Immanuel Kant, Writer, Philosopher

Immanuel Kant is one of the central figures of modern philosophy, and set the terms by which all subsequent thinkers have had to grapple. He argued that human perception structures natural laws, and that reason is the source of morality. His thought continues to hold a major influence in contemporary thought, especially in fields such as metaphysics, epistemology, ethics, political philosophy, and aesthetics.

A black hole in your pocket?


Transcript


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What would happen to you if a black hole the size of a coin suddenly appeared near you?

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Short answer: you’d die.

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Long answer: it depends.

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Is it a black hole with
the mass of a coin,

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or is it as wide as a coin?

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Suppose a US nickel with
the mass of about 5 grams

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magically collapsed into a black hole.

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This black hole would have a radius
of about 10 to the power of −30 meters.

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By comparison, a hydrogen atom is about
10 to the power of −11 meters.

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So the black hole compared
to an atom is as small as

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an atom compared to the Sun.

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Unimaginably small!

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And a small black hole would also have
an unimaginably short lifetime

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to decay by Hawking radiation.

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It would radiate away what little mass it
has in 10 to the power of −23 seconds.

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Its 5 grams of mass will be converted
to 450 terajoules of energy,

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which will lead to an explosion
roughly 3 times bigger than

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the atomic bombs dropped on
Hiroshima and Nagasaki combined.

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In this case, you die.

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You also lose the coin.

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If the black hole had the
diameter of a common coin,

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then it would be considerably
more massive.

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In fact, a black hole with
the diameter of a nickel

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would be slightly more
massive than the Earth.

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It would have a surface gravity
a billion billion times greater

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than our planet currently does.

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Its tidal forces on you would be so strong

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that they’d rip your
individual cells apart.

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The black hole would consume you before
you even realized what’s happening.

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Although the laws of gravity
are still the same,

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the phenomenon of gravity that you’d
experience would be very different

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around such dense objects.

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The range of the gravitational attraction

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extends over the entire
observable universe,

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with gravity getting weaker the farther
away you are from something.

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On Earth right now, your head and your
toes are approximately the same distance

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from the center of our planet.

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But if you stood on
a nickel-sized black hole,

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your feet would be hundreds
of times closer to the center,

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and the gravitational force would be
tens of thousands of times as large

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as the force on your head and
rip you into a billion pieces.

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But the black hole wouldn’t
stop with just you.

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The black hole is now a
dominant gravitational piece

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of the
Earth–Moon–Black-Hole-of-Death system.

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You might think that the black hole would
sink towards the center of the planet

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and consume it from the inside out.

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In fact, the Earth also moves up onto the black hole and begins to bob around,

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as if it were orbiting the black hole,

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all while having swathes of mass eaten with each pass,

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which is much more creepy.

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As the Earth is eaten up from the inside,

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it collapses into a
scattered disk of hot rock,

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surrounding the black hole
in a tight orbit.

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The black hole slowly doubles its mass
by the time it’s done feeding.

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The Moon’s orbit is now highly elliptical.

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The effects on the Solar system
are awesome—

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in the Biblical sense of awesome,
which means terrifying.

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Tidal forces from the black hole would
probably disrupt the near-Earth asteroids,

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maybe even parts of the asteroid belt,

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sending rocks careening
through the Solar system.

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Bombardment and impacts
may become commonplace

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for the next few million years.

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The planets are slightly perturbed, but
stay approximately in the same orbit.

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The black hole we used
to call Earth will now

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continue on orbiting
the Sun in the Earth’s place.

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In this case, you also die.

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This bonus video was made possible
by your contributions on Patreon.

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Thank you so much for your support!

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The topic is based on a question on
the AskScience subreddit

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and the glorious answer by Matt [Caplin?],
who also worked with us on this video.

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Check out his blog, Quarks and Coffee,
for more awesome stuff like this!

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If you want to discuss the video,
we have our own subreddit now.

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To learn more about black holes or equally
interesting neutron stars, click here.

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Subtitles by the Amara.org community

Event horizon of a black hole

a supermassive black hole with millions to billions times the mass of our sun
One of the best-known examples of an event horizon derives from general relativity’s description of a black hole, a celestial object so massive that no nearby matter or radiation can escape its gravitational field. Often, this is described as the boundary within which the black hole’s escape velocity is greater than the speed of light. However, a more accurate description is that within this horizon, all lightlike paths (paths that light could take) and hence all paths in the forward light cones of particles within the horizon, are warped so as to fall farther into the hole. Once a particle is inside the horizon, moving into the hole is as inevitable as moving forward in time, and can actually be thought of as equivalent to doing so, depending on the spacetime coordinate system used.

