Great question—you’re circling a real subtlety of general relativity.
A rotating black hole (a Kerr black hole) doesn’t rotate in the way a solid object does (like a spinning ball with identifiable parts). Instead, its angular momentum is encoded in the structure of spacetime itself.
Let’s break that down clearly.
🌀 What is “rotating” if not matter inside?
You’re right to question this:
- The event horizon is just a boundary, not a physical surface.
- The singularity (in the Kerr case) is a ring-like structure, but it’s not a classical object you can point to as “spinning.”
So where is the rotation?
👉 Answer:
The rotation lives in the gravitational field (the spacetime geometry).
🌌 Angular momentum in general relativity
In general relativity:
- Mass-energy tells spacetime how to curve.
- Motion (including rotation) tells spacetime how to twist.
A rotating black hole has a parameter \( J \), its angular momentum. This shows up in the metric (the Kerr solution), not as spinning “stuff,” but as a twisting of spacetime itself.
🧲 Frame dragging: the key effect
The hallmark of this rotation is frame dragging:
- Spacetime is literally dragged around the black hole.
- Anything nearby (even light) is forced to co-rotate.
This produces:
- The ergosphere (region outside the event horizon)
- Inside it, nothing can remain stationary—you must rotate
So instead of a solid object spinning, you have:
🌀 A vortex-like distortion of spacetime
🕳️ So what’s actually “spinning”?
Not a surface, not the horizon, not a classical object.
Instead:
- The entire geometry carries angular momentum
- Rotation is encoded in how spacetime’s coordinates mix:
- Space and time directions “tilt” into each other
In the Kerr metric, this appears as off-diagonal terms (like \( g_{t\phi} \))—mathematically describing how time and angular direction are coupled.
🧠Intuition analogy
Think of it like:
Fluid analogy
- Not a rigid spinning ball
- More like a whirlpool
But even that analogy is imperfect because:
- There’s no underlying “fluid”
- The geometry itself is doing the swirling
⚠️ Common misconception
It’s easy to imagine:
“The event horizon must be spinning like a surface.”
But that’s misleading.
- The horizon does have an effective angular velocity
- But this is a property of spacetime geometry, not a material rotation
🧩 Where did the angular momentum come from?
From the collapsing object that formed the black hole:
- A rotating star collapses
- Angular momentum is conserved
- The resulting black hole inherits \( J \)
Even though:
- The original matter is gone behind the horizon
- The external gravitational field still carries the angular momentum
✅ Bottom line
A rotating black hole has angular momentum because:
- Its spacetime geometry is twisted, not because something inside is spinning like a rigid object
- The rotation is real and measurable (via frame dragging, ergosphere effects)
- But it’s distributed across the gravitational field, not located at a surface or point
If you want, I can go one step deeper (e.g., how the Kerr metric mathematically encodes rotation or how energy can be extracted from the ergosphere via the Penrose process).
