Black Holes and Scalar Propagation in Three-Dimensional Einstein--Gauss--Bonnet Gravity
Abstract
We derive an analytic black-hole family in three-dimensional scalar--tensor Einstein--Gauss--Bonnet gravity with positive coupling. A single implicit equation determines the static circular metric and a scalar linear in time. We show that these solutions exhaust regular nonextremal exteriors with the stated AdS boundary conditions and a fixed nonzero coefficient of time in the scalar. The coupled metric and scalar perturbations have one propagating degree of freedom. On one branch, its kinetic coefficient is positive, its equation is hyperbolic throughout the exterior, and its bulk spatial energy is positive for perturbations of compact support. Scalar signals can cross the metric horizon outward, so exterior evolution needs information from the interior. For linear perturbations with the original metric and scalar boundary values fixed, nonzero compact initial master displacements with zero velocity can evolve only until their first contact with the AdS boundary. We derive this restriction from the original metric and scalar equations.
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BibTeX
@misc{suryaatmadja2026black,
title = {{Black Holes and Scalar Propagation in Three-Dimensional Einstein--Gauss--Bonnet Gravity}},
author = {Cendikiawan Suryaatmadja},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28158},
eprint = {2609.28158},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28158},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Black Holes and Scalar Propagation in Three-Dimensional Einstein--Gauss--Bonnet Gravity
AU - Cendikiawan Suryaatmadja
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.28158
UR - https://arxiv.org/abs/2609.28158
AB - We derive an analytic black-hole family in three-dimensional scalar--tensor Einstein--Gauss--Bonnet gravity with positive coupling. A single implicit equation determines the static circular metric and a scalar linear in time. We show that these solutions exhaust regular nonextremal exteriors with the stated AdS boundary conditions and a fixed nonzero coefficient of time in the scalar. The coupled metric and scalar perturbations have one propagating degree of freedom. On one branch, its kinetic coefficient is positive, its equation is hyperbolic throughout the exterior, and its bulk spatial energy is positive for perturbations of compact support. Scalar signals can cross the metric horizon outward, so exterior evolution needs information from the interior. For linear perturbations with the original metric and scalar boundary values fixed, nonzero compact initial master displacements with zero velocity can evolve only until their first contact with the AdS boundary. We derive this restriction from the original metric and scalar equations.
ER -