron is the ultimate state for stars.

What happens now? Gravity defeats. The star collapses. Trillions of tons of matter collapse into the core of the star, then bounce back off the core to the star’s outer layers, causing a tremendous explosion called a “supernova”.

Trillions of tons of matter collapse

Graphical representation of supernova 1993J

Source: wikipedia.org

The greater the mass, the stronger the gravitational field. There is no force to prevent  the collapse of the star until it reaches a point – a black hole.

Skepticism of physicists lasted until the ’70s of the last century. The idea of black holes was too eccentric to be taken seriously.

In 1967, Jocelyn Bell made a surprising discovery. She observed a strange star emitting small, rapid pulses of radiation – a neutron star. The cooled remains of a collapsed star give astronomers the hope that perhaps the idea of a black hole is not so extravagant. Maybe they really exist as a result of the collapse of big stars.

So, half a century after Schwarzschild’s idea, who mathematically showed that black holes are possible, physicists have identified a natural process that generates black holes: death of massive stars. These spectacular supernovae create black holes.

American physicist John Wheeler, who was initially skeptical about the reality of these extreme astronomical phenomena, coined the concept of “black hole”.

  1. What influence or effect does a black hole have on its surroundings?

He couldn’t see a black hole directly, as the gravity is so strong that nothing, not even light, can escape.

Two discoveries made before the WW II changed astronomy. First, the discovery by the engineer Karl Jansky, of some mysterious radio waves coming from deep space. Second: the Universe is full of X-rays; this was made using a German rocket carrying Geiger counters.

The electromagnetic spectrum is much wider than the visible region that the human eye can perceive.

Using radio waves or X rays, astronomers have discovered a new way of understanding the universe. X-rays come from the most energetic part of the electromagnetic spectrum, and the universe seems to abound in X-ray sources. X-rays are generated by cosmic objects with temperatures in millions or even tens of millions of degrees.

  1. Cygnus X-1 – the first object considered to be a black hole

One of the first X-ray sources to catch the attention of astronomers is named Cygnus X-1. Cygnus because it was in the constellation Cygnus, X because it was an x-ray source and 1 because it was the first identified source.

In 1970, Paul Murdin, working at the Royal Observatory in the UK, decides to hunt pairs of stars or binaries (stars that are gravitationally coupled, moving around each other).

Murdin wonders if it’s possible to discover binaries where only one of the stars is visible; a star emitting light and another star that emits x-rays. He spots a star whose orbit around an unidentified object lasts for 5.6 days. Could this unidentified x-rays-emitting object be a black hole? It depends on its mass.

In order to be classified as a black hole, this unidentified x-rays-emitting object must have at least 3 times the mass of the Sun. Murdin estimated that the mass of Cygnus X-1 is 6 times the mass of the Sun, so it’s a black hole!

Murdin and his fellow scientist, Louise Webster published their findings, the result of their study, in September 1971. They were modest about the claim that thay were making. The paper they published just mentions the word “black hole” once, right at the end, in the last sentence of the article, “We think this object might be a black hole.”

Theorist Kip Thorne and the noted British physicist Stephen Hawking made a wager, a bet, as to whether Cygnus X-1 really was a black hole or not. Thorne claims that Cygnus X-1 is a black hole, and Hawking claims it’s not a black hole. In june 1990, Hawking acknowledged that he had lost the bet.

It took another 20 years before Murdin’s estimate of the mass of Cygnus X-1 was confirmed by another astronomer. The new, more accurate measurements made by Mark Reid have shown that Cygnus X-1 is 6,000 light-years away from Earth; Reid’s team was also able to determine that the mass is about 15 solar masses, or 15 times the mass of the sun. Cygnus X-1 officially becomes a black hole.

Cygnus X-1 is surrounded by an accretion disk, a disk-shaped cloud of gas and dust outside its event horizon, the point of no return.

As gravity pulls matter toward the black hole, the cloud of gas and dust starts rotating. Within the accretion disk, particles whip around at half the speed of light. These particles collide, which heats them up to millions of degrees. When they get that hot, particles blast out X-rays. These X-rays were discovered by Paul Murdin while investigating the binaries in the Cygnus galaxy.

Cygnus X-1 (right) and its companion star (left)

Cygnus X-1 (right) and its companion star (left)  

Cygnus X-1 devours its companion star. The star orbits so close to Cygnus X-1 that it’s slowly devoured by the black hole. Some of the star material gets into the black hole, but some of it actually comes back out before ever entering the black hole.

Jets of Cygnus X-1. One of the most striking features of Cygnus X-1 is its enormous jets at the two poles. There’s still a lot we do not know about these jets. They are tightly focused and extremely powerful rejecting matter far beyond the limits of the Cygnus galaxy. When gas gets to these high temperatures, there’s a magnetic field that forms around them. We don’t understand exactly how, but this magnetic field is what seems to be generating these extremely powerful jets.

  1. The discovery of quasars – black holes in disguise

By the 1950s astronomers began to discover sources of radio waves (spots emitting radio energy) in the Universe, but it was not clear whether the source of this energy was a star or not. So astronomers name them “quasi-stellar radio sources” – quasars – in 1964.

