The basic idea behind a dark star only requires knowledge of 18th century physics. If a star is dense enough, its escape velocity will be the speed of light, making it impossible for light emitted by the star to escape the stars gravity. The idea of a dark star, as proposed by John Michell is not correct, but it is still important since it introduces some ideas that apply to black holes even in modern theories. The problem is, that the concept of a dark star uses Newton's older theory of gravity instead of Einstein's newer theory. That being said, Newton's theory of gravity is a pretty good approximation to Einstein's theory of gravity, when gravity is weak. It was good enough for us to plan a mission to the moon, for instance. When I mean by weak is this, calculate the escape velocity from a planet or star, and compare the value of its escape velocity to the speed of light. If the escape velocity is tiny compared to the speed of light, then we say that gravity is weak, and Newton's theory of gravity is a good enough approximation. For example, the escape velocity from the Earth is 11.2 kilometers per second, but the speed of light is approximately 27,000 times larger. Since the escape velocity from Earth is so small compared to the speed of light, Newton's gravity is good enough for most calculations near the surface of the Earth. But if the escape velocity is larger, say 10 percent of the speed of light or larger, that means that Newton's theory of gravity is no longer sufficient to calculate the strength of gravity. Since Albert Einstein's equations correctly describe relativistic effects at high speeds, they improved on Newton's theory of gravity. This means that we can predict what happens in situations with strong gravity. Einstein's theory of gravity is called The Theory of General Relativity. In general relativity, mass, energy, and angular momentum are all responsible for creating curvature in space time. The curvature of space time then causes planets, stars, and light to travel on curved paths. To create a dark star, we might start with a large star and compress it inwards to make it smaller and denser while keeping the amount of mass unchanged. As the star shrinks in size, the escape velocity from the surface becomes faster and faster until it becomes equal to the speed of light. At this point, Newton's theory of gravity just predicts that light won't be able to escape from the star, and it will appear dark. However, the predictions from Einstein's theory of gravity demonstrate a so called dark star, would exert a much stronger force due to gravity than predicted by Newton. This additional inwards gravitational force makes it impossible for a star to have a stable size. In order for stars to exist, there is a delicate balance between its gas molecules, which exert a net outwards pressure that is exactly balanced by the attraction of gravity, allowing stars to stay the same size over time. When a star gets so small, that its escape velocity is the speed of light, then the required outward gas pressure is infinite. There is no way to create infinite gas pressure, so the star is unstable and begins collapsing inwards. A black hole is what remains after a star is unable to resist gravity and collapses inwards. A black hole does not have a surface but there is a special boundary that surrounds a black hole called an event horizon. In the case of the simplest black hole, the event horizon is a sphere with a radius called the Schwarzschild radius with the value, event horizon radius equals 2 times G, times the mass of the black hole, divided by the speed of light squared. The amazing thing about the formula for the event horizon radius is that it is exactly the same equation that Michell derive for the radius of a dark star. The event horizon radius is a boundary for light rays. If an astronaut shines a flashlight outside of the event horizon, the light rays can escape and be seen by astronomers far away from the black hole. But if the flashlight is at or inside of the event horizon, all light emitted will be trapped inside of a black hole. And it's not just light, massive objects like cakes, or rockets, or astronauts, can escape as long as they are outside of the event horizon radius and their rocket is good enough. But if a cake eating astronaut crosses the boundary defined by black holes event horizon, no escape is possible. The name black hole didn't enter a common usage until 1967, where it was popularized by John Wheeler. Before then, astronomers used the name Totally Gravitationally Collapsed Objects to describe black holes. This is an accurate phrase, but difficult to say. So it's not surprising that the name black hole caught on so quickly with scientists and science fiction writers alike. The distinguishing difference between Michell's dark stars and black holes, as they are described in general relativity, is whether or not the star within the dark boundary maintains a surface. Michell didn't consider what would happen to the surfaces of a star when its escape velocity reaches the speed of light. Scientists now believe that the creation of an event horizon causes all the material hidden behind it to continue collapsing inwards with