# What are spacetime geodesics?

## 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.

Does flat spacetime have gravity?

In this case, we can say that an asymptotically flat spacetime is one in which the gravitational field, as well as any matter or other fields which may be present, become negligible in magnitude at large distances from some region. …

### How do you know if spacetime is flat?

A spacetime is locally flat if and only if no geodesical deviation exists for congruences of all kinds of geodesics.

It is this curvature of spacetime that gives rise to what we interpret as gravitational acceleration. Note that there is no mass in this equation – it doesn’t matter what the mass of the object is, they all follow the same geodesic (so long as it’s not massless, in which case things are a little different).

#### How do you prove a metric is flat?

Just compute the Riemann tensor. The result is Rμναβ=0. This metric is flat. If you haven’t seen the Riemann tensor yet, then I guess the best way would be to guess functions x and y of u and v such that your statement there is true, and equals a flat geometry.

Why is Minkowski space flat?

There is nothing unusual about the metric – Minkowski metric is just a way of presenting the good old Euclidean space. And as in Special Relativity there is no gravitation (acceleration) to curve this space-time, so it remains flat.

## Is the universe flat open or closed?

This is known as an open universe. The shape of the universe depends on its density. If the density is more than the critical density, the universe is closed and curves like a sphere; if less, it will curve like a saddle.

Is Minkowski space flat?

As a flat spacetime, the three spatial components of Minkowski spacetime always obey the Pythagorean Theorem. Minkowski space is a suitable basis for special relativity, a good description of physical systems over finite distances in systems without significant gravitation.

### Is our universe flat open or closed?

The exact shape is still a matter of debate in physical cosmology, but experimental data from various independent sources (WMAP, BOOMERanG, and Planck for example) confirm that the universe is flat with only a 0.4% margin of error.

Does light bend space-time?

Light travels through spacetime, which can be warped and curved—so light should dip and curve in the presence of massive objects. This effect is known as gravitational lensing GLOSSARY gravitational lensingThe bending of light caused by gravity .

#### Can gravity exist without time?

Hence the answer to your question is, time exists even though their might be no gravity ( which is not possible since gravity is a long range force and extends for infinite distance ) since space still exists ! Yes, time exists without gravity!

Do we live in Minkowski space?

We begin by explaining what “space” and “time” are meaning for us – the 4-dimensional Minkowski space-time, then proceeding to the quantum 4-dimensional Minkowski space-time. In our world, there are fields, or, point-like particles.

## Can a geodesic be a straight line through two events?

For a space-like geodesic through two events, there are always nearby curves which go through the two events that have either a longer or a shorter proper length than the geodesic, even in Minkowski space. In Minkowski space, the geodesic will be a straight line.

How are geodesics related to the theory of general relativity?

Geodesics in general relativity. Part of a series of articles about. General relativity. 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 force, is a particular type of geodesic.

### How are geodesics similar to lines of longitude?

On a flat sheet of paper, a geodesic is a trivial straight line. On a sphere, they are lines of longitude. In both cases, you can move without turns to get from your starting point to your end point. Objects in the universe are embedded in spacetime, which has a curved geometry depending on the masses within it.

How are geodesics related to the theory of UAP?

Geodesics are the trajectories on which a UAP has to move in order to be possible, as discussed on our main UAP page. A geodesic is a straight line on a curved geometry, which means it has no turns. Such a line may not look straight but it is. On a flat sheet of paper, a geodesic is a trivial straight line.