Cosmological Constant in Low Energy $d = 4$ String Leads to Naked Singularity

TL;DR

This paper shows that in four-dimensional non-critical string theories, a non-zero cosmological constant causes naked singularities, constraining the cosmological constant to an extremely small value to avoid such singularities.

Contribution

It demonstrates that non-critical string models in four dimensions inherently lead to naked singularities unless the cosmological constant is nearly zero.

Findings

Curvature scalar becomes singular if $ e 0$

Naked singularities are unavoidable for non-zero $",

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Abstract

In the sigma model approach, the $\beta$-function equations for non critical strings contain a term which acts like a tree level cosmological constant, $\Lambda$. We analyse the static, spherically symmetric solutions to these equations in $d = 4$ space time and show that the curvature scalar seen by the strings is singular if $\Lambda \ne 0$. This singularity is naked. Requiring its absence in our universe imposes the constraint $| \Lambda | < 10^{- 120}$ in natural units. {}From another point of view, our analysis implies that low energy $d = 4$ non critical strings lead to naked singularities.