The violation of the weak energy condition, Is it generic of spontaneous scalarization ?

TL;DR

This paper investigates whether the spontaneous violation of the weak energy condition is a common feature of scalarization in compact objects, concluding it is not generally true across scalar-tensor theories and models.

Contribution

The study demonstrates through numerical analysis that negative-energy densities are not a universal aspect of spontaneous scalarization in scalar-tensor theories.

Findings

Negative-energy densities are not generic in scalar-tensor theories.

Violations of the weak energy condition are mainly localized at the star's outskirts.

The angular parts of the WEC conditions tend to be slightly violated at the star's edges.

Abstract

It was recently shown by Whinnett & Torres \cite{WT} that the phenomenon of spontaneous scalarization (SC) in compact objects (polytropes) was accompanied also by a {\it spontaneous violation of the weak energy condition} (WEC). Notably, by the encounter of negative-energy densities at several star places as measured by a static observer. Here we argue that the negativeness of such densities is not generic of scalar tensor theories of gravity (STT). We support this conclusion by numerical results within a class of STT and by using three realistic models of dense matter. However, we show that the ``angular parts'' of the additional conditions for the WEC to hold $\rho_{\rm eff} + T^{i ({\rm eff})}_{i} \geq 0$ tend to be ``slightly violated'' at the outskirts of the star.