What is rotating in a rotating black hole?

 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).