General Relativity, formulated by Albert Einstein in 1915, is a theory of gravitation that revolutionized our understanding of space, time, and gravity. Unlike Newton's theory of gravitation, which treated gravity as a force between masses, General Relativity posits that gravity is a result of the curvature of spacetime caused by the presence of mass and energy. This chapter serves as an introduction to the fundamental principles of General Relativity and the key concepts that underpin this theory.
One of the central ideas of General Relativity is the equivalence principle, which asserts that there is no distinguishable difference between acceleration due to gravity and acceleration due to other forces. This insight led Einstein to the realization that gravity could be described not as a force, but as a manifestation of the curvature of spacetime. Spacetime, a four-dimensional continuum, is distorted by mass and energy, and this curvature dictates how objects move within it. Objects follow the "straightest" possible paths, known as geodesics, which are curved in the presence of massive objects.
Another cornerstone of General Relativity is the concept of curved spacetime. The presence of mass and energy alters the fabric of spacetime, much like a heavy ball placed on a stretched rubber sheet deforms the sheet's surface. The more massive an object is, the more it warps spacetime. This warping of spacetime is what we perceive as gravity. For example, the Earth orbits the Sun not because the Sun exerts a force on Earth in the traditional sense, but because the Sun's mass curves spacetime, and the Earth follows the geodesic path within that curvature.