No, Einstein's field equations, which form the foundation of general relativity, do not change the fact that massive objects attract each other, as described by Newton's law of universal gravitation. In fact, Einstein's theory of general relativity builds upon and extends Newtonian gravity, providing a more comprehensive and accurate description of gravitational phenomena.
In Newtonian gravity, the force of gravity between two massive objects is given by the equation F = (G * m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
Einstein's general theory of relativity, on the other hand, describes gravity as the curvature of spacetime caused by the presence of mass and energy. In this theory, the motion of objects is determined by the geometry of spacetime, which is influenced by the distribution of matter and energy. The precise mathematical equations that govern the curvature of spacetime are encapsulated in Einstein's field equations.
When these field equations are solved for a particular distribution of mass and energy, they yield the metric of spacetime, which determines the paths of objects moving within that spacetime. In regions of spacetime with a significant mass or energy density, the solutions to the field equations result in a curvature that leads to the familiar effects of gravity, such as the attraction between massive objects.
Therefore, Einstein's field equations do not contradict or negate the idea of gravitational attraction between massive objects but provide a deeper and more precise understanding of the underlying mechanisms behind this attraction.