Topology-changing horizons at large D as Ricci flows

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.

arXiv comment34 pages, 7 figures; v2: minor corrections, refs added; v3: minor corrections, some comments added

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• The Large D Limit of Einstein's Equations
• Black hole collisions, instabilities, and cosmic censorship violation at large D
• Black Ripples, Flowers and Dumbbells at large $D$
• String Theory in a Pinch: Resolving the Gregory-Laflamme Singularity
• The large D effective theory of black strings in AdS
• Black hole interactions at large $D$: brane blobology
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• Black Hole Critical Collapse in Infinite Dimensions: Continuous Self-Similar Solutions
• Robinson-Trautman solutions with scalar hair and Ricci flow
• Critical lumpy black holes in AdS${}_p\times S^q$
• The Black hole Black string phase transition in Einstein-Gauss-Bonnet gravity
• Lattice Black Branes at Large $D$
• Squashed black holes at large $D$