From Eternity to Here

Think back to the checkerboards. What happened at one moment in time was influenced by what happened at the previous moment in time. But what happened at one point in “space”—the collection of squares across a single row—was completely unrelated to what happened at any other point in space at the same time

The arrow of time is driven by an increase in entropy, which ultimately originates in the low entropy near the Big Bang, which is a period in the universe’s history when gravity is fundamentally important. We therefore need to know how entropy works in the presence of gravity

The fact that black holes evaporate away raises a deep question: What happens to the information that went into making the hole in the first place?

The kinds of astrophysical black holes we’ve been talking about, with masses equal to or much greater than that of the Sun, have extremely low Hawking temperatures

An interesting feature of Hawking radiation is that smaller black holes are hotter.

Of course, the microwave background continues to cool down as the universe expands; so if we wait long enough, the black holes will be hotter than the surrounding universe, and begin to lose mass

Bekenstein used ideas from information theory to argue that the area of a black-hole event horizon isn’t just like the entropy; it is the entropy of the black hole

there is a minimum value for the surface gravity of a black hole—zero!—which is achieved when all of the black-hole energy comes from charge or spin, none from “mass all by itself.”

There is also a Third Law of Thermodynamics: There is a minimum possible temperature, absolute zero, at which the entropy is also a minimum

Once it has settled, there are three things that we can measure about a black hole: its total mass, how fast it is spinning, and how much electric charge it has.