Exact solutions in $\mathcal{R}^{2}$ SUGRA

TL;DR

This paper demonstrates that the bosonic sector of four-dimensional $ ^{2}$ supergravity admits various exact solutions, including black holes, wormholes, and wave spacetimes, with specific conditions on auxiliary fields.

Contribution

It provides explicit analytic solutions in $ ^{2}$ supergravity, highlighting the role of auxiliary fields and their influence on spacetime geometries.

Findings

Existence of pp- and AdS wave solutions

Construction of asymptotically flat and AdS black holes and wormholes

Identification of conditions on auxiliary fields for static solutions

Abstract

This letter is devoted to show that the bosonic sector of the $\mathcal{R}^{2}$-SUGRA in four dimensions, constructed with the F-term, admits a variety of exact and analytic solutions which include, pp- and AdS waves, asymptotically flat and AdS black holes and wormholes, as well as product spacetimes. The existence of static black holes and wormholes implies that a combination involving the Ricci scalar plus the norm of the field strength of the auxiliary two-form $B_{\mu\nu}$, must be a constant. We focus on this sector of the theory which has two subsectors depending on whether such a combination vanishes or not.