Kugelblitz Black Hole Calculator
Compute the Schwarzschild radius, mass, energy equivalent, Hawking temperature, radiation power, and evaporation lifetime of a black hole formed from concentrated electromagnetic energy.
Last reviewed: May 2026A kugelblitz — German for "ball lightning," borrowed by John Archibald Wheeler in the 1950s — is a black hole formed not from collapsed matter but from concentrated electromagnetic energy. This calculator applies the Schwarzschild solution (1916) and Hawking's 1974 evaporation formula to convert an event-horizon radius into the corresponding mass, total energy, surface temperature, radiation power, and lifetime. Enter a radius above; the sections below explain exactly how each figure is derived, why a kugelblitz is theoretically permitted by general relativity, and why nobody has ever come close to building one.
What This Calculator Does
Mapping a Radius to a Full Black-Hole Profile
The single input is the Schwarzschild radius rs — the radius of the event horizon, the boundary of no return. From that single number this tool derives six related quantities by inverting the standard general-relativistic formulas. Mass follows from the Schwarzschild relation M = rsc²/(2G). Energy follows from Einstein's mass-energy equivalence E = mc². Hawking temperature follows from Hawking's 1974 derivation T = ħc³/(8πGMkB). Radiation power follows from integrating the Hawking spectrum over the horizon area: P = ħc⁶/(15360πG²M²). Lifetime follows from integrating the power loss: t = 5120πG²M³/(ħc⁴). The mass-comparison line then places the result on a recognizable scale — from subatomic to planetary to galactic.
Why a Single-Input Tool Captures the Whole Object
Karl Schwarzschild's 1916 solution to Einstein's field equations contains a single free parameter: mass. The no-hair theorem (Israel 1967, Carter 1971, Robinson 1975, Hawking 1975) proved that a stationary, uncharged, non-rotating black hole in four-dimensional general relativity is completely specified by that one number. Charge and angular momentum can also appear (giving the Reissner-Nordström and Kerr solutions respectively), but a pure-Schwarzschild kugelblitz has only mass, and mass and horizon radius are interchangeable. This is why a one-input calculator can produce a complete external description of the object.
What "Kugelblitz" Adds Beyond a Generic Black Hole
The word "kugelblitz" emphasizes the formation history: the black hole was assembled from photons, gamma rays, or any other electromagnetic radiation rather than from baryonic matter. By the equivalence of mass and energy and the no-hair theorem, the resulting object is observationally identical to a Schwarzschild black hole of the same mass — but the engineering question (can radiation be concentrated densely enough?) is fundamentally different from the astrophysical question (can a star collapse?). The calculator's outputs apply to either origin; the distinction matters only for the formation discussion.
How to Use It
Step-by-Step Input Workflow
The horizon radius is entered as a scientific-notation pair: a coefficient between 0.001 and 9.999, and an exponent between −30 and 10. The product gives the radius in meters. So an entry of 1 × 10⁻¹⁵ m places the horizon at the proton-radius scale (one femtometer), while 1 × 10⁰ m places it at the meter scale, and 1 × 10³ m places it at the kilometer scale. Every input field updates results live as you type — no submit button, no page refresh. The shareable URL at the bottom encodes both inputs so you can bookmark a specific scenario and share it directly.
Calibration: Known Reference Points to Compare Against
Memorize a few benchmark values so the orders of magnitude become intuitive. Earth's Schwarzschild radius is approximately 8.87 mm (mass 5.972 × 10²⁴ kg compressed into a sphere smaller than a marble). The Sun's Schwarzschild radius is approximately 2,953 m or 2.95 km (mass 1.989 × 10³⁰ kg compressed into a sphere about the size of a small asteroid). Sagittarius A*, the supermassive black hole at the center of the Milky Way, has a Schwarzschild radius of about 1.2 × 10¹⁰ m — roughly 17 times the radius of the Sun, or about a tenth of an astronomical unit. M87*, photographed by the Event Horizon Telescope in 2019, has a Schwarzschild radius near 1.8 × 10¹³ m, about 120 AU. Enter each of these in the calculator to see how the lifetime and Hawking power scale across 16 orders of magnitude in radius.
Reading the Outputs
The primary output is mass in kilograms, displayed in scientific notation with a contextual comparison ("less than 1 kilogram — subatomic scale," "between a mountain and a planet," "X Earth masses"). The four secondary outputs — Hawking power in watts, Hawking temperature in kelvin, evaporation lifetime in seconds-to-years, and total energy equivalent in joules — populate as soon as you change either input. Lifetimes longer than 10¹² years are shown in scientific notation; anything shorter prints in human-readable units automatically.
