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It is known that a smooth LTB model cannot have a positive apparent centralacceleration. Using a local Taylor expansion method we study the low-redshiftconditions to obtain an apparent negative deceleration parameter $q^{app}(z)$derived from the luminosity distance $D_L(z)$ for a central observer in a LTBspace, confirming that central smoothness implies a positive centraldeceleration. Since observational data is only available at redshift greaterthan zero we find the critical values of the parameters defining a centrallysmooth LTB model which give a positive apparent acceleration at $z>0$,providing a graphical representation of the conditions in the$q_0^{app},q_1^{app}$ plane, which are respectively the zero and first orderterms of the central Taylor expansion of $q^{app}(z)$. We finally derive acoordinate independent expression for the apparent deceleration parameter basedon the expansion of the relevant functions in red-shift rather than in theradial coordinate.  We calculate $q^{app}(z)$ with two different methods to solve the nullgeodesic equations, one based on a local central expansion of the solution interms of cosmic time and the other one using the exact analytical solution interms of generalized conformal time. %The expansion of the solution in terms ofcosmic time is quite useful also for other applications requiring foliation %ofspace-time in space-like hyper-surfaces, such as spatial averaging, which ismuch more difficult to study using the %analytical solution in terms of thegeneralized conformal time coordinate.

Conditions for low-redshift positive apparent acceleration in smooth inhomogeneous models