# Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes

## Abstract

**:**

## 1. Introduction

## 2. Inertial Frame Dragging in Brill’s and Cohen’s Slowly Rotating Shell Model

## 3. Rotation in Kerr Spacetime

## 4. Summary and Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Plots of the angular velocity $\mathsf{\Omega}\left(r\right)$ of ZAMOs, as given by the expression in Equation (34), with ${\mathsf{\Omega}}_{Q}=-0.3\phantom{\rule{0.166667em}{0ex}}{\omega}_{s}$ and ${r}_{Q}=5\phantom{\rule{0.166667em}{0ex}}{r}_{S}$. Note that $\mathsf{\Omega}\left(r\right)$ is normalized by ${\omega}_{s}$. The solid curve shows the result for a shell radius $R=3\phantom{\rule{0.166667em}{0ex}}{r}_{S}$. The black dashed curve shows the result for a shell radius equal to its Schwarzschild radius, $R={r}_{S}$. This corresponds to the situation of “perfect inertial dragging”, where the inertial frames in the interior of the shell rotate with the same angular velocity as the shell, independently of the angular velocity of the inertial frames located “at infinity”. The red dashed curve marks the chosen value for ${\mathsf{\Omega}}_{Q}$ (normalized by ${\omega}_{s}$).

**Figure 3.**Plots of the angular velocity $\mathsf{\Omega}\left(r\right)$ of ZAMOs, as given by the expression in Equation (34), with vanishing angular velocity for the shell, ${\omega}_{s}=0$, and ${r}_{Q}\to \infty $, as in Figure 2. Note that here, $\mathsf{\Omega}\left(r\right)$ is normalized by ${\mathsf{\Omega}}_{Q}$.

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**MDPI and ACS Style**

Braeck, S.
Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes. *Universe* **2023**, *9*, 120.
https://doi.org/10.3390/universe9030120

**AMA Style**

Braeck S.
Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes. *Universe*. 2023; 9(3):120.
https://doi.org/10.3390/universe9030120

**Chicago/Turabian Style**

Braeck, Simen.
2023. "Inertial Frame Dragging and Relative Rotation of ZAMOs in Axistationary Asymptotically Flat Spacetimes" *Universe* 9, no. 3: 120.
https://doi.org/10.3390/universe9030120