Worked Example: An Aircraft-Carrier-Mass Kugelblitz
- Target mass
- 1 × 10⁸ kg (≈ 100,000 metric tons, comparable to a Nimitz-class aircraft carrier)
- Required energy (E = mc²)
- ≈ 8.99 × 10²⁴ J
- Schwarzschild radius
- ≈ 1.485 × 10⁻¹⁹ m
- Hawking temperature
- ≈ 1.23 × 10¹⁵ K
- Hawking radiation power
- ≈ 3.56 × 10¹² W
- Evaporation lifetime
- ≈ 8.4 × 10¹² s (~266,000 years)
Step 1 — Establish the Energy Budget
To create a kugelblitz with the mass of a Nimitz-class aircraft carrier (M ≈ 10⁸ kg), Einstein's relation E = mc² fixes the total energy required: E = 10⁸ × (2.998 × 10⁸)² ≈ 8.99 × 10²⁴ J. For context, that is roughly two billion megatons of TNT-equivalent — about four million times the total yield of every nuclear weapon ever detonated by humanity (the cumulative test-and-deployment total since 1945 is on the order of 540 megatons, dominated by the Tsar Bomba and Cold War atmospheric tests). The Sun radiates this much energy in approximately 23 milliseconds, but no Earthbound process can concentrate that energy into a sub-nanometer volume.
Step 2 — Compute the Schwarzschild Radius
Apply rs = 2GM/c² with G = 6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻² and c = 2.998 × 10⁸ m/s: rs = (2 × 6.6743 × 10⁻¹¹ × 10⁸) / (8.988 × 10¹⁶) ≈ 1.485 × 10⁻¹⁹ m. That is about 0.0001 femtometers — roughly 10,000 times smaller than a proton. A 100,000-tonne aircraft carrier, compressed to this density, would fit inside a volume billions of times smaller than a hydrogen atom's nucleus.
Step 3 — Compute the Hawking Temperature and Power
Hawking temperature TH = ħc³/(8πGMkB) = (1.055 × 10⁻³⁴ × 2.694 × 10²⁵)/(8π × 6.6743 × 10⁻¹¹ × 10⁸ × 1.381 × 10⁻²³) ≈ 1.23 × 10¹⁵ K — about a billion times hotter than the core of the Sun and well above the QCD phase-transition temperature. Hawking power P = ħc⁶/(15360πG²M²) ≈ 3.56 × 10¹⁶ W — about 1,900 times humanity's total primary-energy consumption rate of roughly 1.9 × 10¹³ W. The kugelblitz radiates this power almost entirely as gamma rays.
Step 4 — Compute the Evaporation Lifetime
Lifetime t = 5120πG²M³/(ħc⁴) = (5120π × (6.6743 × 10⁻¹¹)² × 10²⁴)/(1.055 × 10⁻³⁴ × 8.078 × 10³³) ≈ 8.4 × 10⁷ s ≈ 2.7 years. A 100,000-tonne kugelblitz is therefore astrophysically fleeting — it evaporates entirely in under three years. For comparison, a one-kilogram kugelblitz evaporates in about 8.4 × 10⁻¹⁷ s (faster than a chemical bond vibration), while a solar-mass kugelblitz evaporates in about 2 × 10⁶⁷ years (roughly 10⁵⁷ times the current age of the universe). The lifetime scales as M³, so each order of magnitude in mass adds three orders of magnitude to the lifetime.
Physics Background: Why a Kugelblitz Can Exist in Principle
Energy as a Source of Spacetime Curvature
Einstein's field equations, Gμν + Λgμν = (8πG/c⁴) Tμν, relate the curvature of spacetime (left-hand side) to the stress-energy tensor Tμν (right-hand side). The stress-energy tensor includes mass-energy density, momentum density, pressure, and shear stress — and crucially, it makes no distinction between rest-mass energy and electromagnetic field energy. Photons carry energy E = hν and momentum p = E/c; their energy density contributes to Tμν on equal footing with the rest-mass energy density of matter. This means any sufficiently concentrated bundle of radiation has the same gravitational effect as the same total energy in matter form. The first observational confirmation that gravity affects light was Arthur Eddington's 1919 eclipse expedition, which measured the deflection of starlight grazing the Sun and confirmed Einstein's prediction to within ~30% — establishing that gravity couples to all forms of energy, not just rest mass.
