Newtonian tidal forces and curvature Today in my physics class, my lecturer said something which confused me. He said: 
"Newtonian tidal forces are reinterpreted as a manifestation of curvature in General Relativity". 
Now I know what tidal forces are (an effect of the force of gravity), a good example is the cause of the waves on the ocean because of the tidal forces with the moon. However I do not see how this shows curvature in the GR sense.
 A: Have a look at my answer to How to explain centripetal force in terms or relativity because much of the discussion there is relevant.
Consider what we mean by a tidal force. Suppose you're floating around in space and you arrange a number of marbles around you so they lie on the surface of a perfect sphere. Now monitor the shape of the surface marked out by those marbles. If the shape changes with time from a sphere to an ellipsoid you would conclude that there must be a force acting on the marbles to pull them apart. In the Newtonian interpretation this is the tidal force.
Now consider the GR interpretation, and this is where the discussion of geodesics in the answer I linked above comes in. Each marble follows a geodesic. In flat spacetime geodesics that are originally parallel remain parallel, so if the marbles are initially stationary with respect to each other they remain stationary with respect to each other, and the sphere does not change shape. However if spacetime is curved then initially parallel geodesics may not remain parallel, but can diverge or converge. Because each marble is following a different geodesic, and the geodesics might not remain parallel, the marbles may move apart and the sphere change shape. No force is acting - it's just that the individual marbles are following different geodesics.
And this is (I would guess) what your lecturer means. Newton would see the sphere change shape and conclude there must be a force acting. Einstein would see the sphere change shape and conclude that spacetime was curved.
A: curvature produces  relative acceleration of geodesics because of equation of geodesic deviation (relation between riemann tensor  and relative accleleration of geodesics) and  also newtonian theory of gravity predicts  tide-producing acceleration  which explain two particle with separation x   parallel to r ,cause evaluating relative acceleration  and x prependecular to r ,have a stated amount of relative acceleration  .so relative acceleration caused by curvature ..
But why we use these thing instead of force , you can find the answer in weightlessness , actually there isnt any real force in a free fall particle 
See page 29 and 30
  gravitation mtw
 for tide-producing acceleration  
