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What happens when the collapsed remnant of a giant star at the end of its life is

Â more than three times the mass of the Sun?

Â Under this situation, there's no force of nature that can resist the continued

Â collapse, not electron degeneracy pressure, not neutron degeneracy pressure.

Â In principle, the stellar remnant must continue to collapse to a state whose

Â properties are as bizarre as any state of matter in the universe, a black hole.

Â To understand black holes fully, we'd have to delve into Einstein's general theory of

Â relativity, a complex and difficult theory involving tensors and

Â ten coupled second-order partial differential equations.

Â Since that level of math is beyond the scope of this course,

Â we'll just approach black holes in a conceptual way.

Â Remember that for weak situations of gravity, which is most of the universe,

Â general relativity produces the same predictions as Newton's theory.

Â But when gravity is strong, it gives much better results, and for some phenomena,

Â they are simply not predicted or understood in terms of Newton's theory.

Â The mathematics and the theory of general relativity are difficult enough

Â that only a handful of very particular situations have been solved fully.

Â The full description of space-time and general relativity is called a metric, and

Â only a handful of metrics have been solved in the 60 or

Â 70 years that people have been doing this research.

Â It's very hard to do real-world problems.

Â So most of the solutions are for very artificial cases,

Â such as a black hole that's not spinning or a black hole that's spinning.

Â Einstein's theory has only been tested in the weak field case,

Â such as with its confirmation in the eclipse of the Sun in 1916.

Â But it's passed all of those tests with flying colors and

Â is considered the correct theory of gravity.

Â We await tests of gravity in the strong field situation or for

Â the predictions that are unique to the general theory of relativity and

Â do not occur in Newtonian gravity.

Â The central conceptual shift in general relativity is the idea that space and

Â time are curved by mass and energy.

Â Mass and energy are themselves equivalent by Einstein's other insight,

Â E equals mc squared.

Â It's, of course, difficult to visualize the curvature of space-time

Â in three dimensions when we occupy three dimensions, so

Â we tend to use analogies in two dimensions or visualizations.

Â The commonly used visualization involves the two-dimensional

Â analogy of a flat sheet made of rubber.

Â In Newtonian theory, the sheet is always flat, and

Â mass objects sit in the sheet without distorting it or changing its properties.

Â In general relativity, any mass, or a combination of mass and

Â energy, distorts the sheet, which is the space-time continuum.

Â And objects traveling through that space-time follow paths determined by

Â the curvature of the space-time.

Â We can think of ball bearings or marbles rolled over

Â a rubber sheet that has depressions in it causes by the mass in space.

Â The higher the mass energy density, the higher the curvature of space.

Â This is the central equivalence of Einstein's theory.

Â In principle, there can be sufficient mass energy density

Â to pinch off space entirely, trapping a region of space-time beyond the view

Â of the rest of the space time and removing it from the visible universe.

Â This in essence is a black hole.

Â Another way to think of black holes is by simple extrapolation or

Â extension of Newton's theory.

Â And in fact, John Michell in 1795, using purely Newtonian theory,

Â made a prediction of black holes and their existence.

Â He just extrapolated from the terrestrial situation where the escape velocity for

Â any object is 11 kilometers per second.

Â From the Sun, the escape velocity is 600 kilometers per second.

Â He recognized that there might be a mass, or

Â in particular, a very high density form of mass, where the escape velocity at

Â the surface would naturally reach 300,000 kilometers per second, the speed of light.

Â By analogy and by extrapolation,

Â this would be a situation where nothing could escape, not even light.

Â Although the analogy is not correct because we have to use general relativity

Â to understand black holes, the concept is correct.

Â Nothing can leave the event horizon of a black hole.

Â The event horizon is not a physical barrier.

Â It's a mathematical description of the place that defines where information is

Â trapped forever.

Â Essentially, it's an information membrane.

Â 4:24

>> The easiest way for us to enter Einstein's universe is

Â to imagine space and time to be like a sheet of rubber.

Â >> [SOUND] If space-time were empty, the sheet would be flat.

Â But massive bodies like the Earth and

Â Sun will bend the sheet and cause it to be curved.

Â >> This curvature is Einstein's concept of gravity.

Â The more mass a star or planet has,

Â the more steeply it bends space-time around it, and so the more gravity it has.

