We investigate properties of the reconnecting current layer in relativistic
pair plasma reconnection. We found that the current layer self-regulates its
thickness when the current layer runs out current carriers, and so relativistic
reconnection retains a fast reconnection rate. Constructing a steady state
Sweet-Parker model, we discuss conditions for the current sheet expansion.
Based on the energy argument, we conclude that the incompressible assumption is
invalid in relativistic Sweet-Parker reconnection. The guide field cases are
more incompressible than the anti-parallel cases, and we find a more
significant current sheet expansion.Comment: Accepted for publication in Astrophysical Journal (to appear in vol.
685