Primary hairs may create echoes

TL;DR

This paper demonstrates that black holes with primary Proca-Gauss-Bonnet hair can naturally produce echoes in their ringdown signals due to modifications in the effective potential, without external matter or exotic physics.

Contribution

It introduces a new mechanism where primary hair on black holes causes echoes in gravitational wave signals, expanding understanding of potential observable signatures in modified gravity.

Findings

Primary hair modifies the effective potential creating a second peak.

Echoes appear in the quasinormal spectrum for scalar and Dirac fields.

The mechanism does not require external matter or exotic horizon physics.

Abstract

In most scenarios studied so far, the appearance of echoes in the ringdown signal requires modifications external to the black hole itself, such as the presence of matter in the near-horizon region, quantum field clouds, or exotic compact objects like wormholes that effectively introduce additional peaks in the effective potential. In this work we show that echoes can naturally arise in a different setting: black holes endowed with primary Proca-Gauss-Bonnet hair. We demonstrate that the primary hair modifies the effective potential in such a way that a second peak is formed, giving rise to late-time echoes without invoking any external environment or exotic horizon-scale physics. Using both the higher-order WKB method with Pad\'e resummation and time-domain integration, we compute the quasinormal spectrum for scalar and Dirac test fields and show the appearance of these echoes. Our results highlight a novel mechanism by which primary hairs alone can leave observable imprints on the ringdown signal of black holes in modified gravity.