Table of Contents

## What are spacetime geodesics?

In general relativity, a geodesic generalizes the notion of a “straight line” to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.

### Is de Sitter space closed?

Conformal embedding of closed-universe models in a de Sitter background suggests a quantisation condition on the available conformal time….Closed Universes, de Sitter Space and Inflation.

Comments: | 38 pages, 25 figures |
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Subjects: | Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc) |

Journal reference: | Phys.Rev.D71:063502,2005 |

#### Why do particles follow geodesics?

Geodesic motion is simply a statement of Newton’s first law, that in an inertial reference frame, inertial objects remain at rest or in uniform motion in a straight line. Curvature of spacetime means that, on larger distance scales, inertial objects follow curved paths, like the orbit of the moon about the Earth.

**What is de Sitter solution?**

More specifically, de Sitter space is the maximally symmetric vacuum solution of Einstein’s field equations with a positive cosmological constant. (corresponding to a positive vacuum energy density and negative pressure).

**Does time create gravity?**

Yes, time goes faster the farther away you are from the earth’s surface compared to the time on the surface of the earth. This effect is known as “gravitational time dilation”. It is predicted by Einstein’s theory of General Relativity and has by verified multiple times by experiments.

## What created space time?

A quantum origin for spacetime. Einstein’s general theory of relativity shows that gravity is the result of a mass, such as a planet or star, warping the geometry of the merger of time and space known as spacetime.

### Is de Sitter space flat?

The most symmetric vacuum solution to Einstein’s equation, of course, is the flat spacetime.

#### What are geodesics used for?

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines. On the sphere, the geodesics are great circles (like the equator).