Effects of Relativistic Heat Flux on Advection-Dominated Accretion Flows Around Schwarzschild Black Holes

We develop a general relativistic, one-dimensional model of advection-dominated accretion flows (ADAFs) around Schwarzschild black holes, incorporating the full viscous shear tensor and all components of the heat flux four-vector. This framework allows for a consistent treatment of anisotropic conduction in curved space-time. Our results highlight the dom inant role of radial and temporal heat flux components, while the vertical component, which is commonly emphasised in earlier studies, has negligible impact. Thermal conduction is found to significantly modify the disc structure in inner regions, enhancing thermal pressure and vertical expansion while reducing density. At larger radii, conduction effects fade and disc properties converge. The energy budget remains advection-dominated, with viscous heating exceeding radiative cooling and a substantial portion of energy carried inward by advection. Additionally, stronger inflow and higher angular momentum intensify all thermal processes through enhanced compression and shear. Our results affirm that realistic modelling of ADAFs around black holes demands inclusion of both anisotropic and fully general relativistic effects in heat transport and viscosity. We further show that the accretion flow exhibits transonic behaviour, characterized by a relativistic Mach number that increases inward and crosses unity as the flow approaches the black hole, marking the transition from subsonic to supersonic regimes. Moreover, the weak Coulomb coupling in such radiatively inefficient flows leads naturally to a two-temperature plasma, in which ions and electrons evolve quasi-independently, with the ion component dominating the thermodynamic structure.