Properties of ultracompact particlelike solutions in Einstein-scalar-Gauss-Bonnet theories

Besides scalarized black holes and wormholes, Einstein-scalar-Gauss-Bonnet theories allow also for particlelike solutions. The scalar field of these particlelike solutions diverges at the origin, akin to the divergence of the Coulomb potential at the location of a charged particle. However, these particlelike solutions possess a globally regular metric, and their effective stress-energy tensor is free from pathologies, as well. We determine the domain of existence for particlelike solutions in a number of Einstein-scalar-Gauss-Bonnet theories, considering dilatonic and power-law coupling functions, and we analyze the physical properties of the solutions. Interestingly, the solutions may possess pairs of lightrings, and thus represent ultracompact objects. We determine the location of these lightrings, and study the effective potential for the occurrence of echoes in the gravitational-wave spectrum. We also address the relation of these particlelike solutions to the respective wormhole and black-hole solutions, and clarify the limiting procedure to recover the Fisher solution (also known as the Janis-Newman-Winicour-Wyman solution).

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