Hawking Radiation in $f(\mathcal{R})$ Gravity: Survival of lighter black holes

Abstract

Einstein's theory of general relativity (GR) has been remarkably successful in describing gravitational phenomena. However, several open questions in modern cosmology and astrophysics (e.g. inflation, dark energy) suggest the need for extensions or modifications to this framework. Modified gravity (MGR) theories, including scalar-tensor models and higher-dimensional approaches, attempt to address these gaps while maintaining consistency with established experimental tests. This work investigates Hawking radiation within an $f(\mathcal{R})$ gravity theory, with $\mathcal{R}$ being scalar curvature, focusing on its implications for primordial black holes (PBHs) as potential dark matter (DM) candidates. Our analysis reveals that PBHs evaporate slowly in MGR compared to GR predictions. Specifically, we find that non-rotating black holes with masses $\sim 5 \times 10^{13}$ g or lower would have survived by the present epoch, depending on the MGR parameter-a mass threshold approximately at least ten times smaller than in GR. This retarded evaporation timeline imposes relaxed new constraints on the viability of PBHs as DM constituents, thereby reshaping the landscape of possible solutions to the DM problem. This motivates further investigation into alternative gravitational theories and their cosmological consequences.