Dear Sameh, your question has not implicated the inclusion of extra dimensions in your desired metric , Nevertheless the Minkowskian manifold metric, for instance, is a tensor of rank two in 4 dimensional continuum of space-time i.e. M3+1 while the attributed metrics of Desitter and Ads , Kaluza Klein , string theory etc, extend through extra dimensions, Therefore for instance the proposed metric in Kaluza Klein has been defined on 5-dimensional manifold that  is a generalization of the Minkowskian metric by adding  an extended extra (wrapped) dimension denoted then with 25 ( i.e.5×5 ) entries .In string theories metric splits to ηij ( defined in 1+d dimensional space-time) and hij (metric on world sheet of string). these generalization of metrics depend on the considered  number of spatial dimensions and in fact on the proposed action in the target theory. Therefore in the response to your question i think  there is not an unique concise generalized metric in the realm of physics, However any metric can be defined in differential geometry for any imaginable manifolds and their topologies.

Yet none can gave an 100% acceptable model of the universe. Actually Einstein was right  "The universe is an eternal riddle..."

Thank you for every one here. I am so sorry for my late.

Dear Manouchehr Amiri, thank you for your interesting answer.  Is there a general finite dimension metric, say of dimension n+1, and has the most general coefficient?

Thank you Charles Francis. Would you clarify your sentence ".... is one which satisfies Einstein's equation" I mean why?

Thank you Haradhan Kumar Mohajan

Can you give me any hint to classify the metrics in groups and generalize every collection in one metric.

Sameh Shenawy - All the static/stationary metrics can be generated easily from a general expression. See Appendix A (Equation A17) of the following:

General Relativity: In Acknowledgement Of Professor Gerardus ‘t Hooft, Nobel Laureate,

http://vixra.org/pdf/1409.0072v2.pdf

The geometry of the universe is hyperbolic

Article The hyperbolic geometry of the universe and the wedding of g...

Book The Hyperbolic Universe.

Dear Prof Mankhout

Thank you for your interesting articles. But this is not an answer of that question. 

Dear Professor Shenaway:

I hope that this is answer you want. I believe the most generalized existing metric for spacetime models is the twisted spacetime metric. Such spacetime models extend the generalized Robertson-Walker spacetimes, replacing the warping function by a twisting function which depends not only on the time but also on position of spatial slices.

The metric of general relativity (Schwarzschild metric) cannot explain Hydrogen spectra. The metric of periodic relativity can explain Hydrogen spectra as well as the rotation curves of galaxies. Only most general metric can do this.

Article Hydrogen spectra using Einstein's field equations