The Map of Black Holes | Black Holes Explained

Here’s a sanitized version of the provided YouTube transcript:

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Hello, welcome back! I’m Dom, and this is the Map of Black Holes. This isn’t a map of where all the black holes are in space; rather, it’s a concept map of the subject of black holes, laying out our current knowledge of them, the evidence for their existence, and the many outstanding mysteries still to be solved. They are indeed very strange and fascinating.

I find concept maps useful for providing a good overall idea of a field of research, so here’s the current state of knowledge about black holes.

On Earth, getting into space in a rocket is quite challenging because we need to overcome Earth’s gravity. However, we are fortunate; if Earth were just fifty percent larger in diameter, it would be impossible to achieve orbit with our current technology. This would mean no astronauts, no satellites, and no GPS or mapping services.

The stronger the gravity of a planet, the higher the escape velocity required. Black holes are the most extreme example of this, where the escape velocity exceeds the speed of light. There is so much mass compressed into such a small volume that nothing can escape, as nothing can travel faster than light. Hence the name “black hole,” which interestingly derives from the Black Hole of Calcutta, a notorious prison where individuals entered but never left alive. Although the term “black hole” became popular in the late 1960s, they were previously referred to as dark stars, frozen stars, or gravitationally collapsed objects.

The original idea that black holes could exist stemmed from our understanding of Einstein’s theory of relativity, published in 1915, where gravity is described as the curvature of spacetime. The denser an object is, the more it curves spacetime, and the greater the curvature, the stronger the gravitational force.

In 1916, Karl Schwarzschild found a solution to the field equations of relativity, predicting a specific distance from the black hole known as the Schwarzschild radius or event horizon, beyond which nothing can escape. This event horizon was long considered a mathematical curiosity until the 1960s and 1970s, when theoretical developments and experimental evidence accumulated, leading to the realization that black holes do exist in our universe.

A common visualization of the warping of spacetime around a black hole shows squiggly lines representing photons that are actually traveling in straight lines. They appear to curve because they are moving through curved spacetime. This phenomenon is known as gravitational lensing.

The inner horizon is a feature of rotating black holes. Rotating and non-rotating black holes exhibit distinct characteristics, which we will explore when discussing their structures.

At the center of a black hole lies a singularity, where all the mass is compressed into an infinitely small region of infinite density, creating an infinite curvature of spacetime. However, this may not be entirely accurate, indicating that we are pushing our current theories into realms they are not equipped to handle. A theory of quantum gravity is needed, and many believe that integrating the laws of quantum mechanics with general relativity could clarify what occurs at the center of a black hole. A theory of quantum gravity is considered the holy grail of theoretical physics, which is why black holes are so intriguing; they are among the few places in the universe where gravity becomes as strong as the other three fundamental forces, necessitating both general relativity and quantum mechanics to explain the phenomena occurring within them.

Another way to visualize the motion of particles near a black hole is through spacetime diagrams. Far from a black hole, squiggly lines traveling at 45 degrees represent light moving at the speed of light. As this is the cosmic speed limit, any object with mass will have trajectories at angles between these limiting cases, traditionally referred to as a light cone. As one approaches the black hole, this light cone bends towards it due to the curvature of spacetime. Crossing the event horizon means that all paths point inward to the center, indicating that no matter the direction of travel, one is always moving toward the center of the black hole—every possible future leads to being crushed. It’s as if space and time switch roles; outside the event horizon, time only moves forward, but inside, the only direction one can move is toward the singularity.

The term “event horizon” signifies that any event occurring inside the black hole cannot be observed from outside. It is literally the boundary beyond which events cannot be seen.

Most black holes we know of are formed from the remnants of dying stars. When stars exhaust their fuel, they perish in various dramatic ways depending on their mass. Stars with cores less than 1.4 times the mass of the sun collapse into white dwarf stars. Above this limit, known as the Chandrasekhar limit, stars explode in a supernova and collapse into neutron stars. The immense pressure from the core’s matter overcomes the electrons’ ability to repel each other, leading to the formation of an incredibly dense star composed of pure neutrons.