The Schwarzschild Radius Formula
In 1916, while serving on the Russian Front during World War I, Karl Schwarzschild derived the first exact solution to Einstein's field equations for the vacuum surrounding a spherically symmetric, non-rotating mass. The metric contains a coordinate singularity at rs = 2GM/c², now called the Schwarzschild radius. For any spherically symmetric mass M compressed within that radius, the escape velocity at the surface equals or exceeds the speed of light — no signal, no particle, and no photon can ever escape. Schwarzschild died of pemphigus in May 1916 at age 42, four months after submitting the paper. His son Martin Schwarzschild went on to become a major figure in 20th-century stellar astrophysics.
Wheeler's Geon and the Origin of "Kugelblitz"
In 1955 John Archibald Wheeler published "Geons" (Physical Review 97, 511), proposing that a sufficiently concentrated bundle of electromagnetic waves could be held together by its own gravitational self-attraction long enough to behave as a quasi-stable particle. Wheeler's geon was a precursor to the full kugelblitz idea: a stable geon does not have an event horizon, but it sits on the spectrum of gravitationally self-bound radiation configurations. When the radiation density exceeds the horizon-formation threshold, the geon collapses into a true kugelblitz black hole. Wheeler borrowed the German term "kugelblitz" (literally "ball lightning") to describe such an object — the same Wheeler who later coined "black hole" itself in a 1967 lecture.
The Engineering Wall: ~10²⁶ W/m² and the Schwinger Limit
The intensity required to form a kugelblitz scales as M⁻². For a kugelblitz the size of a proton, you need approximately 10²⁶ W/m² focused into a femtometer-scale volume. The most powerful laser ever built — the National Ignition Facility's 192-beam ultraviolet pulse delivering 1.8 MJ in a few nanoseconds — reaches peak intensity around 10²² W/cm², roughly 24 orders of magnitude short. The proposed Extreme Light Infrastructure exawatt-class facility might reach 10²⁵ W/cm², still 13 orders of magnitude short. Worse, at intensities above the Schwinger limit (~1.3 × 10²⁹ W/cm² in vacuum), the electromagnetic field spontaneously pair-produces electron-positron pairs from the QED vacuum, draining the focused field before the gravitational threshold is reached. A 2024 paper in Physical Review D by Álvarez-Domínguez and collaborators argued this Schwinger mechanism may make pure-photon kugelblitz formation fundamentally forbidden — the field would dissipate as matter before it could collapse into a horizon.
| Reference object | Mass (kg) | Schwarzschild radius | Hawking temperature | Hawking power | Evaporation lifetime |
|---|---|---|---|---|---|
| Proton-mass | 1.67 × 10⁻²⁷ | 2.48 × 10⁻⁵⁴ m | 7.3 × 10⁴⁹ K | 1.3 × 10⁹⁰ W | 4.0 × 10⁻¹⁰⁰ s |
| 1 kilogram | 1.0 × 10⁰ | 1.49 × 10⁻²⁷ m | 1.23 × 10²³ K | 3.6 × 10³² W | 8.4 × 10⁻¹⁷ s |
| Aircraft carrier (100 kt) | 1.0 × 10⁸ | 1.49 × 10⁻¹⁹ m | 1.23 × 10¹⁵ K | 3.6 × 10¹² W | 266,000 years |
| Primordial-BH candidate | 1.0 × 10¹² | 1.49 × 10⁻¹⁵ m | 1.23 × 10¹¹ K | 3.6 × 10⁴ W | 2.66 × 10¹⁷ years |
| Earth | 5.97 × 10²⁴ | 8.87 × 10⁻³ m | 2.06 × 10⁻²² K | 1.0 × 10⁻¹⁷ W | 5.7 × 10⁵⁰ years |
| Sun | 1.989 × 10³⁰ | 2,953 m | 6.17 × 10⁻⁸ K | 9.0 × 10⁻²⁹ W | 2.1 × 10⁶⁷ years |
Edge Cases and Limitations of the Model
Hawking Radiation and the M⁻² Temperature Scaling
Hawking's 1974 derivation showed that quantum field theory in the curved spacetime around a black hole predicts a thermal spectrum of emitted particles at temperature TH = ħc³/(8πGMkB). The temperature scales inversely with mass: smaller black holes are hotter. A solar-mass black hole has TH ≈ 6 × 10⁻⁸ K — colder than the 2.725 K cosmic microwave background, so it absorbs more energy from the CMB than it radiates and grows rather than evaporates. A primordial black hole with mass around 5 × 10¹⁴ g (Mount Everest scale) has TH ≈ 10¹¹ K and is currently evaporating; its final seconds release a burst of gamma rays detectable by instruments like the Fermi Gamma-Ray Space Telescope, but to date no confirmed evaporation event has been observed.
