Analysis of a regular black hole in Verlinde's gravity

This work focuses on the examination of a regular black hole within Verlinde's emergent gravity, specifically investigating the Hayward-like (modified) solution. The study reveals the existence of three horizons under certain conditions, i.e., an event horizon and two Couchy horizons. Our results indicate regions which phase transitions occur based on the analysis of heat capacity and Hawking temperature. To compute the latter quantity, we utilize three distinct methods: the surface gravity approach, Hawking radiation, and the application of the first law of thermodynamics. In the case of the latter approach, it is imperative to introduce a correction to ensure the preservation of the Bekenstein-Hawking area law. Geodesic trajectories and critical orbits (photon spheres) are calculated, highlighting the presence of three light rings. Additionally, we investigate the black hole shadows. Furthermore, the quasinormal modes are explored using third- and sixth-order WKB approximations. In particular, we observe stable and unstable oscillations for certain frequencies. Finally, in order to comprehend the phenomena of time-dependent scattering in this scenario, we provide an investigation of the time-domain solution.