Of all the weirdnesses about black holes, this one is the weirdest to me.
As you might expect, the event horizon of a black hole gets bigger as the mass gets bigger. That’s because if you add mass, the gravity gets stronger, which means the event horizon will grow.
If you do the math carefully, you find that the event horizon grows linearly with the mass. In other words, if you double the black hole’s mass, the event horizon radius doubles as well.
That’s weird! Why?
The volume of a sphere depends on the cube of the radius (think way back to high school: volume = 4/3 x π x radius3). Double the radius, and the volume goes up by 2 x 2 x 2 = 8 times. Make the radius of a sphere 10 times bigger and the volume goes up by a factor of 10 x 10 x 10 = 1000.
So volume goes up really quickly as you increase the size of a sphere.
Now imagine you have two spheres of clay that are the same size. Lump them together. Is the resulting sphere twice as big?
No! You’ve doubled the mass, but the radius only increases a little bit. Because volume goes as radius cubed, to double the radius of your final clay ball, you’d need to lump together eight of them.
But that’s different than a black hole. Double the mass, double the size of the event horizon. That has an odd implication…
Density is how much mass is packed into a given volume. Keep the size the same and add mass, and the density goes up. Increase the volume, but keep the mass the same, and the density goes down. Got it?
So now let’s look at the average density of matter inside the event horizon of the black hole. If I take two identical black holes and collide them, the event horizon size doubles, and the mass doubles too. But volume has gone up by eight times! So the density actually decreases, and is 1/4 what I started with (twice the mass and eight times the volume gives you 1/4 the density). Keep doing that, and the density decreases.
A regular black hole — that is, one with three times the Sun’s mass — with have an event horizon radius of about 9 km. That means it has a huge density, about two quadrillion grams per cubic cm (2 x 1015). But double the mass, and the density drops by a factor of four. Put in 10 times the mass and the density drops by a factor of 100. A billion solar mass black hole (big, but we see them this big in galaxy centers) would drop that density by a factor of 1 x 1018. That would give it a density of roughly 1/1000 of a gram per cc… and that’s the density of air!
A billion solar mass black hole would have an event horizon 3 billion km in radius — roughly the distance of Neptune to the Sun.
See where I’m going here? If you were to rope off the solar system out past Neptune, enclose it in a giant sphere, and fill it with air, it would be a black hole!
Royal Bank of Scotland, which is being bailed out with £20bn of taxpayers’ money, has signalled it is preparing to pay bonuses to thousands of staff despite government pledges to crack down on City pay.
The bank has set aside £1.79bn to cover “staff costs” – including discretionary bonuses – at its investment banking division for the first six months of the year alone. The same division caused a £5.9bn writedown that wiped out the bank’s profits for the same period.
ABC News’ Steven Portnoy reports: In a conservative radio interview that aired in Washington, D.C. Friday morning, Republican vice presidential nominee Gov. Sarah Palin said she fears her First Amendment rights may be threatened by “attacks” from reporters who suggest she is engaging in a negative campaign against Barack Obama.
“If [the media] convince enough voters that that is negative campaigning, for me to call Barack Obama out on his associations,” Palin told host Chris Plante, “then I don’t know what the future of our country would be in terms of First Amendment rights and our ability to ask questions without fear of attacks by the mainstream media.”
The Constitution also guarantees freedom of association. Thus, by Palin’s ”reasoning,” when newspapers — or Palin herself — criticize Obama for his associations, they’re threatening his constitutional rights.
Jonathan Schwarz has the audio of Palin, issuing her constitutional warning, here. It’s actually more painful to hear it than read it, because you can hear her thinking about the analysis she’s making as it leaves her mouth, and she clearly believes she’s actually making an important and profound point about First Amendment rights.
Maureen Dowd recently made an equally stupid comment when she complained that her First Amendment rights were being violated by the McCain campaign’s refusal to allow her on their campaign plane.
The First Amendment is actually not that complicated. It can be read from start to finish in about 10 seconds. It bars the Government from abridging free speech rights. It doesn’t have anything to do with whether you’re free to say things without being criticized, or whether you can comment on blogs without being edited, or whether people can bar you from their private planes because they don’t like what you’ve said.
If anything, Palin has this exactly backwards, since one thing that the First Amendment does actually guarantee is a free press. Thus, when the press criticizes a political candidate and a Governor such as Palin, that is a classic example of First Amendment rights being exercised, not abridged.
This isn’t only about profound ignorance regarding our basic liberties, though it is obviously that. Palin here is also giving voice to the standard right-wing grievance instinct: that it’s inherently unfair when they’re criticized. And now, apparently, it’s even unconstitutional.
University of Texas poll to be released today shows Republican presidential candidate John McCain and GOP Sen. John Cornyn leading by comfortable margins in Texas, as expected. But the statewide survey of 550 registered voters has one very surprising finding: 23 percent of Texans are convinced that Democratic presidential nominee Barack Obama is a Muslim.
The Texas numbers are unusual because most national polls show that just 5 to 10 percent of Americans still believe Obama is a Muslim — less than half the number of Texans who buy into the debunked theories.