The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body that fits inside this radius (although a rotating black hole operates slightly differently). The Schwarzschild radius of an object is proportional to its mass. Theoretically, any amount of matter will become a black hole if compressed into a space that fits within its corresponding Schwarzschild radius. For the mass of the Sun this radius is approximately 3 kilometers and for the Earth, it is about 9 millimeters. In practice, however, neither the Earth nor the Sun has the necessary mass and therefore the necessary gravitational force, to overcome electron and neutron degeneracy pressure. The minimal mass required for a star to be able to collapse beyond these pressures is the Tolman-Oppenheimer-Volkoff limit, which is approximately three solar masses.

Black hole event horizons are widely misunderstood. Common, although erroneous, is the notion that black holes “vacuum up” material in their neighborhood, where in fact they are no more capable of “seeking out” material to consume than any other gravitational attractor. As with any mass in the Universe, matter must come within its gravitational scope for the possibility to exist of capture or consolidation with any other mass. Equally common is the idea that matter can be observed “falling into” a black hole. This is not possible. Astronomers can only detect accretion disks around black holes, where material moves with such speed that friction creates high-energy radiation which can be detected (similarly, some matter from these accretion disks is forced out along the axes of spin of the black hole, creating visible jets when these streams interact with matter such as interstellar gas or when they happen to be aimed directly at Earth). Furthermore, a distant observer will never actually see something cross the horizon. Instead, while approaching the hole, the object will seem to go ever more slowly, while any light it emits will be further and further redshifted.

Super Massive Blackholes

A supermassive black hole (SMBH) is the largest type of black hole, on the order of hundreds of thousands to billions of solar masses (M☉), and is found in the center of almost all massive galaxies. In the case of the Milky Way, the SMBH corresponds with the location of Sagittarius A.

Ion Ring Blackhole
Side view of black hole with transparent toroidal ring of ionised matter according to a proposed model for Sgr A. This image shows result of bending of light from behind the black hole, and it also shows the asymmetry arising by the Doppler effect from the extremely high orbital speed of the matter in the ring.

Supermassive black holes have properties that distinguish them from lower-mass classifications.

First, the average density of a supermassive black hole (defined as the mass of the black hole divided by the volume within its Schwarzschild radius) can be less than the density of water in the case of some supermassive black holes. This is because the Schwarzschild radius is directly proportional to mass, while density is inversely proportional to the volume. Since the volume of a spherical object (such as the event horizon of a non-rotating black hole) is directly proportional to the cube of the radius, the minimum density of a black hole is inversely proportional to the square of the mass, and thus higher mass black holes have lower average density. In addition, the tidal forces in the vicinity of the event horizon are significantly weaker for massive black holes.

As with density, the tidal force on a body at the event horizon is inversely proportional to the square of the mass: a person on the surface of the Earth and one at the event horizon of a 10 million M☉ black hole experience about the same tidal force between their head and feet. Unlike with stellar mass black holes, one would not experience significant tidal force until very deep into the black hole.


Black Holes Explained


Black Holes Explained

https://youtu.be/e-P5IFTqB98


Transcript

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Black holes are one of the strangest things in existence.

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They don’t seem to make any sense at all.

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Where do they come from…

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…and what happens if you fall into one?

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Stars are incredibly massive collections of mostly hydrogen atoms

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that collapsed from enormous gas cloud under their own gravity.

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In their core, nuclear fusion crushes hydrogen atoms into helium

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releasing a tremendous amount of energy

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This energy, in the form of radiation,

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pushes against gravity,

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maintaining a delicate balance between the two forces.

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As long as there is fusion in the core,

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a star remains stable enough.

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But for stars with way more mass then our own sun

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the heat and pressure at the core allow them to fuse heavier elements

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until they reach iron.

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Unlike all the elements that went before,

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the fusion process that creates iron

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doesn’t generate any energy.

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Iron builds up at the center of the star

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until it reaches a critical amount

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and the balance between radiation and gravity is suddenly broken.

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The core collapses.

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Within a fraction of a second,

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the star implodes.

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Moving at about the quarter of the speed of light,

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feeding even more mass into the core.

