# Topology-changing horizons at large D as Ricci flows

## TL;DR

This paper uses a large D expansion to analyze topology-changing transitions between black strings and black holes, reducing the problem to a Ricci flow of near-horizon geometries described by a nonlinear diffusion equation.

## Contribution

It introduces a novel large-D scaling approach that simplifies the analysis of black hole/black string transitions to a Ricci flow problem involving known solutions.

## Key findings

- Ricci flow equations describe the transition geometries
- Solutions correspond to smoothed conifold geometries
- Method applies across all regimes of the black hole/black string system

## 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.