1. What is the Black Hole Lifetime Equation?

The black hole lifetime equation estimates how long a black hole of given mass would take to completely evaporate via Hawking radiation. This is based on quantum field theory in curved spacetime.

2. How Does the Calculator Work?

The calculator uses the black hole lifetime equation:

Where:

• \( t \) — Black hole lifetime (seconds)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
• \( M \) — Black hole mass (kg)
• \( \hbar \) — Reduced Planck constant (1.055 × 10⁻³⁴ J·s)
• \( c \) — Speed of light (299,792,458 m/s)

Explanation: The equation shows that more massive black holes have much longer lifetimes (∝ M³). A solar mass black hole would take about 10⁶⁷ years to evaporate.

3. Importance of Black Hole Lifetime Calculation

Details: Understanding black hole lifetimes is crucial for studying quantum gravity, information paradox, and the ultimate fate of black holes in the universe.

4. Using the Calculator

Tips: Enter the black hole mass in kilograms. The result will be the theoretical lifetime in seconds until complete evaporation via Hawking radiation.

5. Frequently Asked Questions (FAQ)

Q1: What is Hawking radiation?
A: Quantum effect where black holes emit thermal radiation, causing them to lose mass over time.

Q2: How accurate is this calculation?
A: It's a theoretical estimate assuming only Hawking radiation. Real black holes may accrete matter too.

Q3: What's the lifetime of a 1kg black hole?
A: About 8.41 × 10⁻¹⁷ seconds - they evaporate extremely quickly.

Q4: What happens at the end of a black hole's life?
A: As mass decreases, temperature increases, leading to a final explosive evaporation.

Q5: Has Hawking radiation been observed?
A: Not yet - it's too weak to detect from astrophysical black holes with current technology.