Kugelblitz Black Hole Calculator

Calculate the mass, Hawking radiation power, temperature, and lifetime of a black hole from its event horizon radius.

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1 × 10-15 m = 1 femtometer (nuclear scale)
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Energy Equivalent
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What is a Kugelblitz?

A Kugelblitz (German for "ball lightning") is a theoretical black hole formed entirely from concentrated radiation rather than collapsing matter. If enough photons are focused into a sufficiently small volume, Einstein's mass-energy equivalence (E=mc²) means the energy density itself creates an event horizon. The result is a black hole indistinguishable from one formed by matter collapse.

Hawking Radiation

In 1974, Stephen Hawking predicted that black holes are not truly black. Quantum effects near the event horizon cause particle-antiparticle pairs to appear, with one particle escaping as radiation. The formulas governing this emission are:

Mass: M = rc² / (2G)

Temperature: T = ℏc³ / (8πGMkB)

Power: P = ℏc6 / (15360πG²M²)

Lifetime: t ≈ 5120πG²M³ / (ℏc4)

Kugelblitz as an Interstellar Engine

A micro black hole with a carefully chosen mass could serve as an interstellar propulsion system. A black hole with a radius of about 1 attometer (10-18 m) would have a mass of about 674 million tonnes and produce petawatts of Hawking radiation. By partially confining this radiation with a parabolic reflector, the black hole becomes a photon engine with fuel that literally is the engine itself.

The Inverse Relationship

The key insight is that smaller black holes are hotter and more powerful. A stellar-mass black hole has a temperature near absolute zero and effectively zero Hawking radiation. But shrink the event horizon to subatomic scales, and the temperature soars to trillions of kelvin with enormous power output. This inverse scaling makes micro black holes theoretically useful as energy sources.

Practical Challenges

Creating a Kugelblitz would require focusing more energy into a point than humanity currently produces. Maintaining one requires continuously feeding it mass to prevent evaporation. And containing the intensely energetic Hawking radiation without destroying the spacecraft is an unsolved engineering challenge.

Frequently Asked Questions

A Kugelblitz is a theoretical black hole formed from concentrated light energy rather than collapsing matter. If enough photons are focused into a small enough volume, the energy density creates an event horizon through Einstein's E=mc².
Hawking radiation is the theoretical emission of particles from near a black hole's event horizon. Quantum effects create particle pairs, with one escaping as radiation. Smaller black holes radiate more intensely at higher temperatures.
Theoretically, yes. An attometer-scale Kugelblitz would produce petawatts of Hawking radiation that could be focused as thrust. The challenge is creating and feeding such a black hole, requiring immense energy focused into a subatomic volume.
Lifetime depends on the cube of the mass. A mountain-mass black hole (~10¹² kg) lasts far longer than the age of the universe. A car-mass black hole evaporates in seconds in a burst of gamma radiation.
The Schwarzschild radius is the event horizon radius for a non-rotating black hole: r = 2GM/c². For the Sun it is ~3 km, for Earth ~9 mm. Any mass compressed below this radius becomes a black hole.