# Why doesn't a black hole have linear momentum?

The no hair theorem says that a black hole can have only three properties: mass, charge and angular momentum. But why don't we say that linear momentum is one of its properties? If we throw an object into it at a certain velocity, it's clear the linear momentum will increase. So why isn't it a fundamental property? Is it because its velocity and hence linear momentum depends on the reference frame? But then doesn't its angular momentum as well if the frame is non-inertial?

• "The no hair theorem says that a black hole can have only three properties: mass, charge and angular momentum." - This is incorrect. See: en.wikipedia.org/wiki/No-hair_theorem - "stable black holes can be completely described (in a Cartesian coordinate system) at any moment in time by these eleven numbers: mass-energy, linear momentum (three components), angular momentum (three components, position (three components), electric charge." Nov 19, 2021 at 9:55
• Recent related PBS Space Time video: Are black holes actually fuzzballs? Nov 20, 2021 at 12:26
• The crux of your question lies in the last sentence: Is angular momentum frame-invariant just like linear momentum? i.e.: How can you distinguish a rotating sphere from a stationary one that has the world revolving around it in the opposite direction? I've asked this question before and I think the answer I got basically reduced to "try tossing a ball up", so to speak. It'll land on the same spot if and only if your sphere/planet isn't rotating. And the landing spot clearly doesn't depend on the reference frame. Nov 21, 2021 at 9:31
• Wait, linear momentum is not frame invariant right? Even in newtonian mechanics, would the angular momentum of the Earth from a geostationary satellite be zero? Nov 22, 2021 at 4:05