Charge and Rotation: Reissner-Nordström and Kerr
A pure-Schwarzschild kugelblitz is uncharged and non-rotating. The Reissner-Nordström solution (1916–1918) generalizes Schwarzschild to include electric charge Q; the Kerr solution (Roy Kerr, 1963) generalizes to rotation with angular momentum J. A realistic kugelblitz formed from a focused but not perfectly symmetric pulse would carry some net angular momentum (the Kerr case), and any imbalance in the photon-antiphoton or electron-positron content of the source field could leave residual charge. The no-hair theorem says only M, Q, and J survive: the calculator's pure-mass scaling captures the dominant physics, but a precise prediction for an asymmetric formation event would require the Kerr-Newman metric (rotation + charge) and would change the horizon area by tens of percent at extremal rotation.
Sub-Planckian Masses and the Quantum-Gravity Cutoff
Below the Planck mass (mP = √(ħc/G) ≈ 2.18 × 10⁻⁸ kg, equivalent to a Schwarzschild radius of about 3.2 × 10⁻³⁵ m — the Planck length), the semi-classical Hawking calculation breaks down. The thermal wavelength of emitted radiation becomes comparable to the horizon size, the back-reaction of emitted particles on the metric is no longer perturbative, and full quantum gravity is needed. No such theory has yet been completed; loop quantum gravity, string theory, and asymptotic-safety approaches all make qualitatively different predictions for what happens in the final Planck-scale moments of evaporation. The calculator outputs results in this regime for educational illustration, but they should be regarded as order-of-magnitude only.
Backreaction During Formation
The calculator treats the kugelblitz as a static, fully formed Schwarzschild object. In a realistic formation event, the infalling electromagnetic energy would warp the local metric during collapse — a process described by the Vaidya metric (a non-static generalization of Schwarzschild for radiation infall). The instantaneous Schwarzschild radius grows as energy crosses the apparent horizon, and the apparent horizon and the event horizon are not the same surface during the dynamic phase. For the purpose of estimating the steady-state properties of the final object, the static Schwarzschild treatment is accurate to leading order; for studying the formation dynamics themselves, the Vaidya metric or numerical relativity is required.
Behind the Scenes: A Brief History of the Idea
Schwarzschild 1916: The Original Solution
Karl Schwarzschild solved Einstein's field equations for the spherically symmetric vacuum within weeks of the equations' publication in November 1915, while serving in the German army on the Russian Front. He communicated the result by letter to Einstein in December 1915; Einstein presented it to the Prussian Academy in January 1916. Schwarzschild noticed the singularity at r = 2GM/c² but did not interpret it as a physical horizon; that interpretation took another forty years, culminating in David Finkelstein's 1958 paper showing the surface is a one-way membrane, not a true singularity.
Wheeler's Geons and the Naming of the Kugelblitz
John Archibald Wheeler's 1955 paper "Geons" investigated whether self-gravitating bundles of electromagnetic radiation could mimic stable particles. Wheeler showed that geons are formally possible solutions to the coupled Einstein-Maxwell equations but are dynamically unstable — they either disperse or collapse into a true black hole. The collapsed end-state, which Wheeler called a kugelblitz, is what this calculator models. Wheeler went on to coin the term "black hole" in 1967, popularize "wormhole" and "spacetime foam," and mentor a generation of theorists including Kip Thorne, Richard Feynman, and Hugh Everett.
Hawking 1974: Black Holes Are Not Black
Stephen Hawking's 1974 paper "Black hole explosions?" (Nature 248, 30) applied quantum field theory in curved spacetime to show that black holes emit a thermal spectrum of radiation. The temperature is set entirely by the surface gravity at the horizon, which for a Schwarzschild black hole gives TH = ħc³/(8πGMkB). This was an entirely unexpected result — classical general relativity had said the horizon was strictly one-way — and the consequences are still being worked out today, most notably the long-running black-hole information paradox. The calculator's lifetime and power outputs are direct integrations of Hawking's result.
