Definitions

# Gravitational field

A gravitational field is a model used within physics to explain how gravity exists in the universe. In its original concept, gravity was a force between point masses. Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms of a field model, rather than a point attraction.

In a field model, rather than two particles attracting each other, the particles distort spacetime via their mass, and this distortion is what is perceived subjectively as a "force". In fact there is no force in such a model, rather matter is simply responding to the curvature of spacetime itself.

## In classical mechanics

In classical mechanics, the field is not an actual entity, but merely a model used to describe the effects of gravity. The field can be determined using Newton's law of universal gravitation. Determined in this way, the gravitational field around a single particle is a vector field consisting at every point of a vector pointing directly towards the particle. The magnitude of the field at every point is calculated with the universal law, and represents the force per unit mass on any object at that point in space. The field around multiple particles is merely the vector sum of the fields around each individual particle. An object in such a field will experience a force that equals the vector sum of the forces it would feel in these individual fields.

Because the force field is conservative, there is a scalar potential energy at each point in space associated with the force fields, this is called gravitational potential.

## In general relativity

In general relativity the gravitational field is determined as the solution of Einstein's field equations. These equations are dependent on the distribution of matter and energy in a region of space, unlike Newtonian gravity, which is dependent only on the distribution of matter. The fields themselves in general relativity represent the curvature of spacetime. General relativity states that being in a region of curved space is equivalent to accelerating up the gradient of the field. By Newton's second law, this will cause an object to experience a fictitious force if it is held still with respect to the field. This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface. In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, but there are a number of easily verifiable differences, one of the most well known being the bending of light in such fields.