Thermodynamic, Optical, and Orbital Signatures of Regular Asymptotically Flat Black Holes in Quasi-Topological Gravity

Abstract

This study provides an analytic and numerical characterization of a class of regular, asymptotically flat black holes described by a deformed static spherical metric. The model is grounded in a four-dimensional non-polynomial quasi-topological framework in which higher-curvature corrections remain dynamically nontrivial while the static spherical sector retains a reduced-order structure, enabling tractable black-hole solutions with regular cores. Starting from the existence conditions of horizons and regularity, the allowed parameter domain and the extremal bound are derived. Hawking temperature, shadow radius, photon-ring Lyapunov exponent, and ISCO binding efficiency are then analyzed across the physically allowed parameter space. We further extend the analysis to Novikov--Thorne thin-disk accretion by deriving the flux kernel, effective-temperature profile, and bolometric luminosity scaling, and by providing representative numerical datasets for these quantities. A coherent trend emerges: increasing the deformation parameter drives the solution away from Schwarzschild behavior, reducing temperature, shadow size, and photon-orbit instability rate while enhancing orbital binding efficiency and accretion luminosity; increasing the exponent $ν$ suppresses deformation effects and restores Schwarzschild-like observables. These results provide a compact phenomenological map linking horizon structure, thermodynamics, optical signatures, dynamical instability, and thin-disk accretion diagnostics in this regular black-hole family.

Figures (11)

• Figure 1: Reduced Hawking temperature $\tilde{T}=8\pi M T_H$ versus $\mu$ at fixed $\nu=2$, for selected $\beta$. Increasing $\mu$ lowers $\tilde{T}$, and the suppression is stronger for larger deformation parameter $\beta$.
• Figure 2: Reduced Hawking temperature $\tilde{T}=8\pi M T_H$ versus $\nu$ at fixed $\mu=3$, for selected $\beta$. For fixed $\mu$ and $\beta$, $\tilde{T}$ increases with $\nu$ and approaches the Schwarzschild value $\tilde{T}\to1$.
• Figure 3: Reduced shadow radius $\tilde{R}_{\rm sh}=R_{\rm sh}/(2M)$ versus $\mu$ at fixed $\nu=2$, for selected $\beta$. Larger $\mu$ decreases the shadow size, with a stronger effect at larger $\beta$.
• Figure 4: Reduced shadow radius $\tilde{R}_{\rm sh}$ versus $\nu$ at fixed $\mu=3$, for selected $\beta$. Increasing $\nu$ restores the Schwarzschild value from below.
• Figure 5: Reduced shadow radius $\tilde{R}_{\rm sh}$ versus deformation parameter $\beta$ at fixed $(\mu,\nu)=(3,2)$. The dashed vertical line marks the extremal bound $\beta_c\approx0.385$; approaching extremality reduces the shadow radius.