Astronomers have tried to analyze the electromagnetic energy they emit, the electromagnetic spectrum of radio waves, given that any element has a unique spectral fingerprint.

In 1963, astronomer Maarten Schmidt discovers the fingerprint of hydrogen buried in the quasar’s spectrum. The quasar is moving away from us at fantastic speed. The reason? It’s the result of Big Bang, the beginning of our Universe.

But the mystery remains: an object that is two billion light years away, putting out the energy of a trillion suns each second. What could possibly create that? It can’t be chemical energy. It couldn’t be nuclear energy. There’s no way a quasar could be a star. No star can generate such an amount of energy.

The only source that can generate this energy is gravity. Although we can easily “overcome” gravity on Earth, gravity is an incredible force when concentrated into a black hole.

So astronomers start wondering: what if the energy blasting out from quasars is coming from bright accretion disks around black holes? But not just any black hole. Supermassives, unlike Cygnus X-1.

  1. Sagittarius A*, the black hole with a mass 4 million times the mass of the Sun, in the direction of the center of our own Milky Way Galaxy

The center of our galaxy is in the direction of the Sagittarius galaxy. The Milky Way is only 100,000 light years in diameter, but it’s relatively thin, only about 1000 light years thick. Our solar system is about 26000 light-years from the center of the galaxy.

In the 1990s, astronomers began looking for a possible black hole in center of the Milky Way Galaxy. Andrea Ghez is one of them. She tried to track individual stars orbiting the center of the galaxy.

Using new technologies declassified by the US Army, Andrea begins recording the positions of stars in the central area of ??the galaxy in 1995. And every year since then, they have taken an image. Putting those annual snapshots together, creating a movie, the result was astounding: the stars are whipping around the center of the Milky Way at phenomenal speeds, up to 10000 kilometers per second.

Many body dynamics in an extreme gravitational potential: https://www.youtube.com/watch?v=D5jTfn3K_Ek

To go that fast, the stars must be orbiting something extremely massive, probably an object four million times the mass of the sun. What could be so massive, yet be completely invisible? Nothing but a black hole!

black hole in the center of our galaxy,

The first focalied picture of Sagittarius A*, the black hole in the center of our galaxy, the Milky Way, took by the space-based X-ray telescope NuSTAR (Nuclear Spectroscopic Telescope Array)

  1. A supermassive black hole at the center of any galaxy

At the center of our galaxy there is a massive black hole. In the Milky Way, at least 20 black holes like Cygnus X-1 have been identified. There are probably millions of black holes in our galaxy. But what about other galaxies? Are there black holes at the centers of galaxies?

The Hubble Space Telescope (HST) is a space telescope that was launched into low Earth orbit in 1990, which would take another innovation in astronomy. The Hubble Space Telescope starts delivering clear images of distant galaxies.

A team of astronomers began studying the centers of galaxies. Images delivered by The Hubble Space Telescope show where the stars in the galaxy are, as well as the structure of the galaxy. But the other galaxies are much too far away to measure the speed of individual stars around the galactic center. But by analyzing the way light is shifted from blue to red at different points in the galaxy, astronomers can estimate an average speed of stars orbiting the center, which is accurate enough to create a replica in a computer, to create a computer simulation of the galaxy.

The second step is to try to make a computerized simulation based on observations of a galaxy; building models of galaxies in the computer. It’s known as the “Schwarzschild method” (developed by Martin Schwarzschild, son of Karl Schwarzschild). Computer simulation is a success when observations of the model match the observations taken with the Hubble Space Telescope.

The model match the Hubble observations only when they add a supermassive black hole at the center of the galaxy. Of over 35 galaxies studied by the group of astronomers, they all seem to have a supermassive black hole at the center.

  1. How are supermassive black holes possible? How are quasars possible?

Cygnus X-1 is 15 times as big as our sun. Sagittarius A*, the supermassive at the center of our Milky Way is 4 million times as big as our sun. The black hole in the Andromeda galaxy is 100 million times as big as our sun. There are supermassives ten, even 20 million times the mass of our sun. How is it possible to make such monsters, such gigantic black holes?

Could supermassives have came from collapsed stars? Very unlikely, as we don’t know any stars billions of times bigger, more massive than the sun.

We believe that black holes are devouring anything that comes within their sphere of influence. They form that accretion disk around their events horizon. The cosmic gas in the center of the galaxy coagulates, under the pressure of gravity, in order to form the acretic disk.

The accretion disk is made up of  hydrogen, helium and other elements in a gaseous form. The black hole pulls the gas in toward it; as it swirls around, it orbits closer and closer to the black hole and the feeding begins. The black hole is continuously absorbing cosmic gas, so it actually adds to its mass, becoming more and more massive. And a black hole that “feeds”, it blasts vout X-rays, a process that can be captured by astronomers. Another way for black holes to gain weight mass is “devouring” of nearby stars.

