Origin of Space-time fabric

Question

I have seen on this site some questions regarding the nature of gravitational-force, and the ways in which it could be interpreted. Most of them mention that the space-time fabric came into existence due to the big-bang. But I cannot understand why it came into existence during the big-bang, and had no earlier existence. Also, how should I develop my notion regarding the form of a gravitational-singularity? My current concept holds it that a gravitational singularity, is a compact-clump of spatial and temporal curves, where laws of Classical Physics are rarely(?) valid. But more often, I "like" to compare a garvitational-singularity with a huge go-down of energy, that is longing to burst open, and thus, maximize its entropy, and minimize its energy. If in-any way my current-notion is to a-certain degree acceptable, would it then be correct for me to guess that "minute"(?)-fabrics of space-time come into existence whenever there is a conversion of matter into an equivalent amount of energy, according to Einstein's equation E=m.(c^2) ?

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Please take care of the fact that I am a high-school student-with a corresponding limited-knowledge on Physics, and especially, Quantum-Mechanics.

Answer 1

I will address the part of the question which discusses gravitational singularities.

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There are many types of singularities on manifolds, and more generally topological spaces. In general relativity, you are likely to encounter:

• Coordinate Singularity: These arise because we have used inappropriate coordinates; for example the Schwarzschild black hole metric may be singular at $r=2GM$. However, these are not true physical singularities, and may be removed with diffeomorphisms.
• Curvature Singularity: A true physical singularity which arises when a curvature scalar (as it is invariant under diffeomorphisms) is singular. For example, at the center of a black hole.
• Conical Singularity: A singularity which occurs, for example, when we encounter a point at the tip of a cone, which is taken to be infinitesimally small. To understand why it is problematic, consider a geodesic at that point; when you arrive at the tip which way do you continue?

At curvature singularities, or regions of high curvature, we cannot resort only to general relativity; at this point quantum gravity becomes important. As Professor Tong states, the question of singularities is morally equivalent to high energy scattering. The short-distance (Planck scale) phenomena of spacetime, after Fourier transform, is governed by high energy gravitons.

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Other Singularities:

Another example of a singularity arises when studying orbifolds. Given a smooth manifold $X$ and a discrete isometry group $G$, an orbifold is the quotient space, $X/G$ and a point in the orbifold corresponds to an orbit in $X$ consisting of a point and all its images under the $G$ group action.

If certain elements of $G$ leave a point in $X$ invariant, then the orbifold has an orbifold singularity, which is a type not really encountered in general relativity, but rather string theory. It may be removed with the use of algebraic geometry, for example by replacing certain regions with Eguchi-Hanson spaces for the case of $T^4/\mathbb{Z}_4$.