** **Physically, this principle (sometimes referred as to **EEP** = **Einstein's Equivalence Principle**) postulates that there is no experiment done in a small confined space which can tell the difference between a uniform gravitational field and an equivalent acceleration.

Mathematically, this important observation states that in presence of a gravitational field, **small enough free falling frames will be inertial**, and that in these Local Inertial Frame (LIF), where the metric g_{μν} reduces to η_{μν}, the laws of physics from Special Relativity will hold true.

Refer to the article The Equivalence Principle for more details.

Refer to the below youtube tutorial to get a good overview of the mathematical expression of the principle, i.e. how a local inertial frame (black colour) can be obtained by a general coordinate transformation at any point P of a manifold (blue colour)

Refer to the article 1907 Equivalence Principle first published expression to read the Einstein's first formulation of this principle.