You should be aware that different authors will define specific terms differently. Often the common definitions are equivalent in normal scenarios, but deviate from each other in edge cases.

The following is not an exhaustive list, but some common definitions

1. An inertial frame is a system of coordinates where objects experiencing no net force travel in straight coordinate lines at constant speed.

2. An inertial frame is one where the metric is $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$

3. An inertial frame is a tetrad whose integral curves form a timelike congruence with no expansion, torsion, or proper acceleration.

Your frame would be a valid inertial frame under definition 1, but not under definitions 2 or 3.

Now, whether your frame is an inertial frame is a matter of definitions and categorization. The physics is clear: no massive object can be at rest in your frame whether you call it inertial or not. Furthermore, with the metric in your coordinates all of the other physics can be self consistently calculated, though the results may differ from inertial-frame calculations from authors using a different definition.

It is important to understand how a given author uses a term, particularly when trying to apply derived results by said author to edge cases like this one.

You should be aware that different authors will define specific terms differently. Often the common definitions are equivalent in normal scenarios, but deviate from each other in edge cases.

The following is not an exhaustive list, but some common definitions

1. An inertial frame is a system of coordinates where objects experiencing no net force travel in straight coordinate lines at constant speed.

2. An inertial frame is one where the metric is $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$

3. An inertial frame is a tetrad whose integral curves form a timelike congruence with no expansion, torsion, or proper acceleration.

Your frame would be a valid inertial frame under definition 1, but not under definitions 2 or 3.

In addition to definitions of inertial frames there are also definitions of reference frames that vary from author to author.

1. a reference frame is a system of coordinates covering some region of spacetime

2. a reference frame is an orthonormal tetrad with one timelike and three spacelike vectors.

Similarly, your frame would be valid as a general reference frame under definition 1, but not under 2.

Now, whether your frame is a valid frame or inertial frame is a matter of definitions and categorization. The physics is clear: no massive object can be at rest in your system whether you call it inertial, or a frame, or not. Furthermore, with the metric in your coordinates all of the other physics can be self consistently calculated, though the results may differ from inertial-frame calculations from authors using a different definition.

It is important to understand how a given author uses a term, particularly when trying to apply derived results by said author to edge cases like this one.

You should be aware that different authors will define specific terms differently. Often the common definitions are equivalent in normal scenarios, but deviate from each other in edge cases.

The following is not an exhaustive list, but some common definitions

1. An inertial frame is a system of coordinates where objects experiencing no net force travel in straight coordinate lines at constant speed.

2. An inertial frame is one where the metric is $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$

3. An inertial frame is a tetrad whose integral curves form a timelike congruence with no expansion, torsion, or proper acceleration.

Your frame would be a valid inertial frame under definition 1, but not under definitions 2 or 3.

Now, whether your frame is an inertial frame is a matter of definitions and categorization. The physics is clear: no massive object can be at rest in your frame whether you call it inertial or not. Furthermore, with the metric in your coordinates all of the other physics can be self consistently calculated, though the results may differ from inertial-frame calculations from authors using a different definition.

You should be aware that different authors will define specific terms differently. Often the common definitions are equivalent in normal scenarios, but deviate from each other in edge cases.

The following is not an exhaustive list, but some common definitions

1. An inertial frame is a system of coordinates where objects experiencing no net force travel in straight coordinate lines at constant speed.

2. An inertial frame is one where the metric is $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$

3. An inertial frame is a tetrad whose integral curves form a timelike congruence with no expansion, torsion, or proper acceleration.

Your frame would be a valid inertial frame under definition 1, but not under definitions 2 or 3.

Now, whether your frame is an inertial frame is a matter of definitions and categorization. The physics is clear: no massive object can be at rest in your frame whether you call it inertial or not. Furthermore, with the metric in your coordinates all of the other physics can be self consistently calculated, though the results may differ from inertial-frame calculations from authors using a different definition.

It is important to understand how a given author uses a term, particularly when trying to apply derived results by said author to edge cases like this one.