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## Main Question or Discussion Point

This discussion started as a side clarification of something in this thread https://www.physicsforums.com/showthread.php?p=3971013#post3971013 and although tangentially related it probably deserves a thread of its own so anyone can participate without reservations.

Please keep in mind I am not referring to the question in classical mechanics with the earth's frame of reference and gravity acting as a real force in wich it is obvious there is no work done on a book placed on a table.

Also to simplify things we are using the Schwarzschild exterior solution of GR, so that we can consider the geodesic free-falling frame of reference as static.

The question is, given this setting, with gravity considered as fictitious force in GR does the table do work on a book sitting on it?

And if the book falls off the table and while is falling, does gravity fictitious force do work on the book?

I would like to take a more neutral stance in this thread,and just explain why I would consider good arguments to say that work is done in the particular situation I described.

First by analogy to other fictitious forces like centrifugal force. In my GR scenario we are considering the free-falling frame the "inertial" frame (remember the terms inertial and non-inertial are used differently in newtonian mechanics versus GR), and the book is kept in the non-inertial frame of the surface of the table on the earth.

In the centrifugal force example this force is the apparent outward force that draws a rotating body away from the center of rotation and is caused by the inertia of the body.

By analogy I consider the gravitational (fictitious) force as the apparent downward force that draws the book to the centre of the earth and is caused by the mass of the body.

Now what allows to make the analogy between this two fictitious forces is the equivalence principle that equals the inertial mass to the gravitational mass.

In the above linked thread stevendaryl argued that the equivalence failed because he could find coordinates in the schwarzschild spacetime that made the metric appear time varying.

Being obvious that coordinates can introduce artifacts that don't affect the physics of the situation I still don't know what his point was wrt the physics of the problem at hand.

I believe he was trying to make a point about being able to choose coordinate systems making the metric tensor appear time varying but that is such an obvious thing and so disconnected with the physics of the problem I chose not to follow that distracting path.

Following the analogy with the centrifugal force, I maintain that the table is doing work on the book against the gravitational fictitious force so that as soon as the book falls and as long as no object is in its way the gravitational fictitious force does work on the book as it tries catching up the free-falling frame.

Any objections?

Please keep in mind I am not referring to the question in classical mechanics with the earth's frame of reference and gravity acting as a real force in wich it is obvious there is no work done on a book placed on a table.

Also to simplify things we are using the Schwarzschild exterior solution of GR, so that we can consider the geodesic free-falling frame of reference as static.

The question is, given this setting, with gravity considered as fictitious force in GR does the table do work on a book sitting on it?

And if the book falls off the table and while is falling, does gravity fictitious force do work on the book?

I would like to take a more neutral stance in this thread,and just explain why I would consider good arguments to say that work is done in the particular situation I described.

First by analogy to other fictitious forces like centrifugal force. In my GR scenario we are considering the free-falling frame the "inertial" frame (remember the terms inertial and non-inertial are used differently in newtonian mechanics versus GR), and the book is kept in the non-inertial frame of the surface of the table on the earth.

In the centrifugal force example this force is the apparent outward force that draws a rotating body away from the center of rotation and is caused by the inertia of the body.

By analogy I consider the gravitational (fictitious) force as the apparent downward force that draws the book to the centre of the earth and is caused by the mass of the body.

Now what allows to make the analogy between this two fictitious forces is the equivalence principle that equals the inertial mass to the gravitational mass.

In the above linked thread stevendaryl argued that the equivalence failed because he could find coordinates in the schwarzschild spacetime that made the metric appear time varying.

Being obvious that coordinates can introduce artifacts that don't affect the physics of the situation I still don't know what his point was wrt the physics of the problem at hand.

I believe he was trying to make a point about being able to choose coordinate systems making the metric tensor appear time varying but that is such an obvious thing and so disconnected with the physics of the problem I chose not to follow that distracting path.

Following the analogy with the centrifugal force, I maintain that the table is doing work on the book against the gravitational fictitious force so that as soon as the book falls and as long as no object is in its way the gravitational fictitious force does work on the book as it tries catching up the free-falling frame.

Any objections?