In 1976, Stephen Hawking highlighted a profound paradox: general relativity suggests black holes destroy information upon evaporation, clashing with quantum mechanics' principle of information conservation. When black holes merge, some mass converts to gravitational waves—does this also erase information?
Over the past two years, LIGO and Virgo have detected ten black hole mergers, each losing about 5% of total mass on average as gravitational waves. If information resides in black hole mass, it might seem lost.
General relativity implies that once a particle crosses the event horizon, its properties—baryon number, lepton number, isospin—vanish from the black hole's description. The black hole's entropy appears zero, erasing this data.
Yet this conflicts with thermodynamics and quantum mechanics. Objects with temperature, energy, and properties have positive entropy that never decreases. Matter falling into a black hole increases its entropy, so black holes must have finite, non-zero entropy.
Particle properties like spin, charge, mass, and polarization represent information that must be preserved. Not at the singularity, but perhaps on the event horizon, as John Wheeler proposed.
Related topic: How do gravitational waves escape from black holes?
The Schwarzschild radius, Rs = 2GM/c², ties horizon size to mass. Entropy likely resides on this surface. As mass grows, the horizon expands, accommodating more information. Jakob Bekenstein and Stephen Hawking showed this is encoded as qubits in Planck-scale areas on the horizon.
In a merger, the final black hole's mass is the sum minus ~10% (5% per black hole). For two 1M☉ black holes, the result is 1.9M☉, with 0.1Mc² radiated as gravitational waves.
Three possibilities emerge:
Black hole entropy scales with horizon area, proportional to mass squared. Two initial black holes with entropy S each total 2S. The 1.9M☉ final hole has ~3.6S—ample for initial data, per Bekenstein-Hawking.
Gravitational waves, born from spacetime distortions, likely carry some information tied to energy redistribution. Without quantum gravity, we can't quantify the split.
Mergers don't lose information—final entropy exceeds initial. Extracting it from waves or horizons awaits theoretical advances.