no chance of a stable surface. There are other dark objects that astronomers make reference to, but they aren't black holes. For instance, there are dark nebula which consist of clouds of cool molecules and dust that block out passing light. These types of nebula can be observed if they lie between us and a bright source of light, since we will see that sunlight is blocked out by the nebula. One famous example is the horsehead nebula. The Horsehead is a dense, cool cloud that blocks out the red light that is emitted behind it, allowing us to see it. In addition, dust emits infrared light so we can detect dust clouds if we use an infrared telescope. Dark Matter is a hypothesized type of matter that was introduced to explain the motions of stars and gas and galaxies. Dark Matter is a type of matter that doesn't emit light, which means it can't be observed directly. However, dark matter does have mass, so there is a mutual gravitational attraction between dark matter, and the stars, and gas, in the galaxy. The gravitational attraction of the dark matter affects how the stars in the galaxy move, allowing scientists to infer the existence of dark matter by their observations with theoretical models. In the 1970s, Vera Rubin, observed spiral galaxies and measured the speeds of the stars. She showed that the fast speeds of these stars implies the existence of dark matter. A tiny amount of the dark matter could be black holes but most of the Dark Matter is a type of particle called a WIMP, which means weakly interacting massive particle. Physicists are trying to detect WIMPs using the Large Hadron Collider in Geneva, Switzerland, and SNOLAB in Sudbury, Canada, as well as other laboratories. So far, the dark matter WIMPs have not been detected. The main thing that dark matter and black holes have in common is that they are both detected by observing their gravitational interactions with luminous objects. Dark energy is the name for another mysterious force which appears to act in opposition to the force of gravity. When astronomers measure galaxies far, far away, they measure that the most distant galaxies appear to move away from us more quickly than galaxies that are close. This is one of the pieces of evidence that our universe is expanding from a moment in history referred to as The Big Bang. Since all these galaxies have mass, they are gravitationally attracted to each other, and we might expect that the rate of the universe's expansion should slow down over time. Instead, there is evidence that the expansion is speeding up, as if there were a repulsive force like a very large scale kind of anti-gravity. This force called dark energy has nothing to do with black holes. However, there are some theorist who have considered types of stars that have some dark energy in them to help combat gravitational collapse. Black holes may give some people melanoheliophobia, but in most ways, they are no more dangerous than any other star in the sky. For example, entering into a black hole is dangerous, once you pass through the event horizon, you can't get out. But if you enter into a star, the hot gas would burn you up too. I would say they are both equally dangerous. There are safe ways to visit a star or a black hole. Instead of traveling directly towards a black hole, you could instead, orbit the black hole just as you can orbit around a star. For example, the Earth orbits around the Sun in a safe stable orbit. Similarly, the Earth could orbit a black hole with the same mass as the sun and at the same distance, making the orbit just as safe and stable as it is now. Unfortunately, it would be very cold around a black hole since the sunlight that warms us would no longer be present. There is nothing about the black hole's gravity that would suck in the Earth. Black holes can become dangerous if they are surrounded by an orbiting disc of hot gas, that looks similar to the rings of Saturn. The disc of gas could emit high energy X-rays. So if you were to approach the black hole's disc, you could receive an unhealthy dose of radiation. For this reason, in the movie Interstellar, the script writers decided to make the disc of gas orbiting their black hole be relatively cool, so that it only emits visible light and no harmful X-rays. The tidal force, which is a difference in the strength of gravity at different locations, can become very strong around a black hole. In fact, when it comes to the tidal force, the smaller a black hole is, the more dangerous it becomes. An astronaut venturing too close to a small black hole would be stretched by gravity into long thin spaghetti-like strands. Out of all the types of black holes, the most dangerous are thought to be the isolated black holes. In isolation, a black hole does not have a companion star or an orbiting disc of gas, making them extremely difficult to see. Due to their difficulty of detection, it's possible that you could accidentally stumble across one, and inadvertently cross into its event horizon while you are exploring the universe. Gravitational lensing by the black hole's mass will distort the images of background stars. So, the presence of an isolated black hole could still be deduced, if you are careful.
