q = - \frac{3G M R \varrho}{\lambda} = \frac{3G \mathcal{M}R}{\left(1 - \lambda/\varrho\right)},$$

$$\frac{\lambda}{\varrho} = 1-\frac{3G\mathcal{M}R}{q},$$

the internal metric can be expressed in terms of the external parameters $\mathcal{M}$, $R$, $q$ and a new parameter $$\label{EQX}
      X \equiv \frac{q}{3G \mathcal{M}R}$$ in the form $$\left(B^{-}(r)\right)^2 = \Delta^{-2}(r) = \left[1 - \frac{2G\mathcal{M}r^2}{R^3} \left(1 - \frac{3}{2}X\right)\right]^{-1}$$ $$A^{-}(r) = \frac{\Delta(R)\left[3\Delta(R)\left(2X - 1\right)+\Delta(r)\left(1 - 3X\right)\right]}{2\Delta(R)\left(2X - 1\right) - \Delta(r) X}.$$ The pressure profile can be expressed in the form

$$\frac{p(r)}{\varrho} = \frac{\left[\Delta(r) - \Delta(R)\right] \left(2X - 1\right)}{\left[3\Delta(R) - \Delta(r)\right] \left(X - 1\right) + \left[3\Delta(R) - 2\Delta(r)\right] X}.$$

The observational restrictions obtained from the measurements outside the neutron star then can be applied to the internal parameters using the relations (\[EQq\])–(\[EQX\]).

Limit on existence of uniform density stars
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The limit on the existence of the uniform density spherical configuration is related to their compactness and is determined by the condition of pressure finiteness in their center. We then find the limit on compactness of the star given in terms of the gravitational mass related to the internal geometry [@Ger-Maar:2001:]: $$\label{EQGMR}
      \frac{G M}{R}\leq \frac{4}{9}\left[\frac{1 + \frac{5}{4}\frac{\varrho}{\lambda}}{\left(1 + \frac{\varrho}{\lambda}\right)^2}\right].$$ The lowest order correction is given by $$\frac{G M}{R}\leq \frac{4}{9}\left[1 - \frac{3}{4}\frac{\varrho}{\lambda}\right].$$ Using the external gravitational mass parameter $\mathcal{M}$, 