# Rotating Flat Spacetime in Minkowski Metric

• parsikoo
In summary, the tetrad transforms under a general coordinate transformation, including rotations. For a given metric, the tetrad is only determined up to a Lorentz transformation, where spatial rotations are a subgroup. To make the tetrad rotate with the coordinate system, apply the transformation rule using an angle parameter, such as omega, to rotate the tetrad components.
parsikoo
In Minkowski spactime (Flat), if the coordinate system makes a rotation e.g. around y-axis (centred) , for the metric ds^2, how to make the tertad (flat spacetime) as the coordinate system rotats?

You know how the tetrad transforms under a gct. Just apply this transformation rule for rotations. For a given metric the tetrad is only determined up to a lorentz transfo, of which spatial rotations are a subgroup. So you could start with the tetrad components being equal to 1 if you work in cartesian coordinates, and apply the transformation rule.

Thanks, you mean:
e(mu)=1 diagonal and for instance put e(24)=-e(42)=omega?

I'm not sure about your notation, but writing down the transfo.law for the tetrad and parametrizing the rotation with an angle omega should do it. Just write that transfo. law here and apply the rotation.

I would like to first clarify that the term "tertad" is not a commonly used term in the field of physics. However, based on my understanding, I believe you are referring to the concept of a rotating frame of reference in flat spacetime, which is often used in the study of general relativity.

In this scenario, the Minkowski metric, which describes the geometry of flat spacetime, remains unchanged regardless of the orientation or rotation of the coordinate system. This is because the Minkowski metric is independent of any particular coordinate system and is a fundamental property of spacetime itself.

In order to make the coordinate system rotate, we can use a mathematical transformation called a Lorentz transformation. This transformation allows us to switch between different frames of reference, including rotating frames, while still maintaining the same Minkowski metric. This is similar to how a map can be rotated without changing the actual layout of the terrain it represents.

In summary, while the coordinate system may rotate, the Minkowski metric remains constant and unchanged. The use of a Lorentz transformation allows us to mathematically account for the rotation of the coordinate system and still accurately describe the geometry of flat spacetime.

## 1. What is rotating flat spacetime in Minkowski metric?

Rotating flat spacetime in Minkowski metric is a concept in physics that describes the rotation of a flat spacetime in a four-dimensional space known as Minkowski space. This concept is based on the theory of relativity and is used to understand the behavior of objects in motion.

## 2. How is rotating flat spacetime in Minkowski metric different from rotating spacetime in general relativity?

Rotating flat spacetime in Minkowski metric is a simplified version of rotating spacetime in general relativity. In general relativity, the spacetime is curved due to the presence of matter and energy, while in rotating flat spacetime, the spacetime is flat and only rotates due to the motion of objects.

## 3. What are some applications of rotating flat spacetime in Minkowski metric?

One of the main applications of rotating flat spacetime in Minkowski metric is in understanding the behavior of objects in motion, such as spacecraft and satellites. This concept is also used in the study of black holes and other astronomical phenomena.

## 4. Can rotating flat spacetime in Minkowski metric be observed or measured?

No, rotating flat spacetime in Minkowski metric cannot be directly observed or measured. This concept is used in theoretical physics and is not directly observable in the physical world. However, its effects can be observed and measured through the behavior of objects in motion.

## 5. How does rotating flat spacetime in Minkowski metric relate to the theory of relativity?

Rotating flat spacetime in Minkowski metric is based on the theory of relativity, specifically the special theory of relativity. This theory describes the behavior of objects in motion and how it affects the geometry of spacetime. Rotating flat spacetime is a simplified version of this theory, as it only takes into account the rotation of objects rather than their motion through curved spacetime.

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