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It’s at this very moment that all the heavier elements in the universe are created,

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as the star dies, in a super nova explosion.

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This produces either a neutron star,

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or if the star is massive enough,

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the entire mass of the core collapses into a black hole.

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If you looked at a black hole,

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what you’d really be seeing is the event horizon.

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Anything that crosses the event horizon

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needs to be travelling faster than the speed of light to escape.

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In other words, its impossible.

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So we just see a black sphere

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reflecting nothing.

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But if the event horizon is the black part,

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what is the “hole” part of the black hole?

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The singularity.

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We’re not sure what it is exactly.

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A singularity may be indefinitely dense,

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meaning all its mass is concentrated into a single point in space,

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with no surface or volume,

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or something completely different.

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Right now, we just don’t know.

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its like a “dividing by zero”error.

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By the way, black holes do not suck things up like a vacuum cleaner,

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If we were to swap the sun for an equally massive black hole,

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nothing much would change for earth,

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except that we would freeze to death, of course.

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what would happen to you if you fell into a black hole?

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The experience of time is different around black holes,

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from the outside,

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you seem to slow down as you approach the event horizon,

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so time passes slower for you.

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at some point, you would appear to freeze in time,

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slowly turn red,

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and disapear.

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While from your perspective,

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you can watch the rest of the universe in fast forward,

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kind of like seeing into the future.

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Right now, we don’t know what happens next,

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but we think it could be one of two things:

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One, you die a quick death.

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A black hole curves space so much,

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that once you cross the event horizon,

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there is only one possible direction.

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you can take this – literally – inside the event horizon,

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you can only go in one direction.

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Its like being in a really tight alley that closes behind you after each step.

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The mass of a black hole is so concentrated,

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at some point even tiny distances of a few centimeters,

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would means that gravity acts with millions of times more force on different parts of your body.

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Your cells get torn apart,

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as your body stretches more and more,

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until you are a hot stream of plasma,

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one atom wide.

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Two, you die a very quick death.

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Very soon after you cross the event horizon,

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you would hit a firewall and be terminated in an instant.

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Neither of these options are particularly pleasant.

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How soon you would die depends on the mass of the black hole.

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A smaller black hole would kill you before you even enter its event horizon,

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while you probably could travel inside a super size massive black hole for quite a while.

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As a rule of thumb,

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the further away from the singularity you are,

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the longer you live.

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Black holes come in different sizes.

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There are stellar mass black holes,

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with a few times the mass of sun,

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and the diameter of an asteroid.

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And then there are the super massive black holes,

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which are found at the heart of every galaxy,

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and have been feeding for billions of years.

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Currently, the largest super massive black hole known,

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is S5 0014+81.

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40 billion times the mass of our sun.

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It is 236.7 billion kilometers in diameter,

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which is 47 times the distance from the sun to Pluto.

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As powerful as black holes are,

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they will eventually evaporate through a process called Hawking radiation.

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To understand how this works,

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we have to look at empty space.

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Empty space is not really empty,

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but filled with virtual particles popping into existence

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and annihilating each other again.

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When this happens right on the edge of a black hole,

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one of the virtual particles will be drawn into the black hole,

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and the other will escape and become a real particle.

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So the black hole is losing energy.

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This happens incredibly slowly at first,

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and gets faster as the black hole becomes smaller.

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When it arrives at the mass of a large asteroid,

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its radiating at room temperature.

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When it has the mass of a mountain,

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it radiates with about the heat of our sun.

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and in the last second of its life,

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the black hole radiates away with the energy of billions of nuclear bombs in a huge explosion.

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But this process is incredibly slow,

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The biggest black holes we know,

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might take up a googol year to evaporate.

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This is so long that when the last black hole radiates away,

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nobody will be around to witness it.

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The universe will have become uninhabitable,

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long before then.

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This is not the end of our story,

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there are loads more interesting ideas about black holes,

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we’ll explore them in part 2.

Schwarzschild radius

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light. An example of an object where the mass is within its Schwarzschild radius is a black hole. Once a stellar remnant collapses to or below this radius, light cannot escape and the object is no longer directly visible outside, thereby forming a black hole. It is a characteristic radius associated with every quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916.

The Schwarzschild radius is given as

{\displaystyle r_{s}={\frac {2GM}{c^{2}}}}

where G is the gravitational constant, M is the object mass and c is the speed of light.