Einstein's theory in a three-dimensional space-time

Formation of three-dimensional black strings from gravitational collapse of dust cloud

“…An exact solution of eq. (4.9) is 12) where the collapse time t c is found to be 13) which is clearly finite and positive for all allowed R 0 and u 0 . The behavior of collapsing dust edge is depicted for varying black string masses and initial velocities in Fig.…”

“…(3.2), (3.3), and the solution (3.11), solutions for the dilaton and the energy density are found, 13) where the initial value of the dilaton field is φ 0 ≡ φ(0) = 1 2 ln( a0|v0| |µ| ) and the initial energy density is…”

Gravitationally collapsing dust in 2 + 1 dimensions

“…It is therefore useful in that it provides another opportunity to model classical and quantum dynamics of black holes with a simpler set of field equations. Here we investigate under what circumstances a disk of pressureless dust, (the 3D analog of Oppenheimer-Snyder collapse) will collapse to the black hole solution (2). Provided the initial density is sufficiently large, we show that collapse occurs in finite proper time, and external observers see the event horizon form in infinite coordinate time.…”

“…One has the full structure of the Einstein equations but with an enormous amount of technical simplification due to the fewer number of dimensions. One consequence of this simplicity is that the metric outside of a finite matter source is locally flat [1,2], and the mass affects the space-time only globally, seemingly implying that there are no black hole solutions to 2 + 1 gravity.…”

Four-dimensional anti–de Sitter toroidal black holes from a three-dimensional perspective: Full complexity

“…Before the appearance of this black hole solution there were, however, important works in 3D general relativity which studied the properties of point particles in 3D geometries [3,4] as well as solutions with matter [5], and showed that it provides a testbed for 4D and higher-D theories [6,7]. In addition there were works in 3D string theory with its associated black strings [8,9].…”