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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) ?

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

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

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.

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 $T^4/\mathbb{Z}_4$.

JamalS
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