NR/HEP: roadmap for the future

TL;DR

The NR/HEP roadmap paper outlines how numerical relativity, higher-dimensional gravity, and holography converge to address strong-field and high-energy phenomena. It identifies TeV-scale gravity and AdS/CFT as two principal frameworks where NR can yield testable predictions, while highlighting boundary-value challenges and the need for robust numerical tools in $D>4$. The document surveys higher-dimensional black-hole physics, trans-Planckian scattering, and alternative gravity theories, proposing concrete directions—new exact solutions, stability analyses, and hybrid perturbative–numerical approaches—that could illuminate collider signatures, holographic dynamics, and fundamental gravity. Overall, it presents a multi-angled roadmap combining mathematical, physical, and computational advances to advance understanding of gravity in regimes where nonlinear and quantum effects intertwine.

Abstract

Physics in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high energy physics. The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the gravitational field equations, which now allows highly nonlinear phenomena to be tamed. Numerical relativity simulations, originally developed to understand strong field astrophysical processes, could prove extremely useful to understand high-energy physics processes like trans-Planckian scattering and gauge-gravity dualities. We present a concise and comprehensive overview of the state-of-the-art and important open problems in the field(s), along with guidelines for the next years. This writeup is a summary of the "NR/HEP Workshop" held in Madeira, Portugal from August 31st to September 3rd 2011.

Figures (4)

• Figure 1: A proposed "phase diagram" of different regimes for gravitational scattering (from Giddings:2011xs).
• Figure 2: Left: predicted QCD multijet background with its uncertainties (the shaded band), data, and several reference black-hole signal benchmarks, as a function of $S_T$ in the final state with the multiplicity of 5 or more particles. Right: model-independent upper limits at 95% confidence level on a cross section of a new physics signal decaying in the final state with 5 or more particles, as a function of the minimum $S_T$ requirement. From CMSBH.
• Figure 3: Limits on the minimum black-hole mass as a function of the fundamental Planck scale for a few semi-classical benchmark models with and without black hole rotation and non-evaporating remnant. Note that the semi-classical approximation used in setting these limits is not expected to hold for black hole masses so close to the Planck scale, so this plot should be considered as illustration only. From CMSBH.
• Figure 4: Left: The energy density $\mathcal{E}$ of two colliding sheets of matter in a holographic CFT. Right: the transverse and longitudinal pressures $\mathcal{P}_{\perp}$ and $\mathcal{P}_{||}$ at $z = 0$. The colliding sheets are translationally invariant in the two directions orthogonal to the collision axis $z$. The scale $\mu$ sets the energy density per unit area of the sheets. The sheets propagate at the speed of light and collide at time $v = 0$. Near $v = 0$ the system is very far-from-equilibrium and the transverse and longitudinal pressures are very different. However, after a few units of $1/\mu$ the dynamics of the debris left over from the collision is governed by viscous hydrodynamics with increasing accuracy as time progresses.