But how are quasars possible? Quasars are extremely far away, which means that they’re part of the very early universe. Very bright quasars, 600 million years after the Bing Bang. So how did early supermassives, quasars, get so big, so fast? The answer, some astronomers believe, is to create a black hole directly from a cloud of gas. Under some astronomical conditions, enormous clouds of cosmic gas can collapse directly into a supermassive black hole.

Supermassive black holes don’t exist in isolation. They are integrated into galaxies: the bigger the galaxy is, the more massive the black hole in the center of the galaxy.

Galaxies grow by creating new stars from clouds of hydrogen gas. Gas is essentially the fuel for star formation. So if a galaxy runs out of gas, it stagnates, it cannot create new stars.

Supermassive black holes are interfering with star formation. When a black hole is growing, a huge amount of energy is being liberated into space. Some of that energy heats the cosmic gas, and one of the consequencea is that heated gas will not form stars anymore. So this radiation generated by the supermassive black holes blocks the formation of new stars in their proximity. But black holes have eating or growing phases and then quiescent phases. So they seem to be involved with the formation of galaxies.

James Webb Space Telescope. In the next two years, NASA will launch the most powerful telescope, James Webb Space Telescope. The telescope is designed to look in the infrared. Hopes are high that the James Webb Space Telescope will facilitate important advances in understanding the early Universe and will help solve many of the remaining mysteries around the supermassive black holes.

A daring science project, called the Event Horizon Telescope, is now attempting the impossible: to take a picture of a black hole. The primary target of group of scientists is Sagittarius A*, the suppermasive in the center of our Milky Way Galaxy. The astronomers hope to photograph what is visible of a black hole. In our situation, the “shadow”; as the gas around the back hole hits the event horizon, it leaves a defined shadow on the surrounding light. That’s the picture they are trying to take.

Milky Way as background

A graphical view, using the Milky Way as background, of what might be the first image of a black hole

  1. detection, by the LIGO project, of gravitational waves generated by the union of two black holes

Einstein’s theory of general relativity predicts that when an object moves, it can create distortions of space-time. One of the most important goals for physicists of the twentieth century was to detect these gravitational waves.

The detection of gravitational waves comes with several benefits: it would confirm Einstein’s prediction, it might prove the existence of black holes and solves the problem of supermassive black holes.

But how to detect gravitational waves? The technological challenge was immense, as an extraordinarily sensitive instrument was needed. Here comes physicist Rai Weiss, who has been involved for a long time in the study of sound waves. Rai’s idea was to use light to detect gravitational waves: “send a beam of light from one place to another and measure the time it takes get there.”

That’s how the distance to the moon was calculated with great precision: bouncing a laser beam from the Earth of a mirror left behind by Apollo 11 astronauts.

Rai Weiss’ suggestion was to detect gravitational waves using a tool called a laser interferometer. It works by firing a laser into a splitter. Half of the emitted light continues straight ahead towards a mirror, while the other half  is reflected to another mirror. As the distances are exactly the same, the system is designed so that the two beams cancel each other out, so the photo detector sees nothing. What happens if space is distorted by gravitational waves? The light beams no longer arrive back at the same time to cancel each other out, and the detector (on the right in the picture below) receives light.

electromagnetic waves distort the space

But how much do the electromagnetic waves distort the space? Of course, we need incredibly sensitive instruments to detect them. How big is the difference in length between the two arms of the interferometer? One hundredth the size of the atomic nucleus! So it cannot be measured with the ruler…

So the technological challenge was enormous. Many have thought that such a sensitive instrument is impossible to achieve. It took 40 years and hundreds of millions of dollars, but LIGO (The Laser Interferometer Gravitational-Wave Observatory) has become a reality and its implementation has fundamentally changed physics!



September 14, 2015

On September 14, 2015, at 4 a.m., researcher Robert Schofield from the interferometer in Louisiana (two interferometers were built to confirm any gravitational wave detection without any suspicion of interference or technical errors), decided to stop calibrating the equipment, given that he was tired, although he still had another hour of work to do, so he could have worked and keep the interferometer inoperative.

40 minutes later, with the instruments still in test mode, a signal that had been on its way for 1.3 billion years reaches the two gravitational detectors in Louisiana and Washington, changing the way we understand the Universe…

What have interferometers detected? Oscillations of the mirrors that were slow at first and became faster and faster. And this is exactly what is happening if two massive black holes merge. Two massive black holes, one 29 times the mass of the sun, and the other 36 times the mass of the sun.

gravitational waves by the mutual orbit of two black holes

The generation of gravitational waves by the mutual orbit of two black holes.

Graphical representation

The violent merger has released an enormous amount of energy that has left its mark on space-time and has traveled in the form of gravitational waves along the Universe over 1 billion years.

signal received by the two interferometers

The signal received by the two interferometers

After detecting this collision, LIGO has detected several more collisions of other black holes. In October 2017, Rai Weiss, Kip Thorne (who worked with Weiss) and LIGO’s former director, Barry Barisch, received the Nobel Prize.

The LIGO discoveries prove that black holes can grow bigger by merging two black holes.

On the other hand, LIGO opens a new chapter in astronomy: gravitational astronomy.

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