What happens when the collapse remnant of a giant star at the end of its life is more than three times the mass of the sun? Under this situation, there is no force of nature that can resist the continued collapse, not electron degeneracy pressure, not neutron degeneracy pressure. In principle, the stellar remnant must continue to collapse to a state whose properties are as bizarre as any state of matter in the universe, a black hole. To understand black holes fully, we'd have to delve into Einstein's general theory of relativity, a complex and difficult theory involving tensors and 10 coupled second-order partial differential equations. Since that level of math is beyond the scope of this course, we'll just approach black holes in a conceptual way. Remember that for weak situations of gravity, which is most of the universe, general relativity produces the same predictions as Newton's theory, but when gravity is strong, it gives much better results and for some phenomena, they are simply not predicted or understood in terms of Newton's theory. The mathematics and the theory of general relativity are difficult enough that only a handful of very particular situations have been solved fully. The full description of space time in general relativity is called a metric and only a handful of metrics have been solved in the 60 or 70 years that people have been doing this research. It's very hard to do real-world problems. So most of the solutions are for very artificial cases such as a black hole that's not spinning or a black hole that's spinning. Einstein's theory has only been tested in the weak field case, such as with its confirmation in the eclipse of the sun in 1916, but its passed all of those tests with flying colors and is considered the correct theory of gravity. We aweighed test of gravity in the strong field situation or for the predictions that are unique to the general theory of relativity and do not occur in Newtonian gravity. The central conceptual shift in general relativity is the idea that space and time are curved by a mass and energy. Mass and energy are themselves equivalent by Einstein's other insight, E equals mc squared. It's of course difficult to visualize the curvature of space time in three dimensions when we occupy three dimensions. So we tend to use analogies in two dimensions or visualizations. The commonly used visualization involves the two-dimensional analogy of a flat sheet made of rubber. In Newtonian theory, the sheet is always flat and mass objects sit in the sheet without distorting it or changing its properties. In general relativity, any mass or a combination of mass and energy, distorts the sheet which is the space-time continuum and objects traveling through that space-time, follow paths determined by the curvature of the space time. We can think of ball bearings or marbles rolled over a rubber sheet that has depressions in it caused by the mass in space. The higher the mass energy density, the higher the curvature of space. This is the central equivalence of Einstein's theory. In principle, there can be sufficient mass energy density to pinch off space entirely, trapping a region of space time beyond the view of the rest of the space time and removing it from the visible universe. This in essence is a black hole. Another way to think of black holes is by simple extrapolation or extension of Newton's theory. In fact John Michell, in 1795, using purely Newtonian theory, made a prediction of black holes and their existence. He just extrapolated from the terrestrial situation where the escape velocity for any object is 11 kilometers per second. From the sun, the escape velocity is 600 kilometers per second. He recognized that there might be a mass or in particular, a very high density form of mass, where the escape velocity at the surface would naturally reach 300,000 kilometers per second, the speed of light. By analogy and by extrapolation, this would be a situation where nothing could escape, not even light. Although the analogy is not correct because we have to use general relativity to understand black holes, the concept is correct, nothing can leave the event horizon of a black hole. Event horizon is not a physical barrier, it's a mathematical description of the place that defines where information is trapped forever. Essentially, it's an information membrane. Space time is almost impossible to contemplate because our entire sensory existence is limited to the three dimensions of everyday experience. Holy macaroni. The easiest way for us to enter Einstein's universe is to imagine space and time to be like a sheet of rubber. If space time were empty, the sheet will be flat. But massive bodies like the Earth and Sun will bend the sheet and cause it to be curved. This curvature is Einstein's concept of gravity. The more mass a star or planet has, the more steeply it bends space time around it, and so the more gravity it has. Throw something extremely heavy like a collapsing star onto the sheet and you soon end up with a universe full of hoboles. Watch it cony. As the masses dark holes shrinks, it will curve the space time around it more and more. Eventually, when it shrinks to a certain critical size, that will quite literally create a black hole in space time. Things can fall into a black hole but nothing can get out. There's so much I don't know about astrophysics. I wish I read that book by that wheelchair guy. The most terrifying concept in astrophysics lurks at the bottom of a black hole, the singularity. Everything that has ever fallen into the whole is destroyed at the singularity, crushed into a point of infinite density and infinite smalls. Even space and time are swept out of the existence. All that remains in the outside universe is a perfect sphere of absolute darkness, a gravitational ghost of the star that died. This sphere is called the event horizon and it marks the edge of the abyss. In the theory of black holes, the calculation produces a problem because the center of a black hole is a singularity, an infinity of mass density that is impossible in the theory as Stephen Hawking has said the theory of black holes contains the seeds of its own demise. This suggests that our theory of black holes is not yet complete. General relativity and relativistic astrophysics can be used to model black holes quite accurately. Although a black hole would seem to be a black object invisible to us, it turns out that black holes are unlikely to be completely isolated in space. Although the matter passing the event horizon becomes invisible from view, its acceleration on the way in leads to huge torrents of energy being released. So we might expect black holes to be visible by this mechanism as this visualization shows. This in fact is the key to how we think black holes have actually been proved in space. At the moment, the likelihood that black holes exist is pretty high, perhaps 99 percent. What we look for is a situation of a binary pair where one of the stars is visible and its properties and evolutionary state can be measured. The binary orbit gives the mass of the unseen companion and if that mass must be more than three times the mass of the sun and the stars in a late phase of its life, then it fits the definition of a black hole. Also, this black hole is unlikely to be dark. In a binary system containing a black hole, mass is being siphoned onto the black hole from the companion. It falls into an equatorial disc because the black hole will be spinning extremely rapidly. This disk of material approaches within three to 10 times the event horizon distance and heats up enormously. The inner regions of the disk may be 100,000 to 200,000 Kelvin, the outer region is 30,000 to 50,000 Kelvin. This radiation will be produced at hard X-ray and soft ultraviolet wavelengths. Meanwhile, some of the material is accelerated down the poles of the spinning black hole like a cosmic particle accelerator, sending plasma to large fractions of the velocity of light. This also emits high energy radiation, often visible across the electromagnetic spectrum from radio waves to gamma rays. So this becomes the reason why we think black holes exist. Currently, there are several dozen systems where it's almost certain that the invisible companion is an evolved collapsed star with a mass more than three times the mass of the Sun. This is the basis of our evidence that black holes actually exist. Even more exotic phenomena including gravity waves are predicted when black holes are in orbit around other evolved final states of stars, such as neutron stars. In principle, the gravity waves released from this system and the slow inspiral will produce a bigger black hole when the objects merge. If the collapse remnant at the end of a massive star's life is more than about three times the mass of the Sun, no force of nature can stop it from collapsing to a state called a black hole. The black hole is bounded by the event horizon, an information membrane marking the distance within which all information is trapped and nothing, no matter, no radiation can escape. Do black holes actually exist? We currently have several dozen examples in the nearby universe of binary systems where the invisible companion is almost certainly a black hole. It's expected that throughout the galaxy, there may be 10 million black holes and about 30 to 50 million neutron stars.