On Accretion and Neutrino Investigations of Thermodynamically Reconstructed Black Holes from Three-Parameter Generalized Entropy

Abstract

We study accretion and neutrino-sensitive thermal signatures of 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 $Ξ_h=dS_G/dS|_{S_h}$. 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 $Ξ_h\to1$. The deformation is controlled by $λ_G=1/Ξ_h-1$, while the integer $p\geq2$ determines the radial localization of the near-horizon correction. We compute the photon sphere, critical shadow scale, circular geodesics, ISCO, Novikov--Thorne flux, disk temperature, radiative efficiency, energy-at-infinity luminosity, a redshifted spectral proxy, and neutrino-sensitive temperature moments. In particular, positive $λ_G$ moves the photon sphere and ISCO inward, decreases the shadow scale, raises the radiative efficiency, and concentrates the energy release toward the inner disk. By contrast, negative $λ_G$ produces the opposite trend. Finally, the neutrino sector is modeled conservatively using dimensionless temperature moments instead of a full neutrino-dominated accretion flow or annihilation-deposition calculation. The hierarchy among the $ n=4$, $n=6$, and $n=9$ moments reveals that entropy-induced disk deformation becomes increasingly apparent with higher temperature exponents. Thus, observable changes in compact orbits and thin-disk emission can be directly linked to generalized entropy via the horizon response.