Spherically Symmetric Metric: Is Singularity Free?

In summary, there are several spherically symmetric metrics that do not have a singularity in the middle, including the interior Schwarzschild solution, FLRW, flat spacetime, and Oppenheimer-Snyder. These metrics have different properties and behaviors, but can be compared to Newton's gravity force which is proportional to distance from the center and inversely related to distance.
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sqljunkey
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Is there a spherically symmetric metric that doesn't have a singularity in the middle of it(like the schwartzchild metric). Something like our planet.
 
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  • #2
sqljunkey said:
Is there a spherically symmetric metric that doesn't have a singularity in the middle of it(like the schwartzchild metric). Something like our planet.
Sure. That is the interior Schwarzschild solution. There is also FLRW. Also flat spacetime. And Oppenheimer-Snyder which starts out with no singularity but develops one later.
 
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sqljunkey said:
Something like our planet.

Newton's gravity force is proportional to distance from the center up to the Earth surface and dumps inverse square of distance outward. Together with OP I am interested in the corresponding formula in GR.
 

1. What is a spherically symmetric metric?

A spherically symmetric metric is a mathematical description of the curvature of space-time around a spherical mass. It is a solution to Einstein's field equations in general relativity and is used to describe the gravitational field of objects with spherical symmetry, such as stars and planets.

2. What does it mean for a spherically symmetric metric to be singularity-free?

A singularity in a spherically symmetric metric refers to a point where the curvature of space-time becomes infinite. This can occur at the center of a black hole or at the beginning of the universe in the Big Bang theory. A singularity-free metric means that there are no such points of infinite curvature, and the metric is well-behaved throughout space-time.

3. How do scientists determine if a spherically symmetric metric is singularity-free?

Scientists use mathematical calculations and simulations to analyze the behavior of a spherically symmetric metric. They look for any points of infinite curvature or other irregularities in the metric that could indicate the presence of a singularity. If no such points are found, the metric is considered to be singularity-free.

4. Why is it important for a spherically symmetric metric to be singularity-free?

A singularity-free metric is important because it allows for a more accurate and complete understanding of the behavior of space-time around spherical masses. It also helps to avoid paradoxes and inconsistencies in theories of gravity and the universe. Additionally, a singularity-free metric can provide insights into the nature of black holes and the origin of the universe.

5. Are all spherically symmetric metrics singularity-free?

No, not all spherically symmetric metrics are singularity-free. Some solutions to Einstein's field equations can contain singularities, indicating a breakdown in the mathematical description of space-time. However, scientists continue to study and search for singularity-free metrics to improve our understanding of gravity and the universe.

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