- #106

Dale

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Agreed. To me a condition on the boundary is a boundary condition regardless of whether you found it by solving the differential equation and then specifying the resulting constants or if you inserted in the condition before solving the differential equation. The math doesn't care about the order, but as you say, this is just terminology.PeterDonis said:No argument with that; I just don't like using the term "boundary condition" to refer to this, since it's not something you impose before you derive the solution, it's something you discover in the course of doing the solution. But as I said, that's a matter of terminology, not physics or mathematics.

If you want to distinguish the two then I would suggest "constant of integration" for the post-hoc constants and "boundary condition" for the a-priori constants. Under that categorization (which I wouldn't use) I would agree that the curvature at the horizon arises from a constant of integration rather than a boundary condition.

You can always change a constant of integration into a boundary condition by changing the order of operations.