Why Kugelblitzes Remain Theoretical
No experiment has ever produced anything close to the energy density required to form a kugelblitz, and the Schwinger-limit argument suggests there may be a fundamental quantum-field obstruction. Astrophysically, no known process concentrates pure radiation densely enough — even gamma-ray bursts, the most energetic events in the observable universe, fall many orders of magnitude short. Primordial black holes might have formed in the very early universe (Carr & Hawking, 1974), but these would have collapsed from generic high-density inhomogeneities rather than pure radiation. The kugelblitz remains a clean theoretical limit case rather than an observed object.
Limitations of This Calculator
Assumes Pure Schwarzschild Geometry
The calculator solves the uncharged, non-rotating Schwarzschild metric. Real astrophysical black holes essentially all rotate (Kerr), often near the extremal limit a* ≈ 0.998 (Thorne 1974). Charge is generally negligible in astrophysics because surrounding plasma neutralizes it within microseconds, but a hypothetical electromagnetic-origin kugelblitz could in principle carry residual charge. Adding charge or rotation changes the horizon area (an extremal Kerr black hole has half the horizon area of a Schwarzschild black hole of the same mass), which would change the Hawking temperature and lifetime. Treat the outputs as the Schwarzschild benchmark, not a precise prediction for a rotating or charged object.
Hawking Evaporation Above the Planck Mass
The Hawking lifetime t = 5120πG²M³/(ħc⁴) assumes radiation is a steady thermal process all the way to evaporation. In the final Planck-scale moments — when the remaining mass approaches mP ≈ 2.18 × 10⁻⁸ kg — quantum gravity dominates and the formula loses physical meaning. For masses well above the Planck mass the formula is a good approximation; for masses below, it is heuristic only. The calculator does not flag this transition automatically.
Ignores Backreaction and Greybody Factors
The simple T = ħc³/(8πGMkB) formula assumes a perfect blackbody spectrum. In reality, the curvature of the spacetime around the black hole filters the emitted radiation through frequency-dependent "greybody factors" — transmission probabilities that suppress some modes and enhance others. The actual emitted spectrum is therefore not perfectly Planckian, and the integrated power differs from the ideal blackbody by a factor of order unity. For mass-scale comparisons spanning many decades, the order-of-magnitude formula used here is sufficient; for precise spectrum predictions, a numerical solution of the wave equation in the Schwarzschild background is needed.
No Cosmological Context
The calculator presents lifetime in a flat, empty universe. In reality, any black hole cooler than the 2.725 K cosmic microwave background gains more energy from CMB absorption than it loses to Hawking radiation; net evaporation only begins once the universe has cooled sufficiently (or the black hole's Hawking temperature exceeds the local radiation bath). For a solar-mass kugelblitz with TH ≈ 6 × 10⁻⁸ K, net evaporation cannot begin until the CMB has cooled by approximately eight orders of magnitude — pushing the effective lifetime even further into the cosmological future than the formula suggests.
FAQ: Kugelblitz Physics
What is a kugelblitz?
A kugelblitz is a hypothetical black hole formed from concentrated electromagnetic energy — light, gamma rays, or any other form of radiation — rather than from collapsed matter. The term is German for "ball lightning"; American physicist John Archibald Wheeler borrowed it in the 1950s when investigating whether pure radiation could curve spacetime enough to form an event horizon. General relativity treats energy density as a source of gravitational curvature on equal footing with mass density (the stress-energy tensor includes both), so the equations of Einstein's field theory permit a black hole to form from light alone if the energy is compressed into a small enough volume. Once formed, a kugelblitz is observationally indistinguishable from any other Schwarzschild black hole of the same mass.
Can a kugelblitz actually exist?
In principle yes; in practice the engineering challenge is staggering. To form a kugelblitz with the mass of an asteroid you need to concentrate roughly 10²⁷ joules of electromagnetic energy into a region a few hundred nanometers across — an intensity of about 10³⁶ watts per square meter. The most powerful lasers ever built (the National Ignition Facility's 1.8 MJ ultraviolet pulse, the Extreme Light Infrastructure's projected 100 PW exawatt class) fall short by 18 orders of magnitude or more. A 2024 paper in Physical Review D by Álvarez-Domínguez and colleagues even argued that QED pair-production effects (the Schwinger limit) drain the focused field into electron-positron pairs before the gravitational threshold is reached, suggesting a kugelblitz may be fundamentally forbidden in our universe regardless of available power. So "allowed by GR, possibly blocked by quantum electrodynamics" is the current honest answer.
Why is the Schwarzschild radius so small for everyday masses?
