bksree said:
A freely falling body (falling in earth) accelerates with time. However, an object inside the body remains at rest (if it was initially at rest) or moves with a constant velocity if it was initially moving with constant velocity. In other words a frame fixed to the body is an inertial frame. But since the frame is fixed to an acceleating bod, it is also accelerating. Then how can it be an inertial frame ?
It is not an inertial frame in the full sense of the term in special relativity, which extends over all space and time, and in which mathematical terms called Christoffel symbols are zero, and the derivatives of the Christoffel symbols are also zero everywhere.
In the frame attached to a freely fallling body, the Christoffel symbols are zero at the origin attached to the body, which is why this is called a local inertial frame. However, the Christoffel sumbols are not zero away from the origin, and the derivatives of the Christoffel symbols are not zero even at the origin, which is why it is not an inertial frame in the full sense of the term in special relativity.
See also pervect's post #10, which makes the same point. He refers to "tidal forces" which are essentially the same thing as the derivatives of the Christoffel symbols.
https://arxiv.org/abs/0806.0464
An electromagnetic perpetuum mobile?
Øyvind Grøn, Sigurd Kirkevold Næss
"The principle of equivalence has a local character. The mentioned equivalence is only valid as far as the measurements does not reveal a possible curvature of space"
https://arxiv.org/abs/1102.0529
The motion of point particles in curved spacetime
Eric Poisson, Adam Pound, Ian Vega
See Equations 9.14 to 9.16 and the brief comment following.