Black Hole Bound on the Number of Species and Quantum Gravity at LHC

TL;DR

The paper argues that a large number N of gravitationally coupled species enforces a bound linking the Planck scale to the species mass, yielding a reduced gravitational cutoff $\Lambda_G \approx M_P/\sqrt{N}$. It presents three lines of evidence—non-perturbative black-hole lifetimes, perturbative central-charge considerations, and maximal-temperature bounds—that support a single-cutoff gravity regime below $\Lambda_G$. It illustrates realizations in ADD and RS-type setups where $M_P^2$ scales with $N$ (e.g., $M_P^2 \sim N k^2$ or $M_P^2 \sim N \Lambda_G^2$), connecting the bound to extra dimensions and holography. The work further analyzes TeV-scale black-hole phenomenology, arguing that micro BHs preserve a memory of their origin species and predominantly decay within their own sector, implying locality in species space and distinctive collider signatures.

Abstract

In theories with a large number N of particle species, black hole physics imposes an upper bound on the mass of the species equal to M_{Planck}/\sqrt{N}. This bound suggests a novel solution to the hierarchy problem in which there are N \approx 10^{32} gravitationally coupled species, for example 10^{32} copies of the Standard Model. The black hole bound forces them to be at the weak scale, hence providing a stable hierarchy. We present various arguments, that in such theories the effective gravitational cutoff is reduced to Λ_G \approx M_{Planck}/\sqrt{N} and a new description is needed around this scale. In particular black-holes smaller than Λ_G^{-1} are already no longer semi-classical. The nature of the completion is model dependent. One natural possibility is that Λ_G is the quantum gravity scale. We provide evidence that within this type of scenarios, contrary to the standard intuition, micro black holes have a (slowly-fading) memory of the species of origin. Consequently the black holes produced at LHC, will predominantly decay into the Standard Model particles, and negligibly into the other species.

Figures (2)

• Figure 1: We consider as possible solution of the hierarchy problem the existence of $10^{32}$ particle species interacting gravitationally.
• Figure 2: A box filled with radiation violates the entropy bound prematurely.