1. What is the Black Hole Temperature Equation?

The Hawking temperature equation describes the thermal radiation emitted by black holes due to quantum effects near the event horizon. This temperature is inversely proportional to the black hole's mass.

2. How Does the Calculator Work?

The calculator uses the Hawking temperature equation:

Where:

• \( \hbar \) — Reduced Planck constant (J·s)
• \( c \) — Speed of light (m/s)
• \( G \) — Gravitational constant (m³/kg·s²)
• \( M \) — Black hole mass (kg)
• \( k_B \) — Boltzmann constant (J/K)
• \( T \) — Temperature (K)

Explanation: The equation shows that smaller black holes are hotter and emit more radiation than larger ones.

3. Importance of Black Hole Temperature

Details: Hawking radiation is crucial for understanding black hole thermodynamics, information paradox, and the ultimate fate of black holes.

4. Using the Calculator

Tips: Default values are provided for fundamental constants. Enter the black hole mass in kilograms for temperature calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why do black holes have temperature?
A: Due to quantum effects near the event horizon, black holes emit thermal radiation (Hawking radiation) with a characteristic temperature.

Q2: What's the temperature of a solar mass black hole?
A: About 6×10⁻⁸ K - much colder than cosmic microwave background radiation.

Q3: Can we detect Hawking radiation?
A: Not yet for astrophysical black holes, but analog black holes in labs may allow observation.

Q4: What happens as black holes lose mass?
A: They get hotter and evaporate faster, with the final stages being explosive.

Q5: How accurate is this calculation?
A: It's theoretically sound but assumes a non-rotating, uncharged black hole (Schwarzschild solution).