Black Hole Temperature Calculator
Calculate Hawking temperature and black hole properties using mass-temperature relationship
Calculate Black Hole Temperature
Mass of the black hole to calculate Hawking temperature
Black Hole Properties
Hawking Temperature
Black Hole Mass
Hawking Formula: T = ℏc³/(8πGMkB)
Schwarzschild Radius: Rs = 2GM/c²
Evaporation Time: ~0.00e+0 seconds
Temperature Analysis
Example Calculation
Stellar Mass Black Hole
Mass: 10 solar masses (1.99 × 10³¹ kg)
Constants:
• ℏ = 1.055 × 10⁻³⁴ J⋅s
• c = 2.998 × 10⁸ m/s
• G = 6.674 × 10⁻¹¹ N⋅m²/kg²
• kB = 1.381 × 10⁻²³ J/K
Calculation
T = ℏc³/(8πGMkB)
T = (1.055×10⁻³⁴)(2.998×10⁸)³ / [8π(6.674×10⁻¹¹)(1.99×10³¹)(1.381×10⁻²³)]
T ≈ 6.17 × 10⁻⁹ K
Schwarzschild radius ≈ 29.5 km
Black Hole Scale Comparison
Micro Black Holes
Mass < 1 kg
Extremely hot, evaporate instantly
Stellar Mass
3-100 solar masses
From massive star collapse
Supermassive
10⁶-10¹⁰ solar masses
Galaxy centers, very cold
Hawking Radiation Insights
Smaller black holes are paradoxically hotter
All black holes eventually evaporate via Hawking radiation
Temperature is inversely proportional to mass
Virtual particle pairs at event horizon create radiation
Understanding Black Hole Temperature and Hawking Radiation
What is Hawking Temperature?
Hawking temperature is the temperature of thermal radiation emitted by a black hole due to quantum effects near its event horizon. This phenomenon, predicted by Stephen Hawking, shows that black holes are not completely black but emit thermal radiation.
The Hawking Radiation Process
- •Virtual particle pairs appear near the event horizon
- •One particle falls into the black hole, other escapes
- •Escaping particles form thermal radiation
- •Black hole gradually loses mass and energy
The Temperature-Mass Relationship
T = ℏc³/(8πGMkB)
- T: Hawking temperature (K)
- ℏ: Reduced Planck constant
- c: Speed of light
- G: Gravitational constant
- M: Black hole mass
- kB: Boltzmann constant
Key Insight: Temperature is inversely proportional to mass - more massive black holes are colder!
Fascinating Consequences
Black Hole Evaporation
As black holes emit Hawking radiation, they lose mass and become hotter, leading to faster evaporation in a runaway process.
Information Paradox
Hawking radiation appears thermal and random, raising questions about what happens to information that falls into black holes.
Cosmological Impact
Current black holes are colder than cosmic background radiation, so they actually absorb more energy than they emit.