The 5-D Choptuik critical exponent and holography

TL;DR

This paper improves the numerical calculation of the 5-dimensional Choptuik critical exponent, revealing a close but not exact match with the holographically related BFKL saturation exponent, thus refining the understanding of holographic duality in black hole formation.

Contribution

The paper provides a more precise numerical estimate of the 5D Choptuik critical exponent, enhancing the accuracy of holographic relations with the BFKL saturation exponent.

Findings

New calculation of $oldsymbol{\gamma_{5d}}$ with reduced error

Close numerical agreement between $oldsymbol{\gamma_{5d}}$ and $oldsymbol{\gamma_{BFKL}}$

Refinement of holographic correspondence in black hole critical phenomena

Abstract

Recently, a holographic argument was used to relate the saturation exponent, $\gamma_{BFKL}$, of four-dimensional Yang-Mills theory in the Regge limit to the Choptuik critical scaling exponent, $\gamma_{5d}$, in 5-dimensional black hole formation via scalar field collapse \cite{alvarez-gaume}. Remarkably, the numerical value of the former agreed quite well with previous calculations of the latter. We present new results of an improved calculation of $\gamma_{5d}$ with substantially decreased numerical error. Our current result is $\gamma_{5d} = 0.4131 \pm 0.0001$, which is close to, but not in strict agreement with, the value of $\gamma_{BFKL}=0.409552$ quoted in \cite{alvarez-gaume}.