Accretion and Neutrino-Motivated Thermal Diagnostics of Thermodynamically Reconstructed Black Holes from Three-Parameter Generalized Entropy

Abstract

We study accretion and thermal diagnostics motivated by neutrino processes for a static black hole reconstructed from a three-parameter generalized entropy. The construction is thermodynamic by design: the entropy deformation is not mapped to a radial-coordinate redefinition or to a prescribed Reissner--Nordström-like correction. Instead, the generalized entropy fixes the horizon response factor ${\Xi }_h=d{S}_G/dS{|}_{S_h}$. The effective exterior geometry is then reconstructed by requiring its surface-gravity temperature to reproduce the generalized thermodynamic temperature. As a result, the metric preserves the horizon area and the Schwarzschild asymptotics, and reduces smoothly to Schwarzschild when ${\Xi }_h\to 1$. The entropy response is encoded in ${\lambda }_G=1/{\Xi }_{\mathrm{h}}-1$, whereas the exterior radial dependence requires an additional localization prescription. The detailed accretion analysis is performed for the power-law family $h(x)=x^{-p}$, with $p\ge 2$. Within this reconstruction family, positive ${\lambda }_G$ moves the photon sphere and ISCO inward, decreases the critical shadow scale, raises the radiative efficiency, and concentrates the energy release toward the inner disk, while negative ${\lambda }_G$ produces the opposite trend. A complementary comparison with exponential and rational localization functions shows that this qualitative ordering is preserved for the profiles tested, although the magnitude of the strong-field shifts remains profile-dependent. Finally, the neutrino-motivated thermal sector ...

arXiv comment20 pages, 6 figures. Published in: JHEAp