Static spherically symmetric three-form stars

Abstract

We consider interior static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field $$A_{\alpha \beta \gamma }$$ A α β γ , which generates, via the field strength and a potential term, a new component in the total energy-momentum tensor of the gravitational system. We formulate the field equations in Schwarzschild coordinates and investigate their solutions numerically for different equations of state of neutron and quark matter, by assuming that the three-field potential is either a constant or possesses a Higgs-like form. Moreover, stellar models, described by the stiff-fluid, radiation-like, bag model and the Bose–Einstein condensate equations of state are explicitly obtained in both general relativity and three-form gravity, thus allowing an in-depth comparison between the astrophysical predictions of these two gravitational theories. As a general result we find that, for all the considered equations of state, three-form field stars are more massive than their general relativistic counterparts. As a possible astrophysical application, we suggest that the 2.5$$ M_{\odot }$$ M ⊙ mass compact object, associated with the GW190814 gravitational wave event, could be in fact a neutron or a quark star described by the three-form gravity theory.

Traversable wormhole in Einstein 3-form theory with self-interacting potential

“…Our approach does not require an additional fluid or scalar field and as such is "minimal". We remark that 3-form black hole solutions [49,52] and 3-form stellar models [53] have also been discussed.…”

Gravitational Lensing by Traversable Wormholes Supported by Three‐Form Fields

“…Consequently, the three-form fields are also used to study relativistic stars and black holes. [38][39][40] Recently, the three-form wormholes are studied in detail by using the Higgs type three-form potential [41] and the authors in this work have solved the Einstein equation to construct the traversable three-form wormhole. Moreover, they have also studied the location of the photon sphere and the innermost stable circular orbit (ISCO) of the three-form wormholes.…”