Gravitating defects of codimension-two

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Thin gravitating defects with conical singularities in higher codimensions and with generalized Israel matching conditions are known to be inconsistent for generic energy–momentum. A way to remove this inconsistency is proposed and realized for an axially symmetric gravitating codimension-two defect in six-dimensional Einstein gravity. By varying with respect to the brane embedding fields, alternative matching conditions are derived, which are generalizations of the Nambu–Goto equations of motion of the defect, consistent with bulk gravity. For a maximally symmetric defect the standard picture is recovered. The four-dimensional perfect fluid cosmology coincides with conventional FRW in the case of radiation, but for dust it has ρ4/3 instead of ρ. A four-dimensional black hole solution with the Schwarzschild form with a short-distance r−2 correction is presented.