3.9 The charged case

We end this section with a discussion of the spherically-symmetric Einstein–Vlasov–Maxwell system, i.e., the case considered above with charged particles. Whereas the constraint equations in the uncharged case, written in Schwarzschild coordinates, do not involve solving any difficulties once the distribution function is given, the charged case is more challenging. However, in [123] it is shown that solutions to the constraint equations do exist for the Einstein–Vlasov–Maxwell system. In [122] local existence is shown together with a continuation criterion, and global existence for small initial data is shown in [121].

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