For sufficiently small circle length L, the homogeneous black string is the only static SO(3)-invariant Ricci-flat metric in a small L-bounded neighborhood with zero boundary data.
Towards a uniqueness theorem for static black holes in Kaluza-Klein theory with small circle size
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Local uniqueness of the Black String with small circle size
For sufficiently small circle length L, the homogeneous black string is the only static SO(3)-invariant Ricci-flat metric in a small L-bounded neighborhood with zero boundary data.