# Echoes of Gravitational Waves

Recently a paper was published that reported on the tentative ($3 \sigma$) detection of ‘echoes’ in the gravitational wave signal detected by LIGO. If true, this detection has far-reaching implications for our theories of gravity and the search for a quantum theory of gravity. This post will outline the proposed theoretical cause of these echoes, and the problem in causes for general relativity

### Introductory quantum mechanics

A key principle of quantum mechanics is that of unitarity - the conservation of information, i.e. given a bunch of quantum systems each with a particular probability, all the probabilities must sum to 1.

If we smash together two particles (e.g. in the LHC at CERN) then gather all the possible information on the particles that result (trajectories, charge, baryon number etc.) we should be able to recreate all the information about the original 2 smashed particles. This is because information is conserved in quantum mechanics. However we run into a problem when we try to apply this principle to black holes.

### Cause of the echoes - a firewall

Stephen Hawking’s famous result is that black holes radiate. This is Hawking radiation. A pair of virtual particles pop into existence near the event horizon. One with negative energy is taken into the black hole, whilst the other escapes. The black hole gains a particle with negative energy and so loses mass. Consequently over time black holes slowly evaporate. Another famous theorem about black holes is the No-hair theorem which says that all properties of a black hole - including the radiation it emits - are determined by just 3 parameters, the mass, charge and angular momentum. This is a problem because it means that Hawking radiation is independent of the sort of material entering the black hole. There is no way to find out all the information about what was thrown into the black hole by getting all the possible information contained in the Hawking radiation. This is known as the black hole information paradox.

A proposed solution to this information paradox is known as a black-hole firewall. The ideas is that when one virtual particle is absorbed by the black hole, the entanglement between the particle pair is broken. This releases huge amounts of energy and results in a firewall around the black hole, just outside the event horizon, that would incinerate any matter that attempts to pass through it. Correlations between emitted particles would then carry the information about the particles that fell into the black hole (note this is quite a heuristic explanation - see the original ‘AMPS’ paper for a more involved discussion).

The (potentially) detected echoes in the LIGO signal occur as a direct result of this firewall. The model considers the event horizon as a mirror and the firewall as a partially permeable surface. Gravitational waves would oscillate between these two boundaries, with some gravitational radiation being released each time the wave strikes the firewall, which we then detect as echoes.

### The Problem for GR

The problem with this firewall solution is that it violates the equivalence principle, which we can state in this case as ‘the event horizon is not a special place’. According to classical GR, an infalling observer would notice nothing different as she passed the event horizon. However, the firewall solution defies this principle - she would notice something different as she is thermalised into dust by the firewall! The reason this is a problem is that the equivalence principle is the key foundation stone in our General Relativity.

If the report of these echoes is true (Note they are still far off the required $5 \sigma$ significance), then it would mean that a firewall exists, and consequently the equivalence principle does not hold globally. That is, clearly the equivalence principle is somewhat right - it has been used to form GR which has passed a plethora of tests in the weak field regime - but perhaps it does not apply to every corner of the universe. Perhaps close to the surface of black holes, where we expect quantum effects to play a more significant role, the equivalence principle does not hold.

The solution will require the development of a full quantum theory of gravity, the two main strands of which are string theory and loop quantum gravity. For discussion on either of these two theories, see: Give a description of Loop Quantum Gravity your grandmother could understand

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