The theory suggests that a star with a core mass exceeding 2.17 times that of the sun will collapse into an even denser object: a black hole. There is a possibility that other dense objects, such as quark stars or strange stars, exist between neutron stars and black holes, but these remain hypothetical with no current evidence.

Exploding stars are just one mechanism for black hole formation. There are also supermassive black holes with masses ranging from millions to tens of billions of times that of the sun. The process by which they became so massive is still an open question. Did they grow over time by absorbing other matter and black holes? Did they form from the universe’s earliest massive stars? Or perhaps they formed directly after the Big Bang from primordial gas collapsing in on itself? This remains an active area of research.

At the smaller mass scale, it is theoretically possible to have very low-mass black holes. The key feature of a black hole is not its mass but the extremely high density of that mass. Some have speculated that tiny black holes might be created in particle collisions, such as those in the Large Hadron Collider at CERN. You may recall media reports suggesting that a black hole could be created in Switzerland that would consume the Earth. However, this was unfounded, as cosmic rays from space possess much higher energies than anything produced on Earth or at CERN, and they do not create black holes in the atmosphere. Therefore, there is no evidence that miniature black holes are formed from particle collisions, suggesting there may be a lower mass limit to black holes that we are unaware of—another open question.

Here’s how different masses of black holes are typically classified:

– Micro-black holes: up to the mass of the moon, with event horizon radii of 0.1 millimeters or less.
– Stellar black holes: approximately ten times the mass of the sun and about thirty kilometers in radius.
– Intermediate black holes: around a thousand times the mass of the sun, similar in size to Earth, with a radius of about a thousand kilometers.
– Supermassive black holes: from a hundred thousand to tens of billions of solar masses, with sizes reaching up to four hundred astronomical units. For context, one astronomical unit is the distance from Earth to the sun, so four hundred astronomical units is about ten times the orbit of Pluto, which is astonishing to consider.

Let’s take a closer look at the anatomy of black holes. We’ve discussed the event horizon and singularity, but there are many other intriguing features to explore.

Near a black hole, clocks run slow due to the highly curved spacetime, causing time dilation. This means the experience of someone falling into a black hole would differ significantly from that of an observer watching them fall in. If you crossed the event horizon, you wouldn’t notice anything unusual. However, depending on the size of the black hole, it wouldn’t be long before you experienced spaghettification.

If you were observing someone falling into a black hole, they would appear to move in slow motion as their local clock slowed down, becoming increasingly redshifted until they looked like a red smudge on the event horizon, gradually fading from view as the wavelength of light they emitted lengthened.

The singularity, as previously mentioned, is a region of infinite curvature where all mass is compressed into zero volume with infinite density. This suggests a breakdown of general relativity, indicating that a theory of quantum gravity is necessary.

Other important features of a black hole include the innermost stable circular orbit, located at three times the Schwarzschild radius, which marks the minimum distance a test particle can orbit the black hole in a stable circular path. This also defines the inner edge of an accretion disk of infalling matter around the black hole.

At 1.5 times the Schwarzschild radius is the photon sphere, the only possible circular orbit for massless particles. If you were situated here, you could theoretically see the back of your own head, as photons would travel around the black hole. This also marks the closest distance any elliptical orbit can approach; anything traveling below this will either be flung out of the black hole’s gravity or spiral in.

Additionally, black holes emit Hawking radiation from the event horizon, although this is extremely faint and currently undetectable unless we could somehow get very close to a black hole.

It’s important to note that black holes do not possess any special suction powers; they do not roam the galaxy consuming everything in their path. The gravitational field of a black hole is shaped like that of any other massive body, so at a distance, being near a black hole feels similar to being near any other star of the same mass. They are unique due to their density, which results in significantly higher gravity when one approaches them.

