Calculator Inputs
Large screens show three columns, smaller screens collapse automatically.Example Data Table
| Example | Model | Mass | a* | q* | Temperature | r+ |
|---|---|---|---|---|---|---|
| Primordial-scale example | Schwarzschild | 1.000000e+11 kg | 0 | 0 | 1.226901e+12 K | 1.485232e-16 m |
| Lunar-mass charged case | Reissner Nordstrom | 1 M☾ | 0 | 0.35 | 1.668 K | 0.000106 m |
| Solar-mass rotating case | Kerr | 1 M☉ | 0.8 | 0 | 4.627555e-8 K | 2,362.671506 m |
| Ten-solar baseline | Schwarzschild | 10 M☉ | 0 | 0 | 6.170074e-9 K | 29,533.393821 m |
| Supermassive combined case | Kerr Newman | 1.000000e+6 M☉ | 0.4 | 0.3 | 5.868606e-14 K | 2.755503e+9 m |
Formula Used
For a non-rotating, uncharged black hole, the calculator uses the Hawking temperature equation:
TS = ħc3 / (8πGMkB)
For Kerr, Reissner-Nordström, and Kerr-Newman cases, the calculator applies a surface-gravity correction using normalized spin and charge:
Δ = √(1 - a*² - q*²)
T = TS × [4Δ / ((1 + Δ)² + a*²)]
The event horizon radius is evaluated as r+ = (GM/c²)(1 + Δ), and the inner horizon radius is r− = (GM/c²)(1 - Δ).
How to Use This Calculator
- Enter the black hole mass and select the most useful unit.
- Choose the physical model that matches your scenario.
- For rotating cases, enter the dimensionless spin parameter a*.
- For charged cases, enter q* directly or switch to coulombs.
- Click the calculate button to show results above the form.
- Review the metric cards, graph, and example table for context.
- Use the CSV or PDF buttons to export your result summary.
- Keep a*² + q*² less than or equal to 1.
FAQs
1. What is black hole temperature?
It is the theoretical temperature associated with Hawking radiation. The value describes the thermal spectrum expected from quantum effects near the event horizon.
2. Why do smaller black holes run hotter?
The Hawking temperature varies inversely with mass for the Schwarzschild case. As mass decreases, the calculated temperature rises sharply.
3. How does spin change the result?
Spin lowers the temperature because it changes the horizon structure and surface gravity. As a rotating black hole approaches its extremal limit, temperature approaches zero.
4. How does charge affect temperature?
Electric charge also reduces surface gravity and therefore reduces Hawking temperature. Stronger normalized charge q* pushes the result downward and can reach zero at the extremal limit.
5. What is the extremal limit?
It is the boundary where a*² + q*² equals 1. At that limit, the inner and outer horizons merge and the Hawking temperature becomes zero.
6. Why are stellar black hole temperatures tiny?
Astrophysical black holes carry enormous mass, and the temperature formula scales downward with increasing mass. That makes the predicted temperature extremely small in kelvin.
7. Can this tool confirm observed Hawking radiation?
No. This is a theoretical calculator based on standard equations. It helps compare scenarios, but it does not prove direct observational detection.
8. Which model should I choose?
Choose Schwarzschild for a neutral, non-rotating case. Use Kerr for rotation, Reissner-Nordström for charge, and Kerr-Newman when both spin and charge matter.