Explanation:

That time is a dimension of spacetime (sometimes called the fourth dimension) is another valid definition.

For example, consider the Minkowkski metric

ds²= -c²dt² + dx² + dy² + dz².

Then that temporal dimensions, and the usual coordinate time t in particular, are different form spatial dimensions like x,y, and z, is indicated by the fact that the coefficient of the temporal summand is negative, while it is positive for like spatial summandsTwo bus stops are 1200 m apart. A bus ACCELERATES at 0.95 m s–2 from rest

through the first quarter of the distance and then travels at constant speed for

the next two quarters and decelerates to rest over the final quarter.

(a) What was the maximum speed? (b) What was the total time taken for the

journey? (c) Draw a v–t graph of the journey.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

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.

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