# How does electric charge affect spacetime?

Electric charge does not affect spacetime. Mass curves spacetime. This means that if there are two particles A and B, which are spherically symmetrical and have the same mass, even if A is charged and B is uncharged, they both must curve the spacetime in the same way.

There is RN metric for non-rotating charged black hole and KN metric for rotating charged black hole. The Schwarzschild metric and the Kerr metric should be enough.

However, this is not the case. This means that electric charge affects spacetime.

How does electric charge affect spacetime?

• “Electric charge does not affect spacetime.” … “This means that electric charge affects spacetime.” It’s confusing to state something and then conclude the opposite. Commented Apr 4, 2023 at 18:53
• Your mistake is thinking that only mass curves spacetime. On the right side of Einstein’s field equation is not mass but the energy-momentum-stress tensor. Mass is only one thing that contributes to that tensor. Commented Apr 4, 2023 at 18:56

Charge does effect spacetime. Einstein's Field Equations relate gravity not to strictly mass, but the stress-energy tensor. Mass is energy via $$E=mc^2$$. There's also other energy contributions, eg. motion of the source particles. Charged particles also imply stresses.