Primordial black hole evolution in tensor-scalar cosmology
Ted Jacobson
TL;DR
The paper analyzes primordial black hole evolution in tensor-scalar cosmology where a changing scalar field $\varphi$ couples to matter. By exploiting scale separation, it shows the scalar perturbation at the horizon can follow the cosmological evolution, with explicit horizon-regular solutions in both Schwarzschild and Kerr spacetimes, so the horizon value tracks $\varphi_c(t)$ with negligible lag. It then demonstrates that the black hole mass in the Einstein frame remains essentially constant under adiabatic changes, while in the Jordan-Fierz frame the mass grows as $A^{-1}(\varphi)$, leading to potential substantial mass magnification if $A(\varphi)$ evolves over cosmic time. This has important implications for Hawking evaporation and the PBH mass spectrum in the Jordan frame, since the frame-dependent luminosity and horizon/Jeans mass scales are tied to the conformal coupling $A(\varphi)$ and the parameters $\alpha=d\ln A/d\varphi$.
Abstract
A perturbative analysis shows that black holes do not remember the value of the scalar field $φ$ at the time they formed if $φ$ changes in tensor-scalar cosmology. Moreover, even when the black hole mass in the Einstein frame is approximately unaffected by the changing of $φ$, in the Jordan-Fierz frame the mass increases. This mass increase requires a reanalysis of the evaporation of primordial black holes in tensor-scalar cosmology. It also implies that there could have been a significant magnification of the (Jordan-Fierz frame) mass of primordial black holes.