Definition of Inertial Frame in GR: Math Explained

Thread starter Kontilera
Start date Feb 25, 2013
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Definition Frame Gr Inertial Inertial frame

In summary, an inertial frame in General Relativity is a reference frame in which the laws of physics appear to be the same everywhere and at all times, with no acceleration or gravitational forces affecting the objects within the frame. This is in contrast to a non-inertial frame, where the laws of physics do not appear to be the same due to the presence of acceleration or gravitational forces. In General Relativity, an inertial frame is defined as a coordinate system where the Christoffel symbols are equal to zero. Multiple inertial frames can exist in General Relativity, as long as they are related by a constant velocity or uniform gravitational field. The concept of an inertial frame is important in General Relativity because it allows for a

Feb 25, 2013

Kontilera

How do we mathematically define a inertial frame in GR?
Is it only a basis in some tangentspace or does it have to be induced by a coordinatechart? :/

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Feb 25, 2013

Ben Niehoff

Science Advisor

Gold Member

It's only a basis in the tangent space. But you can always find local coordinates that induce this basis at a single point. They are called normal coordinates.

Related to Definition of Inertial Frame in GR: Math Explained

What is an inertial frame in General Relativity?

An inertial frame in General Relativity is a reference frame in which the laws of physics appear to be the same everywhere and at all times. In other words, there is no acceleration or gravitational forces affecting the objects within the frame.

How is an inertial frame different from a non-inertial frame?

A non-inertial frame is a reference frame in which the laws of physics do not appear to be the same everywhere and at all times. This is due to the presence of acceleration or gravitational forces acting on the objects within the frame.

What is the mathematical definition of an inertial frame in General Relativity?

In General Relativity, an inertial frame is defined as a coordinate system in which the Christoffel symbols, which represent the curvature of spacetime, are equal to zero.

Can there be multiple inertial frames in General Relativity?

Yes, there can be multiple inertial frames in General Relativity. However, in order for two frames to be considered inertial, they must be related by a constant velocity or a uniform gravitational field.

Why is the concept of an inertial frame important in General Relativity?

The concept of an inertial frame is important in General Relativity because it allows us to describe the behavior of objects in a consistent and predictable manner, without the influence of external forces. This is crucial in understanding the effects of gravity and the curvature of spacetime on the motion of objects.