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The strongest existing constraints on primordial black holes with masses inthe range of $m_{\rm BH} \sim 10^{15}-10^{17} \, {\rm g}$ have been derivedfrom measurements of the local cosmic-ray electron-positron flux by Voyager 1,and MeV-scale gamma-ray observations of the Inner Galaxy by COMPTEL andINTEGRAL. In this paper, we evaluate the sensitivity of future MeV-scalegamma-ray telescopes such as e-ASTROGAM or AMEGO to Hawking radiation. We showthat such an instrument would be able to provide the strongest constraints onblack holes in the mass range of $m_{\rm BH} \sim (0.6-20) \times 10^{16} \,{\rm g}$, typically exceeding current constraints by approximately two ordersof magnitude. In scenarios in which the observed 511 keV excess is the resultof Hawking radiation, we find that e-ASTROGAM or AMEGO would not only be ableto detect the Hawking radiation from the Inner Galaxy, but could preciselymeasure the abundance and mass distribution of the black holes responsible forthis signal.

The Sensitivity of Future Gamma-Ray Telescopes to Primordial Black Holes