Black Hole Mergers and Entropy

You're absolutely right to sense that black hole mergers raise a lot of deep and not entirely resolved questions — both classical and quantum. Let’s unpack this step by step, following the actual physics involved as best we currently understand it.


1. What is "merging" in a black hole merger?

When two black holes spiral into each other due to gravitational wave emission, they don't "crash" in a hard sense — spacetime itself is smooth and continuous. As they draw near, each black hole's event horizon (which is a causal boundary, not a physical surface) begins to distort due to the other's intense gravity.Eventually, a common event horizon forms around both of them. This new horizon envelops both of the old ones before they actually touch. This is known as the apparent horizon formation, and it's a locally defined concept in general relativity — a surface from which light cannot escape locally, not just asymptotically.So, what actually happens is:

  • The individual event horizons become trapped surfaces.
  • A larger, outer apparent horizon forms and becomes the final, stable event horizon.
  • The interior geometry "settles down" into that of a new, larger Kerr black hole (if there's spin) after a period of violent oscillations called ringdown, shedding energy via gravitational waves.

2. What happens to an object during a merger?

Let’s suppose there's a small object orbiting one of the black holes, or even falling in.

Classically:

Once inside the event horizon of either black hole, the object has no causal influence on anything outside. However, if the merger happens before the object crosses the horizon, it may be swept into the newly forming common horizon.But here's a twist: from the outside, you'll never actually see the object cross the horizon due to extreme gravitational time dilation. The light it emits is infinitely redshifted. From its own frame, it experiences free fall and passes the horizon without noticing anything special.

During the merger:

  • The object becomes part of the internal structure of the merged spacetime. The precise geodesic it follows will change dramatically due to the nonlinear dynamics of the merger.
  • Any internal structure is obliterated — remember, under the no-hair theorem, the final black hole only remembers mass, spin, and charge. Everything else becomes inaccessible.
  • The internal geometry may involve Cauchy horizons, mass inflation, or other exotic features we still don't fully understand.

3. What’s actually happening to the horizons geometrically?

Here’s where it gets fascinating and slightly surreal.Event horizons are global, teleological constructs — their shape depends on the entire future evolution of spacetime. That is, to know where the horizon is now, you must know what happens later. This makes simulations very subtle.In numerical relativity:

  • You often track apparent horizons, which are local.
  • Then, you reconstruct the event horizon retrospectively by ray-tracing null geodesics. As the black holes approach, their individual apparent horizons distort and elongate toward each other. The new outer apparent horizon then forms in a kind of topological bifurcation (like a bubble swallowing two smaller bubbles). The original horizons either merge into the new one or become hidden within it before dissipating.

Bonus: What questions are still unsolved?

  • What happens quantum-mechanically to the information inside the black holes? The information paradox is still unresolved, though proposals like holography and black hole complementarity offer some routes.
  • How do spacetime singularities behave inside a merger? The interiors of black holes in mergers are still largely unknown — numerical relativity often avoids simulating that region directly.
  • Can we describe the merger with quantum gravity? Not yet — but if we had a full theory of quantum gravity, black hole mergers would be a crucial testing ground.

In short: during a merger, the horizons don't "crash"; they combine, forming a larger enclosing causal boundary. The process is continuous in general relativity but extremely dynamic, shedding mass-energy as gravitational waves. Objects inside either original black hole become part of the merged interior, and the resulting spacetime remembers nothing except conserved charges.


Q1: Can we actually visualise the internal geometry of a merged black hole — does it resemble a connected topology or a wormhole?Q2: What happens if a third object falls in during the merger? Does it affect the horizon dynamics or get "swallowed" mid-transition?Q3: How do simulations handle the undefined regions near singularities during black hole mergers — do they just cut them out or is there a trick to stabilising those zones?