An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

A hypothetical state of → infinite energy density representing an infinite → gravitational field and infinite → space-time curvature. The singularity arises from using Einstein's theory of → general relativity concerning gravity. We know, however, that when the density and heat become extremely large, quantum physics of gravity becomes important. Yet Einstein's equations ignore quantum effects. In other words, in certain extreme conditions, Einstein's equations do not apply.

→ Big Bang; → singularity.

An instant of infinite density, infinite pressure, and infinite temperature where the equations of general relativity break down, if the standard Big Bang theory is extrapolated all the way back to time zero. → singularity.

→ initial; → singularity.

A singularity that is not surrounded by an event horizon. It will therefore be visible and communicable to the outside world.

→ naked; → singularity.

A → square matrix that is not a → singular matrix.

→ non-; → singular; → matrix.

A region of infinite → space-time curvature postulated to lie within a → black hole.

→ Schwarzschild black hole; → singularity.

Math.: 1) Of or pertaining to a linear transformation from a vector space to itself that is not one-to-one.
2) Of or pertaining to a matrix having a determinant equal to zero.

M.E., from O.Fr. singuler "single, separate," from L. singularis "single, solitary," from singulus "one, individual, separate," from sim- (stem of simplus) + diminutive suffix.

Takin, from tak "single, alone," related to tâq "odd, single," tâ, tâh "piece, part; fold, plait, ply;" Mid.Pers. tak "single," tâg, tâk, tâi "unit, piece, after numerals" + -in adj. suffix.

In models of star formation, an isothermal sphere in which the density distribution in the static or nearly static outer envelope obeys an r^-2 power law. In the limit of infinite central concentration, the unstable equilibrium approaches the singular isothermal sphere which has the density and mass distributions ρ(r) = (a²/2πG)r^-2 and M(r) = (2a²/G)r, where a is the isothermal → sound speed inside the cloud, G is the → gravitational constant, and r the distance from the center (F. H. Shu, 1977, ApJ 214, 488).

→ singular; → isothermal; → sphere.

A → square matrix that does not have a → matrix inverse.

→ singular; → matrix.

The point M₀(x₀,y₀) of the curve F(x,y) = 0, where at least one of the → partial derivatives ∂F/∂x and ∂F/∂y vanishes. See also → ordinary point.

→ singular; → point.

Of partial differential equations, the solution which cannot be obtained from the general solution by particular choice of arbitrary functions. → general solution; → particular solution.

→ singular; → solution.

1) Math.: A point at which a given mathematical object is not defined.
2) Physics: A point in → space-time in which gravitational force causes space-time to have infinite curvature; matter is crushed to infinite density and zero volume. This happens at the center of a → black hole where space and time cease to exist as we know them, and the known laws of physics break down. See also → Schwarzschild singularity; → initial singularity.

→ singular + → -ity.