A 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.
blackhole
-- 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.
An arithmetic density is a population density measured as the number of people per unit area of land.
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.
Infinite amounts.
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.
"Singularity" is a term from Math. It means something that you can get as close toas you want, but you can never get exactly there, because when you're exactlythere, something about it becomes either infinite or zero.If present hypotheses explaining black holes are correct, then:-- A black hole has a large mass but occupies only a point.-- Its radius, diameter, length, width, height, area, and volume are all zero.-- Since it has mass but no volume, its mass is finite, but its density is infinite.-- Since the black hole exists only at a single point, any other mass can be any distancefrom it, no matter how small, just as long as the distance isn't zero. And since the mutualforce of gravitational attraction between two masses is inversely proportional to thedistance between them, the force between a black hole and any other mass can beanything imaginable, no matter how large, and it can get as close to infinite forceas you want it to.
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.
linear density area density volume density linear density area density volume density
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.
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.
-- 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.