Cosmological accretion onto braneworld black holes: a relativistic treatment
Higher-dimensional black holes have been extensively studied over the years, primarily from heuristic and fundamental perspectives or within the context of holographic applications. However, their interaction with ordinary matter confined to the brane is also of particular interest in cosmology. In this work, we revisit accretion within the Randall-Sundrum type II framework, employing the covariant Shiromizu-Maeda-Sasaki formalism together with the Gauss-Codazzi and energy conservation equations. We analyse information propagation in the cosmological fluid and implement a fully relativistic treatment of accretion following Michel's prescription. We find that braneworld effects play a significant role in the early Universe, strongly impacting the evolution of light primordial black holes (PBHs). In particular, the mapping between initial conditions and present-day PBH populations is substantially modified by an extended phase of early-time accretion that is significantly more efficient than previously found. For certain regions of parameter space, PBHs that could contribute to the present-day dark matter abundance may have formed with masses below the effective four-dimensional Planck scale. The discrepancy between our black hole masses and the most optimistic previous estimates grows as $t^{0.34}$-a significant difference that reaches up to several orders of magnitude by the end of the strong-accretion epoch, particularly for black holes that form early and for small values of the fundamental Planck scale $M_5$, reaching up to $\sim 10^5$ for the smallest $M_5$ permitted by observations.