The Schwarzschild radius is rs = 2GM/c², and the constant 2G/c² is roughly 1.485 × 10⁻²⁷ m/kg. That coefficient is what makes black holes "expensive" to form: a kilogram's worth of mass-energy produces an event horizon only 1.485 × 10⁻²⁷ meters across — about a trillion times smaller than a proton. The Earth (5.97 × 10²⁴ kg) compressed into a black hole would have a Schwarzschild radius of about 8.87 mm; the Sun (1.989 × 10³⁰ kg), about 2,953 meters or 2.95 km; a billion-solar-mass supermassive black hole, about 3 × 10¹² m, which is roughly 20 astronomical units. The radius scales linearly with mass, so doubling the mass exactly doubles the horizon.
How fast would a kugelblitz evaporate?
Hawking radiation drains energy from any black hole at a rate proportional to M⁻², so evaporation time scales as M³. The standard formula is t = 5120 π G² M³ / (ħ c⁴), which gives a one-solar-mass black hole a lifetime of about 2 × 10⁶⁷ years — vastly longer than the age of the universe. A primordial black hole with the mass of Mount Everest (~10¹¹ kg) evaporates over roughly 13 billion years, which is why some cosmologists have searched for the gamma-ray flash signatures of evaporating primordial black holes today. A microscopic kugelblitz with mass below about 10⁻¹⁹ kg evaporates faster than the Planck time (5.4 × 10⁻⁴⁴ s) — meaning quantum-gravity effects dominate and the semi-classical Hawking formula breaks down entirely.
Did John Wheeler invent the kugelblitz concept?
Wheeler coined the modern usage but the underlying physics goes back further. In 1916 Karl Schwarzschild published the first exact solution to Einstein's field equations describing a non-rotating, uncharged spherically symmetric vacuum — what we now call the Schwarzschild metric. In 1955 Wheeler proposed the "geon" (gravitational-electromagnetic entity), a hypothetical bundle of electromagnetic waves held together by its own gravitational self-attraction, in his paper "Geons" (Physical Review 97, 511). He later used the German word kugelblitz (ball lightning) to describe a localized concentration of light intense enough to form a horizon. So the lineage is Schwarzschild (1916) → Wheeler's geon (1955) → kugelblitz as a Wheelerian variant where the radiation density exceeds the black-hole formation threshold.
Could we use a kugelblitz for energy or spaceship propulsion?
Science fiction (notably Adam Crowl and Louis Crane's 2009 paper "Are Black Hole Starships Possible?" and the 2014 film Interstellar) has explored powering interstellar ships with a small artificial black hole that converts mass to Hawking radiation with near-100% efficiency. The arithmetic is appealing: a 10⁶ kg black hole radiates at about 10¹⁵ W with a 60-year lifetime and could in principle accelerate a payload to relativistic speeds. The problems are formidable. First, you have to make one — see the Schwinger-limit obstacle above. Second, you have to feed it matter at exactly the rate it radiates to keep mass constant (under-feed and it evaporates explosively, over-feed and it grows unboundedly). Third, the gamma-ray Hawking emission must be directed — a black-hole drive radiates isotropically by default. No experimentally validated path to any of these problems currently exists.
How does the no-hair theorem apply to kugelblitzes?
The no-hair theorem, formalized by Werner Israel, Brandon Carter, David Robinson, and Stephen Hawking between 1967 and 1975, proves that a stationary black hole in four-dimensional general relativity is completely characterized by just three externally observable parameters: mass (M), electric charge (Q), and angular momentum (J). Everything else — the composition, history, polarization, frequency spectrum of the infalling material — is erased at the horizon. This means a kugelblitz formed from a pulse of pure gamma rays is, after it settles into a stationary state, exactly identical to a black hole of the same M, Q, J formed by stellar collapse. There is no observable property that distinguishes "made from light" from "made from neutron-star matter" once the horizon forms.
Why does general relativity say light can make a black hole?
Einstein's field equations, Gμν = (8πG/c⁴) Tμν, relate spacetime curvature (Gμν, the Einstein tensor) to the stress-energy tensor Tμν, which encodes both mass density and energy density — including the energy density of electromagnetic fields. There is nothing special about matter on the right-hand side. Photons carry energy E = hν and momentum p = E/c, and their energy density contributes to Tμν just as much as a stationary kilogram's rest-mass energy does. Compress enough light into a small enough volume and you reach the same critical density that would form a horizon for matter of equivalent total energy. The equivalence is fundamental: gravity couples to all forms of energy, not just rest mass — which is exactly why a photon is deflected by the Sun's gravity (general relativity's first observational confirmation, Eddington's 1919 eclipse expedition).