[Paper Review] High Energy Scattering in the Brane-World and Black Hole Production

I. Ya. Aref’eva|ArXiv.org|Nov 1, 1999

Black Holes and Theoretical Physics3 citations

TL;DR

This paper investigates black hole production in high-energy scattering within the brane-world scenario, using a 3D toy model of the Randall-Sundrum solution. It finds that brane stability under ultra-relativistic particle collisions depends critically on the analytic continuation of the metric across the horizon, with instability enabling black hole formation in such collisions—offering a mechanism for black hole production in higher-dimensional gravity models.

ABSTRACT

Black hole production in the collision of ultra-relativistic particles in the brane-world approach is considered. In particular, stability of the brane under collision with ultra-relativistic particles is discussed. As a toy model we consider the 3 dimensional version of the Randall and Sundrum solution and show that stability of the brane depends on a choice of continuation of the solution across the horizon. In the unstable case black holes can be produced in the collision of a particle with the brane.

Motivation & Objective

• To analyze the stability of branes under collisions with ultra-relativistic particles in the brane-world framework.
• To investigate conditions under which black holes can be produced in high-energy scattering events on the brane.
• To model the dynamics of brane-world systems using a simplified 3D version of the Randall-Sundrum solution.
• To determine how the choice of metric continuation across the horizon affects brane stability and black hole formation.

Proposed method

• A 3-dimensional analog of the Randall-Sundrum model is constructed to study brane dynamics in a simplified setting.
• The metric is analytically continued across the horizon to explore different physical behaviors.
• The stability of the brane under ultra-relativistic particle impact is assessed via the behavior of the metric and energy conditions.
• The model examines whether the collision leads to trapped surface formation, indicating black hole production.
• The analysis focuses on the role of the metric's analytic structure in determining whether the brane remains intact or collapses into a black hole.
• The study uses a toy model to isolate the gravitational dynamics relevant to black hole formation in higher-dimensional spacetimes.

Experimental results

Research questions

• RQ1 Under what conditions does a brane remain stable when struck by an ultra-relativistic particle in the brane-world scenario?
• RQ2 How does the choice of analytic continuation of the metric across the horizon influence brane stability?
• RQ3 Can black hole production occur in high-energy scattering on the brane due to instability induced by particle collisions?
• RQ4 What role does the dimensionality and geometry of the brane-world model play in determining black hole formation?
• RQ5 Is there a critical threshold in energy or curvature that triggers black hole formation in this setup?

Key findings

• The stability of the brane under ultra-relativistic particle collisions is highly dependent on the choice of analytic continuation of the metric across the horizon.
• In the unstable continuation, the brane collapses under high-energy impact, leading to the formation of a trapped surface.
• Black hole production is thus possible in the unstable case, indicating a mechanism for black hole formation in brane-world models.
• The 3D toy model successfully reproduces key features of black hole production in higher-dimensional gravity.
• The results suggest that black hole formation in brane-world scenarios is not generic but contingent on specific geometric and analytic properties of the spacetime solution.
• The study provides a framework for assessing black hole production in more complex brane-world models based on metric continuity conditions.