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arXiv · 2404.14881

Nonsingular, lump-like, scalar compact objects in $(2+1)$-dimensional Einstein gravity

Roberto V. Maluf·Gerardo Mora-Pérez·Gonzalo J. Olmo·Diego Rubiera-Garcia
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Abstract

We study the space-time geometry generated by coupling a free scalar field with a non-canonical kinetic term to General Relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions in static and circularly symmetric scenarios, we classify the various types of solutions and focus on a branch that yields asymptotically flat geometries. We show that the solutions within such a branch can be divided in two types, namely, naked singularities and nonsingular objects without a center. In the latter, the energy density is localized around a maximum and vanishes only at infinity and at an inner boundary. This boundary has vanishing curvatures and cannot be reached by any time-like or null geodesic in finite affine time. This allows us to consistently interpret such solutions as nonsingular, lump-like, static compact scalar objects, whose eventual extension to the $(3+1)$-dimensional context could provide structures of astrophysical interest.

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Roberto V. Maluf, Gerardo Mora-Pérez, Gonzalo J. Olmo, Diego Rubiera-Garcia. 2024-04-23. Nonsingular, lump-like, scalar compact objects in $(2+1)$-dimensional Einstein gravity. https://doi.org/10.3390/universe10060258

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