# Properties of Mass in Curved Space-Time

• danielatha4
In summary: You would go faster on the road, as the car is stable and doesn't veer. But if you took the same car and drove on the grass, the car would spin around because there is no center of gravity to keep it stable. This is analogous to what happens in curved spacetime- the area with more distortion (more mass) will pull objects towards it.

#### danielatha4

From what I understand of GR, time dilates due to the gravity of massive bodies. I like to think of it as the three coordinates of space drag, or lag, through time at a slower rate resulting in distortion of space-time. Correct me if my logic is flawed.

But my question is this; why do bodies of mass fall towards areas of greater time dilation? or I guess in a 2 dimensional model of space it falls to the "lowest" point, the dip caused by the massive body? Does mass long to travel through time at slower rates?

danielatha4 said:
From what I understand of GR, time dilates due to the gravity of massive bodies. I like to think of it as the three coordinates of space drag, or lag, through time at a slower rate resulting in distortion of space-time. Correct me if my logic is flawed.
Intrinsic curvature means a distortion of distances, but you can alternatively visualize it as variable density of a medium, that slows down the advance trough it.

danielatha4 said:
But my question is this; why do bodies of mass fall towards areas of greater time dilation?
Speaking in the "variable density" metaphor: For the same reason light rays bend towards the denser region in a medium. Note that the light ray represents a world line (space-time path) of an object, in this analogy.

danielatha4 said:
or I guess in a 2 dimensional model of space it falls to the "lowest" point, the dip caused by the massive body? Does mass long to travel through time at slower rates?
There is no "lowest point" because there is no "down direction", but there is a point with the locally lowest potential, where the gravitational time dilation is maximal as well.

To understand why everything tends toward that point in terms of geodesics in curved space-time I recommend these links:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.relativitet.se/spacetime1.html

why do bodies of mass fall towards areas of greater time dilation?

Because that's where curved spacetime moves them.

Naty1 said:
Because that's where curved spacetime moves them.

Why not towards areas of space that travel through time at a faster rate?

Does the Principle of Least Activity have anything to do with this?

danielatha4 said:
Why not towards areas of space that travel through time at a faster rate?
Space doesn't travel trough time. Space and time are dimensions other stuff can travel trough. This picture explains how gravitational time dilation and gravitational pull are connected:

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_time.gif

danielatha4 said:
Does the Principle of Least Activity have anything to do with this?
In a way, yes. Moving locally straight ahead on a distorted grid, leads you towards the area with more 'stretched' distances.

In the alternative 'variable density' analogy you are pulled towards the denser area which breaks you more. Imagine driving a car with two wheels on the road, and two on the grass.

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## 1. What is the concept of mass in curved space-time?

The concept of mass in curved space-time refers to the way that mass and energy affect the curvature of space-time according to Einstein's theory of general relativity. In this theory, mass and energy are considered to be two aspects of the same thing, and their presence creates a distortion in the fabric of space-time, causing objects to follow curved paths.

## 2. How does mass affect the curvature of space-time?

Mass affects the curvature of space-time by creating a gravitational field around it. The more massive an object is, the greater its gravitational field and the more it curves space-time. This is why larger objects, such as planets and stars, have a greater effect on the curvature of space-time compared to smaller objects, such as asteroids.

## 3. How does curved space-time impact the behavior of objects?

Curved space-time impacts the behavior of objects by influencing the way they move. Objects with mass will follow the curved paths created by the distortion of space-time, resulting in the phenomenon we know as gravity. The more massive an object is, the more it will affect the curvature of space-time and the stronger its gravitational pull will be.

## 4. Can the properties of mass in curved space-time be observed in everyday life?

Yes, the properties of mass in curved space-time can be observed in everyday life. For example, when we see objects falling towards the ground, we are observing the effects of curved space-time. Similarly, the orbit of planets around the sun is a result of the curvature of space-time caused by the sun's mass.

## 5. How does the concept of mass in curved space-time differ from Newton's theory of gravity?

The concept of mass in curved space-time differs from Newton's theory of gravity in that it takes into account the curvature of space-time as the cause of gravitational attraction between objects, rather than an invisible force acting at a distance. Newton's theory is still accurate for most everyday situations, but Einstein's theory of general relativity provides a more complete understanding of the nature of gravity and its relationship to mass and space-time.

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