Â [NOISE] Throw something extremely heavy, like a collapsing star,

Â onto the sheet, and you soon end up with a universe full of holes.

Â >> [NOISE] Ow, watch it, coney.

Â [NOISE] [SOUND] Oops.

Â >> [NOISE] As a massive star cools and shrinks,

Â that will curve the space-time around it more and more.

Â [NOISE] Eventually, when it shrinks to a certain critical size,

Â it will quite literally create a black hole in space-time.

Â Things can fall into a black hole, but nothing can get out.

Â [NOISE].

Â >> Oh, there's so much I don't know about astrophysics.

Â I wish I read that book by that wheelchair guy.

Â 5:54

[NOISE].

Â >> The most terrifying concept in astrophysics lurks at the bottom of

Â the black hole, the singularity.

Â [NOISE] Everything that has ever fallen into the hole is

Â destroyed at the singularity, crushed into a pin,

Â pinpoint of infinite density and infinite smallness.

Â Even space and time are squelched out of existence.

Â [NOISE] All that remains in the outside universe

Â is a perfect sphere of absolute darkness,

Â a gravitational ghost of the star that died.

Â This sphere is called the event horizon and it marks the edge of the abyss.

Â >> In the theory of black holes, the calculation produces a problem

Â because the center of a black hole is a singularity,

Â an infinity of mass density that is impossible in the theory.

Â As Stephen Hawking has said,

Â the theory of black holes contains the seeds of its own demise.

Â This suggests that our theory of black holes is not yet complete.

Â General relativity and

Â relativistic astrophysics can be used to model black holes quite accurately.

Â And although a black hole would seem to be a black object, invisible to us,

Â it turns out that black holes are unlikely to be completely isolated in space.

Â Although the matter passing the event horizon becomes invisible from view,

Â its acceleration on the way in leads to huge torrents of energy being released.

Â So we might expect black holes to be visible by this mechanism,

Â as this visualization shows.

Â This, in fact,

Â is the key to how we think black holes have actually been proved in space.

Â At the moment, the likelihood that black holes exist is very high, perhaps 99%.

Â What we look for is a situation of a binary pair, where one of the stars

Â is visible and its properties and evolutionary state can be measured.

Â The binary orbit gives the mass of the unseen companion.

Â And if that mass must be more than three times the mass of the Sun, and the star's

Â in a late phase of its life, then it fits the definition of a black hole.

Â Also, this black hole is unlikely to be dark.

Â In a binary system containing a black hole,

Â mass is being siphoned on to the black hole from the companion.

Â It falls into an equatorial disc because the black hole will be spinning extremely

Â rapidly.

Â This disk of material approaches within three to ten times

Â the event horizon distance and heats up enormously.

Â The inner regions of the disk may be 100 to 200 thousand kelvin,

Â the outer regions 30 to 50 thousand kelvin.

Â This radiation will be produced at hard x-ray and soft ultraviolet wavelengths.

Â Meanwhile, some of the material is accelerated

Â down the poles of the spinning black hole, like a cosmic particle accelerator sending

Â plasma to large fractions of the velocity of light.

Â This also makes high energy radiation,

Â often visible across the electromagnetic spectrum from radio waves to gamma rays.

Â So this becomes the reason why we think black holes exist.

Â Currently, there are several dozen systems where it's almost certain

Â that the invisible companion is an evolved collapsed star with a mass

Â more than three times the mass of the Sun.

Â This is the basis of our evidence that black holes actually exist.

Â Even more exotic phenomena, including gravity waves,

Â are predicted when black holes are in orbit around

Â other evolved final states of stars, such as neutron stars.

Â In principle, the gravity waves released from this system and

Â the slow inspiral will produce a bigger black hole when the objects merge.

Â If a collapsed remnant at the end of a massive star's life is

Â more than about three times the mass of the Sun,

Â no force of nature can stop it from collapsing to a state called a black hole.

Â The black hole is bounded by the event horizon, an information membrane

Â marking the distance within which all information is trapped, and

Â nothing, no matter, no radiation can escape.

Â Do black holes actually exist?

Â We currently have several dozen examples in the nearby universe of binary systems

Â where the invisible companion is almost certainly a black hole.

Â It's expected that throughout the galaxy, there may be 10 million black holes,

Â and about 30 to 50 million neutron stars.

Â