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Topology-changing horizons at large D as Ricci flows | | Roberto Emparan
; Ryotaku Suzuki
; | | Date: |
3 May 2019 | | Abstract: | The topology-changing transition between black strings and black holes
localized in a Kaluza-Klein circle is investigated in an expansion in the
inverse of the number of dimensions D. Performing a new kind of large-D scaling
reduces the problem to a Ricci flow of the near-horizon geometry as it varies
along the circle direction. The flows of interest here simplify to a non-linear
logarithmic diffusion equation, with solutions known in the literature which
are interpreted as the smoothed conifold geometries involved in the transition,
namely, split and fused cones, which connect to black holes and non-uniform
black strings away from the conical region. Our study demonstrates the
adaptability of the 1/D expansion to deal with all the regimes and aspects of
the static black hole/black string system, and provides another instance of the
manner in which the large D limit reduces the task of solving Einstein’s
equations to a simpler but compelling mathematical problem. | | Source: | arXiv, 1905.1062 | | Services: | Forum | Review | PDF | Favorites | |
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