In 2016, the LIGO collaboration announced the first detection of gravitational waves predicted 100 years earlier by Einstein in his theory of general relativity. These waves were emitted during the merger of two black holes, the mass of the final black hole being less than the sum of the masses of the two initial black holes. In the case of black holes, general relativity is clear:nothing can escape their event horizon. So how was energy able to escape from black holes during the merger?
For a black hole, all of its mass/energy is concentrated at its center, within an object called a singularity. This singularity is separated from the exterior by the presence of an event horizon. Once past the event horizon, any particle, whether massive or not, regardless of its speed or energy, will take a trajectory that will inevitably lead it to the singularity in which it will be absorbed.
In his theory of general relativity, Einstein demonstrated that when a massive body accelerates, it produces gravitational waves. A gravitational wave is a ripple in spacetime that travels at the speed of light in a vacuum. It causes a contraction/dilation of space-time as it passes, and carries a certain amount of energy. And according to the mass-energy equivalence E =mc², mass is just a particular form of energy.
On September 14, 2015, LIGO detected gravitational waves from the merger of two black holes of 36 and 29 solar masses. However, the final black hole from the merger is only 62 solar masses. Where have the other 3 solar masses gone? Answer:in the energy of the gravitational waves emitted. When two black holes of similar masses spiral and merge, up to 5% of the total mass can be dissipated as gravitational waves.
However, every black hole has an event horizon, whether it is the two initial black holes or the final black hole. And at no point in the process do the singularities become bare, i.e. devoid of an event horizon. So how do gravitational waves escape from black holes?
Same topic: How are gravitational waves detected?
An analogy can be formulated with these questions:where does the mass go when two protons fuse into deuterium, then into helium-3 and finally into helium-4 at the heart of the Sun? Why is helium-4 less massive than the masses of the four fused protons from which it results? Because of nuclear binding energy. A bound state is more stable and less energetic (therefore less massive) than an unbound state.
Similarly, when two black holes spiral and merge, they become more gravitationally bound. The loss of energy, and therefore mass, is due to gravitational binding energy, not because energy (mass) leaks out of the event horizon.
This can also be understood from the point of view of Newtonian gravitation. Imagine two masses of 1 kg each, at rest, and separated by an infinite distance. According to E =mc², they have an energy of 1.8×10 17 J. Now let's reduce the distance between them:
Of course, at these scales, general relativity is used, and not Newtonian gravity, but the phenomenon remains the same. It is not the black holes that lose mass, but the total amount of energy in the system that is transformed from one form (two separate, unbound masses) to another form (gravitationally bound masses + gravitational waves).
The orbital properties and masses of black holes determine how much of the initial total mass is converted into gravitational binding energy. When the two masses are similar, up to 5% of the mass can be converted. If the value of their spin is very high and these spins are aligned, it can go up to 11%. But when one black hole is much more massive than the other, this percentage decreases. For example, a black hole of one solar mass merging with a black hole of one million solar masses can only convert 0.0001% of its mass.
In summary, when two black holes merge, nothing escapes the event horizon. Gravitational waves detected by interferometers like LIGO simply reflect the readjustment of spacetime as gravitational binding energy is released during coalescence and fusion.
