On the vacuum Einstein equations along curves with a discrete local rotational and reflection symmetry

Understand

We discuss the possibility of a dimensional reduction of the Einstein equations in S3 black-hole lattices.

• It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotational and reflection Symmetry (LDRRS) can be carried out via a system of ODEs along these curves.
• However, 3+1 Numerical Relativity computations demonstrate that this is not the case, and we show analytically that this is due to the presence of a tensorial quantity which is not suppressed by the symmetry.
• We calculate the term analytically, and verify numerically for an 8-black-hole lattice that it fully accounts for the anomalous results, and thus quantify its magnitude in this specific case.