# Gravity on a Large Scale—Does It Necessarily Look like It Does on a Small Scale?

## Abstract

**:**

## 1. Introduction

## 2. Local Inertiality

## 3. Field of Inertial Frames: The Coordinate Description

## 4. Curvature Tensor

## 5. Field Dynamics—A Variational Approach

## 6. Gravity as We Know It Today

## 7. Electromagnetic Sector of the Theory

## 8. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | Furthermore, he was already aware of the fact that there is no natural splitting of “spacetime” into “space” and “time” and, whence, equations of motion (2) must always be four-dimensional, like, e.g., in electrodynamics, where we have: ${F}^{\lambda}=q\xb7{f}^{\lambda \kappa}{u}_{\kappa}$. |

2 | In this context “generalizations” towards non-symmetric connections is a nonsense, because such a connection is not an irreducible object. It splits canonically into two disjoint terms: (1) a symmetric connection and (2) a tensor (torsion). The tensor fields appear in this framework as matter fields, but a field of inertial frames defines uniquely a symmetric connection, which we identify with gravitational field. |

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**MDPI and ACS Style**

Kijowski, J.
Gravity on a Large Scale—Does It Necessarily Look like It Does on a Small Scale? *Astronomy* **2024**, *3*, 29-42.
https://doi.org/10.3390/astronomy3010004

**AMA Style**

Kijowski J.
Gravity on a Large Scale—Does It Necessarily Look like It Does on a Small Scale? *Astronomy*. 2024; 3(1):29-42.
https://doi.org/10.3390/astronomy3010004

**Chicago/Turabian Style**

Kijowski, Jerzy.
2024. "Gravity on a Large Scale—Does It Necessarily Look like It Does on a Small Scale?" *Astronomy* 3, no. 1: 29-42.
https://doi.org/10.3390/astronomy3010004