What is a local Lorentz reference frame? How exactly does it differ from an inertial reference frame or a locally inertial reference frame? Are there synonyms of this expression?
1 Answer
Lorentz frame and inertial frame are synonymous.
When you move from special to general relativity it is not always possible to find a coordinate system$^1$ such that the metric is the Minkowski metric at all points. You can however find local inertial coordinate systems such that the metric is Minkowski at a point, these are the "local inertial frames" and they correspond to an observer free-falling in the gravitational field.
In special relativity a local inertial frame is a global inertial frame.
$^1$ Note the use of "coordinate system" rather than "frame". In special relativity we usually (although we don't have to) deal with special coordinate systems that correspond to inertial obervers. In general relativity this restriction is lifted and any admissible coordinate system (cylindrical, polar etc.) is fair game.