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∙ 13y agoA singularity is NOT a (specific) place. It is a property of a function where the value of that function approaches infinity. For example, the function f: x ⟼ 1/x has a singularity at x = 0 because lim_{x → 0⁺} f(x) = +∞.
A singularity is the set of points where a metric is undefined. It is a geometric property of a manifold that is not limited to black holes, and is not necessarily a single point.
A singularity can be just a coordinate singularity that disappears if you choose a different coordinate system for the manifold. For example, the Schwarzschild metric that describes non-rotating electrically neutral black holes has a coordinate singularity at the event horizon in Schwarzschild coordinates, but not in Kruskal–Szekeres coordinates.
By contrast, every known black hole metric has a true (curvature) singularity with all coordinate systems in or near the center of a black hole.
That singularity does not need to be a point either. For example, in the Kerr and Kerr–Newman metrics that describe rotating black holes (with angular momentum J ≠ 0) the singularity is a ring (a set of adjacent points/events).
Also, it is important to understand that singularities with black holes are not (a set of) points in space, but in space*time*: they are a set of *events*.
A spacetime singularity does not have to be a spacetime *curvature* singularity. For example, the Schwarzschild metric, the spacetime metric of a spherical mass distribution with total mass M, zero angular momentum, and zero electric charge, has a singularity at the Schwarzschild radius r = rₛ := 2 G M/c²:
ds² = ±(1 − rₛ/r) c²dt² ∓ 1/(1 − rₛ/r) dr² ∓ r² (dθ² + sin²θ dφ²).
Because r = rₛ ⇒ 1/(1 − rₛ/r) = 1/0 ⇒ lim_{r → rₛ} ds² = ∓∞.
However, this is NOT a spacetime *curvature* singularity because it can be avoided by using a different coordinate system. For example, the metric is in Kruskal–Szekeres coordinates:
ds² = 32G³M³/r exp(−r/(2 G M)) (±dT² ∓ dX²) ∓ r² (dθ² + sin²θ dφ²),
where c = 1. Now,
r = rₛ = 2 G M/c² ⇒ ds² = 16G²M² exp(−1) (±dT² ∓ dX²) ∓ 4G²M² (dθ² + sin²θ dφ²) ≠ ±∞,
and the spacetime singularity at r = rₛ disappears.
There is still a spacetime *curvature* singularity at r = 0 because 32G³M³/0 is not defined in these coordinates, and there are no known coordinates that can avoid that.
Finally, even a spacetime *curvature* singularity does NOT have to be point-like. The curvature singularity of the Kerr and Kerr–Newman metrics, for a black hole with non-zero angular momentum, is *ring*-shaped.
Nikhil Govind
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∙ 13y agoblackhole
-- Find out the population of the area. -- Find out the area of the area. -- Divide the population by the area. The result is the population density of the area.
The area doesn't tell us the dimensions. It doesn't even tell us the shape. There are an infinite number of possibilities. - One possibility is a circle with diameter = 105.32 feet . - Another possibility is a square with sides 93.34 feet long. - Another possibility is a rectangle that's 2 inches wide and 9.9 miles long. All of these have 8,712 square feet of area, and there are an infinite number of other shapes and sizes that do too.
There will be 1 circle, 1 square, an infinite number of ellipses, an infinite number of rectangles, an infinite number of other quadrilaterals, an infinite number of polygons with 5 or more sides, an infinite number of odd shapes. In all, a lot.
An arithmetic density is a population density measured as the number of people per unit area of land.
Infinite amounts.
It is called a black hole.
They are called Black Holes or singularities.
The term "singularity" is used in several contexts. In mathematics, this is the point at which the plot of the graph turns straight up or becomes discontinuous. In physics, a singularity is a point of transition, where the normal laws of physics would yield nonsensical results. In astronomy, an example of a "singularity" is the extremely dense center of a black hole, where the math we use to describe gravity suddenly does not make sense. (This is generally understood to mean that we really do not understand yet what is going on under these conditions. We'll figure it out eventually.) The other example in astronomy is the singularity at the start of the Universe in the Big Bang Theory. In philosophy, especially the philosophy of technology, the term "singularity" is used in a similar fashion; a time when the normal continuous path of human progress shifts abruptly. For example, the development of a brain-computer interface would cause a discontinuity in human development and evolution. This is sometimes referred to with the capital letter phrase "The Singularity". Author Ray Kurzweil has written a book "The Singularity Is Near" concerning this phenomenon.
There is no such term. It could be a line, a curve, a finite or infinite area in space with any number of dimensions.
That's basically the description of a black hole.
The inside of a black hole is called a singularity because it is a point in space where matter is infinitely dense and the laws of physics as we know them break down. At the singularity, the gravitational pull becomes infinite and the curvature of spacetime becomes so extreme that conventional physics cannot describe what happens.
In general, the plane is infinite in length and breadth and so infinite in area.
Since a parabola is an open infinite curve, the area inside it is infinite.
The area is infinite. All forces have "carrier particles" that implement them. Electromagnetic fields are a phenomenon created by photons. According to the laws of quantum mechanics, the area affected by a force particle with no mass is infinite. Gravity is another example of an infinite force. There is nowhere in the universe that a small gravitational or electromagnetic field cannot reach you.
The area is infinite. All forces have "carrier particles" that implement them. Electromagnetic fields are a phenomenon created by photons. According to the laws of quantum mechanics, the area affected by a force particle with no mass is infinite. Gravity is another example of an infinite force. There is nowhere in the universe that a small gravitational or electromagnetic field cannot reach you.
Migration can affect population distribution by causing the population of one area to increase while simultaneously decreasing the population of another. This can also cause one area to be more densely populated than another.
One method of limiting density is through zoning regulations, which determine how land can be used and developed. This can include restrictions on the size and height of buildings, as well as requirements for open spaces. Another approach is the use of transferable development rights, where development rights in one area can be transferred to another area to limit density.