This description applies to non-rotating black holes. The scenario for rotating black holes is more complex. You may wonder if non-rotating black holes exist, as everything in the universe is in some way spinning. Theoretically, non-rotating black holes can exist because Hawking radiation gradually removes some angular momentum from the black hole, slowing its spin over an extended period.

Non-rotating black holes are spherical, while rotating black holes take on a squashed oval shape. The singularity at the center is no longer a point but a ring. Rotating black holes also have a region outside the event horizon called an ergosphere, where it would be impossible to remain stationary due to the rotation of the black hole dragging spacetime around it in a process known as frame dragging, similar to a whirlpool of spacetime. Inside the ergosphere, the frame dragging is so rapid that one would need to travel faster than light just to remain still. Movement within the ergosphere is only possible in the direction of the black hole’s rotation.

At the edge of the ergosphere is the innermost stable orbit, the minimum distance at which a particle can maintain a stable orbit around the black hole.

Many real black holes are surrounded by an accretion disk, a cloud of material falling into the black hole, generating significant heat and energy as particles collide. Accretion disks are bright sources of X-ray radiation and high-energy particles that can escape the ergosphere with more energy than they entered, effectively stealing angular momentum from the black hole as they do so.

The intense gravity surrounding a black hole leads to fascinating gravitational lensing effects on the accretion disk, resulting in a familiar image. In reality, the accretion disk is pancake-shaped, but we can observe parts of it that would typically be hidden behind the black hole because light traveling upwards or downwards is bent around the black hole and directed toward us. Thus, it appears as though there is an accretion disk above and below the black hole, but we are actually seeing the top and bottom of the accretion disk that is behind the black hole.

I’ve been speaking for a while, but how do we know black holes actually exist? Over the past fifty years, we have accumulated a substantial body of observational evidence from various techniques.

The first evidence came from X-ray astronomy, as the radiation from the accretion disk is primarily X-ray radiation. The process producing this X-ray radiation in the accretion disk is one of the most efficient energy-producing processes known, with spiraling material converting up to 40% of its rest mass into energy. To grasp how remarkable this is, we can compare it to the nuclear fusion process powering the sun and other stars, which converts only 0.7% of rest mass into energy—significantly less than 40%. Thus, the accretion disk is nearly sixty times more energetic than a burning star.

The first black hole discovered was Cygnus X-1 in 1971. Since then, around a hundred more have been identified, although this is just a small sample of the estimated number of black holes in our galaxy. It is believed that every galaxy contains a supermassive black hole at its center.

Accretion disks are often accompanied by relativistic jets, which emit even higher energy particles and radiation than the accretion disk itself. The mechanism behind these jets is not yet understood.

We observe many high-energy sources in space, many of which are thought to be caused by matter accreting into black holes. These include active galactic nuclei and quasars, believed to be the accretion disks of supermassive black holes, as well as ultraluminous X-ray sources thought to originate from intermediate-mass black holes.

Additionally, X-ray binaries likely consist of a normal star and a black hole orbiting each other, with the black hole gradually siphoning matter from the star. Short-lived streamers are thought to be stars that shine brightly as they are consumed by a black hole before disappearing.

Another line of evidence comes from the center of our galaxy, where the orbits of about 100 stars have been tracked around an invisible massive object known as Sagittarius A*. By analyzing these orbits and measuring the velocities of the stars, astrophysicists have calculated the mass of this central body to be approximately 4.3 million times that of the sun, confined to a region of less than 0.002 light-years, indicating it must be a supermassive black hole.

In 2019, the first direct image of the accretion disk around a black hole was created from radio waves emitted by the galactic center of the Messier 87 galaxy. The image displayed features consistent with our expectations for an accretion disk, albeit somewhat blurry. Constructing this image was a remarkable achievement in radio astronomy, accomplished by combining signals from eight radio telescopes worldwide to create a virtual telescope the size of the Earth.

