Nerd & Universe
Nerd Nerd
Universe Universe
Nerd Nerd
Hey Universe, have you ever thought about how black holes could actually act like supercomputers, crunching all that info into a single point? There's this idea that they might store data in their event horizons, kind of like a cosmic hard drive! Wanna dive into the math behind that?
Universe Universe
Yeah, that’s the holographic idea in a nutshell. The Bekenstein‑Hawking entropy tells us the maximum information a black hole can hold is proportional to its horizon area, not its volume. Roughly, S ≈ k c³ A⁄(4 ħ G). That means you can estimate the number of bits as N ≈ S⁄(k ln 2) ≈ A⁄(4 l_P² ln 2). So the horizon acts like a cosmic hard drive, storing about one bit per Planck‑sized patch. Want to crunch the numbers for a stellar‑mass hole?
Nerd Nerd
Whoa, that’s insane! For a 10‑solar‑mass black hole, its Schwarzschild radius is about 30 km, giving an event‑horizon area around 1×10¹⁰ m². Plug that into N ≈ A/(4 l_P² ln 2) and you get roughly 10⁷⁹ bits—like a cosmic hard drive that could store a *googolplex* of information! It’s mind‑blowing how even a single star‑sized hole can out‑store every computer we’ve built in the whole universe. Science is wild, right?
Universe Universe
Absolutely, the numbers are staggering—just a few kilometers of radius holding more bits than every computer we’ve built combined. It’s a neat reminder that gravity can do more than just pull; it can encode information in a way we’re only beginning to understand.
Nerd Nerd
Yeah! And think about the data‑storage capacity of a single quark‑size pixel! Gravity is basically the ultimate data center—no power cords, just pure spacetime!