## What is General Theory of Relativity?

General relativity, or the general theory of relativity, is the geometric theory of gravity published by Albert Einstein in 1916, and is the theory today thought to describe gravity in modern physics. It generalizes general relativity, special relativity, and Newton’s law of universal gravitation, allowing gravity to be described in space and time or space-time. The main difference of this theory from Newton’s theory of gravity is that it explains gravity not with a force arising from the masses of objects, but with the curvature of space. According to the general theory of relativity, the mass causes the space it is in to bend, and free objects moving between two points (with no force acting on them) follow the shortest path in between.

Since it is very difficult to visualize the bending of three-dimensional space, let’s explain exactly what curved space means with a simple example: The surface of a sphere is a two-dimensional curved space. On any circle dividing the sphere into two equal parts, take two points close to each other and draw two parallel lines from these points perpendicular to the circle. The distance between the two lines will decrease over time and they will intersect at some point. The fact that two lines that were originally parallel to each other later intersect is a result of the curvature of space. Light rays moving in this space will follow the lines you draw – according to the general theory of relativity.

The general theory of relativity is supported by many empirical data. For example, the shifts observed in Mercury’s orbit are predicted with great precision by the general theory of relativity. The fact that light is affected by the gravitational field also confirms the general theory of relativity.

**Geometry of Newtonian gravity**

At the core of classical mechanics lies the combination of the free (or accelerated) motion of a body’s motion and the deviations from this free motion. These deviations are caused by the existence of external forces acting on the body and the definition of the force is given by Newton’s second law. The second law states that the net force acting on an object will be the product of the object’s inertial mass and its acceleration. The inertial motion of the object depends on the geometry of space and time: As a standard, free-moving objects move along straight lines with a constant velocity in the reference frames of classical mechanics. In today’s terminology, these paths of objects in curved space-time are called geodesics. Rather, one would expect inertial motions defined by observing and tolerating external forces (such as electromagnetism and friction), as well as a time coordinate, to be used to determine the geometry of space. But as soon as gravity kicks in, there is uncertainty. According to Newton’s law of universal gravitation and the independently verified Eötvös experiment and its successors, free fall has a universality. (also known as the universal equation of inert and passive gravitational mass or the weak equality principle): the trajectory of the test object in free fall depends only on its position and initial velocity, but not on material properties. A simplified version of this is embodied in Einstein’s elevator experiment, in the figure shown to the right. For an observer in a small closed room, it is not possible to decide whether the room is in empty space in a gravitationally stationary or gravitationally-generating and accelerating rocket, by mapping its trajectories like an object dropped down. Considering the universality of free fall, there is no observable difference between inertial motion and motion under gravitational force. This supports the definition of a new class of inertial motion called free-falling bodies under the influence of gravity. The new class of preferred motions also explains the geometry of space and time in mathematical terms. It is a geodetic motion associated with a special connection that depends on the degree of change of a gravitational potential. Space in this structure still has a typical Euclidean geometry. But spacetime as a whole is more complex. As can be demonstrated using a simple thought experiment following the free-fall trajectories of different test particles, the result of transporting space-time vectors (such as time vectors) that can represent a particle’s velocity will vary with the particle’s trajectory; mathematically speaking, the Newtonian relation cannot be integrated. From this it can be deduced that spacetime is curved. The result is a geometric equation of Newtonian gravity using only covariate concepts, i.e. a valid definition desired in any coordinate system. In this geometric definition, tidal effects are related to the relative acceleration of free-falling bodies—the derivative of the coupling showing how the presence of mass changes the geometry.

According to general relativity, an object in a gravitational field behaves similarly to an object accelerating in a closed box. For example, the observer inside the rocket (left) and the observer on Earth (right) perceive the ball’s fall as the same. This is because the acceleration of the rocket creates the same relative force.

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