# Is the Schwarzschild black hole solution a special case of the Kerr solution?

Generally, when a solution to a system defined by an equation or set of generalized equations that is generally applicable to a broad range of possible initial conditions, or boundary constraints, is itself applicable only to a narrow subset of that broad range, the more specific constrained solution can be derived from the more general solution by fixing, or constraining, within the analysis, the values of the variable representing that constraint.

So, my question is: Can the Schwarzschild solution to GR be derived from the Kerr solution by simply setting the rotation rate to zero?

• Have you just plugged $J=0$ into the standard form of the Kerr metric to check? Commented Mar 10 at 15:30
• No, Unfortunately, I am not mathematically literate enough to try that. But I will give it a try! B Commented Mar 11 at 2:28

Yes. The most general solution is the Kerr-Newman black hole solution, which has a mass $$M$$, electric charge $$Q$$, and angular momentum $$J$$.
1. Set $$Q=J=0$$ to get the Schwarzschild black hole.
2. Set $$Q=0$$ to get the Kerr black hole.
3. Set $$J=0$$ to get the Reissner–Nordström black hole