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Angelos Papadopoulos
Architecture,Astronomy,Science,Tech,and Art Lover! A Sci-Fi Geek Freak, who Loves to Laugh!CzechGreekCypriot,Politically Incorrect Atheist Leftist!Dreaming a Better World!
Architecture,Astronomy,Science,Tech,and Art Lover! A Sci-Fi Geek Freak, who Loves to Laugh!CzechGreekCypriot,Politically Incorrect Atheist Leftist!Dreaming a Better World!

Angelos's posts

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Do ripples in space-time herald a new theory of gravity? | Aeon Essays

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How many great minds does it take to invent a telescope? | Aeon Ideas

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There are people who spend their time yelling at the Mars Curiosity rover on Twitter | The Outline

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In search for unseen dark matter, physicists turn to shadow realm | Science | AAAS

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Interview with a Theoretical Physicist: Sabine Hossenfelder

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Black Hole Computers - Scientific American

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It's not easy to make a black hole.


The critical volume for a given mass, known as the Schwarzschild radius is pretty easy to calculate for a non-rotating black hole. It turns out to be R = 2GM/c2, where G is Newton’s gravitational constant, c is the speed of light, and M is the mass. Compress the mass into a sphere of that radius, and you get a black hole. At least that’s how the story is told. Technically, if you compress a mass into a sphere of that volume, then it already is a black hole. But is there a minimum volume you could reach so that the mass is fated to become a black hole? Do you have to actively squeeze the mass all the way to a black hole, or can you squeeze it to a point and let nature takes its course?

This turns out to be a very interesting question. If we simply compress a certain amount of matter into an ever smaller volume, the matter itself will try to push back. As matter is squeezed, it heats up, so eventually our matter would heat to the point of vaporizing, and the gas pressure would try to oppose us. Squeeze hard enough and the nuclei of the material will start fusing, which would heat the mass further and generate more pressure. Squeeze even harder and the matter will eventually reach a point where the electrons of the material are moving at nearly the speed of light, and the quantum pressure of electrons will push against you. This is what happens within a white dwarf star. But there’s a limit to how strongly electron pressure can push back, known as the Chandrasekhar limit. If we squeeze matter harder than that, the electrons and nuclei of the material will collapse together, forming a sea of neutrons.

Since fast moving neutrons occupy less space than fast moving electrons, for a time the mass gets easier to compress. But eventually the neutrons start approaching the speed of light, and push against each other in much the same way as the electrons did. This neutron pressure is what keeps neutron stars from collapsing on themselves. As with electrons, there’s a limit to how strongly neutrons can push back, known as the Tolman-Oppenheimer-Volkoff (TOV) limit. Squeeze the mass beyond that limit, and the neutrons will collapse into each other.

According to our current understanding of physics, beyond the TOV limit the matter will collapse into a black hole. The observed upper mass of neutron stars is about twice the mass of our Sun. Such neutron stars are about 20 kilometers in diameter, while the Schwarzschild radius for such a mass is about 6 kilometers. This would imply that if we squeezed mass into a radius about 1.7 times larger than the Schwarzschild radius, then it’s doomed to become a black hole.

But what if the TOV limit isn’t the last line of defense against a black hole? What if the quarks that make up protons and neutrons behave in ways we don’t expect at really high densities, or what if quarks are comprised of something even more fundamental, and they have an even stronger limit. It is possible that something could oppose our squeezing? Could such it create so much pressure that a black hole is impossible to form?

It turns out the answer is no, and the reason is because of relativity. One of the key aspects of relativity is that energy and mass are related. Mass can be converted into energy, and energy can be converted into mass. When matter generates pressure to oppose our squeezing, that pressure has a certain energy, and that energy has a gravitational weight just like mass. So the more strongly matter pushes against us, the more gravity helps us. This is a game of diminishing returns, and there is a point where no matter how strongly the mass opposes us, gravity is even stronger. This limit is known as the Buchdahl limit. If the mass is spherical and of uniform density, this limit is 9/8 times the Schwarzschild radius. Squeeze past that point, and nothing can oppose the eventual formation of a black hole. There are more general calculations that don’t assume uniform density, but the end result is similar. So it turns out we don’t have to squeeze a ball of mass all the way to its Schwarzschild radius to make a black hole. We just have to get within about 10% of the radius the mass will collapse into a black hole on its own.

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Spomenik Database | Explore the Spomenik of Yugoslavia

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Greek War of Independence Today 25. March 1821

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Physicist Fotini Markopoulou Left Theoretical Physics to Create Wearable Technology at Doppel
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