Equally impressive was the detection of gravitational waves by LIGO in 2016, which uses finely tuned lasers in a giant L-shape to detect minute changes in distance caused by rippling spacetime when gravitational waves pass through the Earth. The first gravitational waves detected were produced by a pair of stellar-mass black holes spiraling into each other and merging into a larger black hole, converting about 5% of their mass into gravitational waves. Since then, LIGO and VIRGO have detected many more collisions.

Lastly, there is a proposed method called microlensing, which has been observed for stars but not, as far as we know, for black holes. The strong gravitational field around a black hole creates a lensing effect. The idea is to use this effect to detect black holes when they pass in front of a star. We have seen phenomena like supernovae being gravitationally lensed by massive objects such as entire galaxies. If we found a binary system where a star orbits a black hole, we could potentially observe the radiation from the star being bent toward us as it passes behind the black hole, providing information about the black hole it orbits. This could be a fascinating technique for future black hole observations.

Now, let’s briefly review the theoretical understanding of black holes, which began in 1916 but was significantly developed in the 1960s and 1970s when black holes were recognized as real physical objects rather than mere mathematical curiosities.

Here is the equation for the radius of a non-rotating black hole, which establishes a simple relationship with its mass, where G is the gravitational constant and c is the speed of light. The situation becomes more complex if the black hole possesses spin or charge.

The general description of black holes, developed in the 1960s, is known as the no-hair theorem, which states that a stationary black hole can be completely characterized by just three parameters: mass, angular momentum, and electric charge.

In the 1970s, a theory of black hole thermodynamics was formulated, explaining the connections between black hole mass and energy, how the surface area of a black hole relates to its entropy, and how surface gravity correlates with temperature.

Stephen Hawking later applied quantum field theory to black holes, demonstrating that they emit Hawking radiation from the event horizon with a characteristic black body spectrum, where temperature is proportional to the surface gravity of the black hole. Consequently, black holes gradually lose mass over time by radiating Hawking radiation, but this evaporation occurs most slowly for the largest black holes and most rapidly for the smallest. This means that micro-black holes would have short lifespans, while supermassive black holes could exist for over 10^100 years—a staggering duration, making them the last objects to remain before the heat death of the universe.

This overview provides insight into our understanding of black holes, but many mysteries persist, primarily due to our lack of a theory of quantum gravity.

I’ve already mentioned that singularities likely do not exist as infinitely small points with infinite density. This raises the question: what happens to matter at the singularity? Unfortunately, if we were to discover this experimentally, the event horizon would prevent us from communicating the results, complicating our understanding of singularities.

In the context of spinning or charged black holes, there is a hypothetical possibility that they could contain unstable wormholes, allowing one to exit the black hole but in a completely different spacetime. There are also regions within black holes where it might be possible to travel to one’s own past along closed timelike curves, leading to time-travel paradoxes. However, while these ideas are intriguing from a science fiction standpoint, they may vanish with a proper quantum description of black holes.

Other theoretical objects have been proposed, but there is currently no evidence for them. These include stars that exist between neutron stars and black holes, which remain speculative. Additionally, white holes are theorized to function like black holes but allow information to escape while preventing anything from entering. Naked singularities are singularities that could be observed because they lack an event horizon, but these are considered unphysical and unlikely to exist.

However, these concepts are less compelling than the real theoretical puzzles. One significant puzzle is the holographic principle, which is complex to explain but suggests that black holes might indicate the universe is a hologram. This arises from the entropy of a black hole; in every other entity in the universe, entropy scales with volume, but in black holes, it scales with surface area. This implies that events occurring within a volume of spacetime can be described by data on the surface of that volume, suggesting we are all part of a hologram. Yet, we need a theory of quantum gravity to accurately calculate black hole entropy, making this an ongoing area of research.

Finally, one of the most significant unsolved mysteries regarding black holes is what happens to the information that falls into them. Since black holes are defined by only three