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In classical mechanics, a gravitational field is a physical quantity. [5] A gravitational field can be defined using Newton's law of universal gravitation.Determined in this way, the gravitational field g around a single particle of mass M is a vector field consisting at every point of a vector pointing directly towards the particle.
Putting together these two basic facts of general relativity and electrodynamics, we seem to encounter a paradox. For if we dropped a neutral particle and a charged particle together in a gravitational field, the charged particle should begin to radiate as it is accelerated under gravity, thereby losing energy and slowing relative to the neutral particle.
In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity.
This formulation is dependent on the objects causing the field. The field has units of acceleration; in SI, this is m/s 2. Gravitational fields are also conservative; that is, the work done by gravity from one position to another is path-independent. This has the consequence that there exists a gravitational potential field V(r) such that
The magnitude of the gravitational field that would pull a particle at point in the x-direction is the gravitational field multiplied by where is the angle adjacent to the x-axis. In this case, cos ( θ ) = p p 2 + R 2 {\displaystyle \cos(\theta )={\frac {p}{\sqrt {p^{2}+R^{2}}}}} .
The intense gravitational fields around black holes create phenomena which are attributed to both gravitational and quantum effects. In these situations, a particle's Killing vector may be rotated such that its energy becomes negative. [7]
The gravitational field g (also called gravitational acceleration) is a vector field – a vector at each point of space (and time).It is defined so that the gravitational force experienced by a particle is equal to the mass of the particle multiplied by the gravitational field at that point.
In special relativity, the rest mass of a particle can be defined unambiguously in terms of its energy and momentum (see Mass in special relativity). Generalizing the notion of the energy and momentum to general relativity, however, is subtle. The main reason for this is that that gravitational field itself contributes to the energy and momentum.