Where is the mass in a black hole?

 This is one of the deepest conceptual points in general relativity—you’re asking exactly the right question.

Let’s answer it carefully, because the intuitive “mass sits somewhere” picture breaks down.

🧭 Short answer

After a black hole forms:

The mass is not sitting at a place like ordinary matter.
Instead, it is encoded in the entire spacetime geometry outside the horizon.

🪐 Before collapse: easy

For a star:

• Matter is distributed throughout a volume
  
• The gravitational field comes from that matter
  

So you can say:
👉 “The mass is where the matter is.”

🕳️ After collapse: the picture changes

Once the star collapses into a black hole:

• All matter is hidden behind the event horizon
  
• Classical general relativity says it ends up at (or near) the singularity
  

But here’s the key twist:

🔑 The external gravitational field no longer “points” to a location of matter.

🌌 Where is the mass really?

In GR, mass isn’t like a lump sitting somewhere.

Instead:

• Mass is defined by how spacetime behaves far away
  
• This is called the ADM mass (or similar global quantities)
  

So:

✅ The mass is a global property of spacetime, not a local object.

🧠 Crucial idea: gravity without matter

After formation:

• The outside region is vacuum (no matter present)
  
• Yet gravity is still there
  

This is not a bug—it’s a feature of GR:

Spacetime curvature can exist without local matter, as long as it’s sourced somewhere in the past.

🧲 Analogy (imperfect but helpful)

Imagine:

• You create a whirlpool in water using a paddle
  
• Then remove the paddle
  

The water keeps swirling.

Where is the cause of the swirl now?

• Not at a point
  
• It’s in the motion of the fluid itself
  

Similarly:

The black hole’s mass is encoded in the curvature pattern of spacetime.

🕳️ What about the singularity?

You might think:

“Okay, so the mass must be at the singularity.”

But this is tricky:

• The singularity is not part of spacetime (it’s where the theory breaks down)
  
• GR does not describe it physically
  

So we can’t really say:

✅ “The mass is located there” in any normal sense

Instead:

The singularity is a sign that our description has failed, not a well-behaved object holding mass.

🧩 The key shift in thinking

In Newtonian physics:

• Matter → causes gravity
  
• Gravity → points back to matter
  

In GR:

• Matter helps determine spacetime
  
• But once formed, spacetime can carry:
• Mass
  
• Energy
  
• Angular momentum
  

Even in regions with no matter present

🌀 Back to your rotation question

Now this ties directly to your earlier question:

• The black hole’s angular momentum is not stored in spinning matter
  
• The mass is not sitting somewhere like a lump
  

Both are:

✅ Encoded in the geometry of spacetime itself

🧠 A sharper statement

The most precise answer is:

A black hole’s mass is defined by how spacetime curves at infinity, not by a localized distribution of matter inside.

⚠️ Important limitation

All of this is within classical general relativity.

We expect:

• A future theory of quantum gravity may give a clearer answer
  
• Possibly replacing the singularity with something physical
  

But right now:

“Where is the mass?”
has the answer:
👉 Not anywhere local you can point to.

✅ Bottom line

• The matter that formed the black hole has fallen behind the horizon
  
• It no longer acts like a normal mass distribution
  
• The mass lives in the gravitational field (spacetime curvature) itself
  
• The singularity is not a usable physical “location” of mass
  

If you want, the next natural step is exploring how mass can be defined purely from geometry (e.g., ADM mass or Komar mass), which makes this idea fully precise.

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).