In 1976, following his work on black holes, Stephen Hawking raised a paradox:according to general relativity, the information absorbed by a black hole is lost when it evaporates. However, the laws of quantum mechanics impose a conservation of information. Similarly, when two black holes merge, they lose some of their total mass. Does this phenomenon also lead to a loss of information?
In the ten black hole mergers detected by the LIGO and Virgo interferometers over the past two years, each of the black holes involved has lost a fraction of total mass in the process, around 5% on average. If information is encoded in the mass of black holes, then it should be lost.
In any case, this is what general relativity says. When a particle falls into a black hole, all of its properties — baryon number, lepton number, isospin, etc — no longer play any role in the physics of the black hole. Information about these properties is supposed to be lost. In other words, according to Einstein's theory, the entropy of a black hole is zero.
However, this consideration comes into conflict with the laws of thermodynamics and quantum mechanics. Any object with defined temperature, energy and physical properties has non-zero entropy, and this can never decrease. If the matter from which the black hole originates has non-zero entropy, then throwing matter into it would only increase its entropy. The black hole must therefore have finite, positive and non-zero entropy.
According to these rules, all the properties of a particle (spin, charge, mass, polarization, etc.) falling into a black hole constitute information which must therefore be stored somewhere. If it's not the singularity, then it's somewhere else. And it was physicist John Wheeler who first suggested that this information could be stored on the event horizon.
Related topic:How do gravitational waves escape from black holes?
According to the Schwarzschild radius formula Rs =2GM/c², it is the mass of a black hole that determines the size of its event horizon. It is therefore natural to think that the entropy can actually be located on the surface of this horizon.
As a black hole's mass increases, its event horizon expands, storing additional entropy/information absorbed. According to the work of Jakob Bekenstein and Stephen Hawking, this information would be encoded in the form of qubits in Planck areas.
During the merger of two black holes, the mass of the resulting black hole is equivalent to the sum of the mass of the two black holes, reduced by 10% (5% of mass lost for each of the objects). Thus, if each black hole has a mass of 1 M, the final black hole will have a mass of 1.9 M. This means that, simultaneously, gravitational waves are emitted and carry an energy of 0.1 Mc².
From this observation, three scenarios are possible:
The entropy of a black hole is proportional to the surface area of its event horizon, which itself is proportional to the squared mass. This means that if two initial black holes have an entropy of S, then a final black hole of 1.9 times the mass of the two black holes has an entropy of 3.6 S, which is clearly sufficient to store the information of the initial black holes. This is the Bekenstein-Hawking entropy postulate.
Nevertheless, gravitational waves must carry some of this information. Indeed, they are generated by the changes imprinted on the geometry of space-time during the fusion, and their energy comes from the change of distribution of matter-energy of space-time. However, without an effective quantum gravity theory, it is impossible to determine how much information is retained by the final black hole and how much is transferred to gravitational waves.
In any case, during the merger of two black holes, there is no loss of information, since the entropy of the final state is higher than that of the initial state. But there is currently no way to extract the amount of entropy or information from gravitational waves or the event horizon of a black hole. Only theory is capable of providing some information here.
