<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>r</mml:mi> </mml:math> -mode stabilization in rotating hyperon-rich neutron stars and its implications for GW190814

The GW190814 event, involving a black hole of mass $22.2$--$24.3 M_{\odot}$ and a compact object of mass $2.50$--$2.67 M_{\odot}$, challenges our understanding of the mass gap between the heaviest neutron stars and the lightest black holes. If the secondary is a neutron star exceeding $2.5 M_{\odot}$, hyperons are likely to appear in its core, softening the equation of state. Rapid rotation can offset some of this softening, enabling higher maximum masses, but it may simultaneously excite the Chandrasekhar--Friedman--Schutz $r$-mode instability. Bulk viscosity arising from nonleptonic weak interactions in hyperonic matter provides an efficient damping mechanism that can stabilize such configurations. In this work, we investigate the combined effects of rotation, thermal evolution, and hyperon-induced bulk viscosity on the stability of massive neutron stars. We demonstrate a direct connection between the suppression of $r$-mode instabilities and the long-term dynamical stability of hyperon-rich stars, offering a plausible interpretation of the GW190814 secondary as a rapidly rotating, hyperon-rich neutron star rather than a low-mass black hole. Our unified framework extends beyond previous studies restricted to static equations of state or extreme viscous damping assumptions, providing new insights into the stability of massive, exotic neutron star configurations.