The Hawking Radiation Formula
The lifetime of a black hole is determined by a process called Hawking radiation. This theoretical process describes how black holes can slowly evaporate due to quantum effects at their event horizon.
The formula for the lifetime of a black hole is:
t = (5120πG²M³)/(hc⁴)
Where:
* t is the lifetime in seconds
* G is the gravitational constant (6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²)
* M is the mass of the black hole (in kilograms)
* h is Planck's constant (6.626 × 10⁻³⁴ Js)
* c is the speed of light (2.998 × 10⁸ m/s)
The Problem with Solar Mass Black Holes
Let's plug in the mass of the Sun (M = 1.989 × 10³⁰ kg) into the formula. You'll find that the resulting lifetime is incredibly long – on the order of 10⁶⁷ years. This is far longer than the current age of the universe!
Key Takeaway
While the formula is correct, it highlights that solar-mass black holes are practically "eternal" on our timescale. They evaporate so slowly that it's not something we'd ever observe.
Important Note: The Hawking radiation formula is still theoretical. Although it has strong support within quantum field theory, we haven't directly observed Hawking radiation from black holes.
Black Holes and Their Lifespans
* Small black holes: Black holes with very small masses, possibly created in the early universe, would have much shorter lifespans.
* Supermassive black holes: These are the behemoths at the centers of galaxies. They have lifetimes that far exceed the age of the universe.
The Bottom Line: While the formula is powerful, it's important to understand the context. For solar-mass black holes, the concept of "lifetime" is essentially meaningless for practical purposes.
