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John Titor's Legacy
Titor's Donut Shaped Singularity
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<blockquote data-quote="Martian" data-source="post: 126883" data-attributes="member: 6511"><p>I'm not an expert on black holes, but it seems to me that they needn't be small, at least not when they're first formed. Also, they don't even need to be dense at first, if there's enough matter. The escape velocity is determined by equating kinetic energy to gravitational energy and solving for velocity:</p><p></p><p>½mv² = GMm/r</p><p>½v² = GM/r</p><p>v = sqr(2GM/r)</p><p></p><p>Then assume the escape velocity is the speed of light:</p><p></p><p>v = c = sqr(2GM/r)</p><p></p><p>We can then find the Schwarzschild radius by solving for r:</p><p></p><p>r = 2GM/c²</p><p></p><p>Next assume that we have a giant, homogeneous sphere of density p. We can define it as:</p><p></p><p>p = M/V</p><p></p><p>where the volume V is defined as:</p><p></p><p>V = (4/3)*pi*r³</p><p></p><p>If we choose a value for p, we can then solve for the radius at which it forms an event horizon. This would be a sphere that just barely forms a black hole.</p><p></p><p>p = M / ((4/3)*pi*r³)</p><p>M = ½rc²/G</p><p>p = ½rc² / ((4/3)*G*pi*r³)</p><p>p = (3/8)c² / (G*pi*r²)</p><p>r² = (3/8)c² / (p*G*pi)</p><p>r = sqr((3/8)c² / (p*G*pi))</p><p></p><p>It comes out to a huge number, but it's not infinite for any nonzero density. It makes me wonder how much interstellar hydrogen, etc, is required for a black hole to spontaneously form.</p><p></p><p>*shrug* I'm bored. lol</p></blockquote><p></p>
[QUOTE="Martian, post: 126883, member: 6511"] I'm not an expert on black holes, but it seems to me that they needn't be small, at least not when they're first formed. Also, they don't even need to be dense at first, if there's enough matter. The escape velocity is determined by equating kinetic energy to gravitational energy and solving for velocity: ½mv² = GMm/r ½v² = GM/r v = sqr(2GM/r) Then assume the escape velocity is the speed of light: v = c = sqr(2GM/r) We can then find the Schwarzschild radius by solving for r: r = 2GM/c² Next assume that we have a giant, homogeneous sphere of density p. We can define it as: p = M/V where the volume V is defined as: V = (4/3)*pi*r³ If we choose a value for p, we can then solve for the radius at which it forms an event horizon. This would be a sphere that just barely forms a black hole. p = M / ((4/3)*pi*r³) M = ½rc²/G p = ½rc² / ((4/3)*G*pi*r³) p = (3/8)c² / (G*pi*r²) r² = (3/8)c² / (p*G*pi) r = sqr((3/8)c² / (p*G*pi)) It comes out to a huge number, but it's not infinite for any nonzero density. It makes me wonder how much interstellar hydrogen, etc, is required for a black hole to spontaneously form. *shrug* I'm bored. lol [/QUOTE]
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Titor's Donut Shaped Singularity
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