On a soliton-type spacetime defect

Abstract

We review the construction of a particular soliton-type solution of the classical Einstein and matter-field equations. This localized finite-energy static classical solution can be interpreted as a single spacetime defect embedded in Minkowski spacetime and may give rise to several new effects. For a Skyrme-type theory with small enough matter-field energy scale compared to the Planck energy scale and for a sufficiently small defect length scale, the existence of a globally regular solution requires a negative active gravitational mass, so that the defect repels a distant test particle ("antigravity"). There also exist "stealth defects" which have a vanishing asymptotic gravitational mass. These stealth defects are, however, not entirely invisible as they bring about a new type of gravitational lensing.

Nonsingular bouncing cosmology from general relativity: Scalar metric perturbations

“…Ansatz describes what may be called a "spacetime defect" (see Ref. [9] for a review). The matter content of the corresponding nonsingular bouncing cosmology is entirely standard, without any problem whatsoever as regards unitarity and microcausality (see, e.g., Sec.…”

“…The metric from (2.1) is degenerate (with a vanishing determinant at t = 0) and describes a spacetime defect with characteristic length scale b ; see Ref. [9] for a general review of this type of spacetime defect and Ref. [10] for a detailed discussion of related mathematical aspects (other mathematical aspects of degenerate metrics have been discussed in Ref.…”

Regularized big bang singularity

“…[7] and further discussion of the physics of this particular type of spacetime defect in Refs. [6,9,10].…”

“…Awaiting the definitive theory of "quantum gravity," we propose to remain within the domain of 4-dimensional general relativity but to allow for degenerate metrics. In fact, a particular degenerate metric has already provided a "regularization" of the Schwarzschild singularity [5][6][7][8][9][10], removing the divergent behavior at the center (radial coordinate r = 0) at the price of introducing a spatial 2-surface (r = b > 0) with a vanishing determinant of the metric. In the present article, we propose doing something similar with the big bang singularity (at cosmic time coordinate τ = 0, in a notation that will be explained later), by the introduction of a spatial 3-surface (at | τ | = b/c > 0) with a vanishing determinant of the metric.…”

“…(This submanifold may be considered to correspond to a "spacetime defect" [6][7][8][9][10], as will be explained in Sec. III.)…”