both possibilities $\lambda > 0$, $\lambda < 0$ for completeness. The internal geometry is matched to the external geometry at the surface of the star $r = R$. The line element of the internal solution is given by the metric coefficients $A^{-}(r)$, $B^{-}(r)$ that are determined by [@Ger-Maar:2001:]

$$A^{-}(r) = \frac{\Delta(R)}{\left(1+p(r)/\varrho\right)}\label{EQamin}$$

and $$\left(B^{-}(r)\right)^2 = \frac{1}{\Delta^{2}(r)} = \left[1-\frac{2G M}{r}\left(\frac{r}{R}\right)^3 \left(1+\frac{\varrho}{2\lambda}\right)\right]^{-1},$$ where $M = \frac{4}{3}\pi\varrho R^3$.

The pressure radial profile is given by $$\frac{p(r)}{\varrho} = \frac{\left[\Delta(r) - \Delta(R)\right]\left(1 + \varrho/\lambda\right)}{3\Delta(R) - \Delta(r) + \left[3\Delta(R) - 2\Delta(r)\right]\left(\varrho/\lambda\right)}.$$ For $r = R$, there is $p(r)/\varrho = 0$. The maximum of the pressure profile is at $r = 0$.

The reality condition on the metric coefficient $B^{-}(r)$ (taken at $r = R$) implies a relation between $\lambda$, $\varrho$ and $R$ that can be expressed in the form $$\label{EQRm2GM}
      \frac{G M}{R-2G M} \geq \frac{\varrho}{\lambda}.$$

Considering the restriction $R > 2 G M$ ($R < 2 G M$), we can see that the reality condition (\[EQRm2GM\]) is satisfied for all $\lambda < 0$ (forbidden for all $\lambda > 0$), while for positive tension $\lambda > 0$ (negative tension $\lambda < 0$), we obtain a limit on the positive (negative) tension given by [@Ger-Maar:2001:] $$\lambda \geq \left(\frac{R - 