been shown to be accurate. Around a spherically symmetric object, the Newtonian theory of gravity predicts that objects will be physically accelerated towards the center on the object by the rule where G is Newton's Gravitational constant, M is the mass of the gravitating object, r is the distance to the gravitation object, and is a unit vector identifying the direction to the massive object. In the weak-field approximation of general relativity, an identical coordinate acceleration must exist. For the Schwarzschild solution (which is the simplest possible spacetime surrounding a massive object), the same acceleration as that which (in Newtonian physics) is created by gravity is obtained when a constant of integration is set equal to 2MG/c2). For more information, see Deriving the Schwarzschild solution. Transition from Newtonian mechanics to general relativity Some of the basic concepts of general relativity can be outlined outside the relativistic domain. In particular, the idea that mass/energy generates curvature in space and that curvature affects the motion of masses can be illustrated in a Newtonian setting. General relativity generalizes the geodesic equation and the field equation to the relativistic realm in which trajectories in space are replaced with Fermi–Walker transport along world lines in spacetime. The equations are also generalized to more complicated curvatures. Transition from special relativity to general relativity The basic structure of general relativity, including the geodesic equation and Einstein field equation, can be obtained from special relativity by examining the kinetics and dynamics of a particle in a circular orbit about the earth. In terms of symmetry, the transition involves replacing global Lorentz covariance with local Lorentz covariance. Conservation of energy–momentum In classical mechanics, conservation laws for energy and momentum are handled separately in the two principles of conservation of energy and conservation of momentum. With the advent of special relativity, these two conservation principles were united through the concept of mass-energy equivalence. Mathematically, the general relativity statement of energy–momentum conservation is: where is the stress–energy tensor, the comma indicates a partial derivative and the semicolon indicates a covariant derivative. The terms involving the Christoffel symbols are absent in the special relativity statement of energy–momentum conservation. Unlike classical mechanics and special relativity, it is not usually possible to unambiguously define the total energy and momentum in general relativity, so the tensorial conservation laws are local statements only (see ADM energy, though). This often causes confusion in time-dependent spacetimes which apparently