# The portrait of eikonal instability in Lovelock theories

## TL;DR

This paper provides a comprehensive analysis of eikonal instabilities in black holes and branes within the most general Lovelock theories, combining analytical and numerical methods to map instability regions across parameter spaces.

## Contribution

It extends previous studies by analyzing the full parameter space of Lovelock theories, offering both analytical inequalities and numerical instability regions with accessible code.

## Key findings

- Analytical inequalities for stability regions
- Numerical maps of eikonal instability regions
- Provision of Mathematica code for parameter exploration

## Abstract

Perturbations and eikonal instabilities of black holes and branes in the Einstein-Gauss-Bonnet theory and its Lovelock generalization were considered in the literature for several particular cases, where the asymptotic conditions (flat, dS, AdS), the number of spacetime dimensions $D$, non-vanishing coupling constants ($\alpha_1$, $\alpha_2$, $\alpha_3$ etc.) and other parameters have been chosen in a specific way. Here we give a comprehensive analysis of the eikonal instabilities of black holes and branes for the \emph{most general} Lovelock theory, not limited by any of the above cases. Although the part of the stability analysis is performed here purely analytically and formulated in terms of the inequalities for the black hole parameters, the most general case is treated numerically and the accurate regions of instabilities are presented. The shared Mathematica(R) code allows the reader to construct the regions of eikonal instability for any desired values of the parameters.