(2+1)-dimensional stars

Abstract

We investigate, in the framework of (2+1) dimensional gravity, stationary, rotationally symmetric gravitational sources of the perfect fluid type, embedded in a space of arbitrary cosmological constant. We show that the matching conditions between the interior and exterior geometries imply restrictions on the physical parameters of the solutions. In particular, imposing finite sources and absence of closed timelike curves privileges negative values of the cosmological constant, yielding exterior vacuum geometries of rotating black hole type. In the special case of static sources, we prove the complete integrability of the field equations and show that the sources' masses are bounded from above and, for vanishing cosmological constant, generally equal to one. We also discuss and illustrate the stationary configurations by explicitly solving the field equations for constant mass-energy densities. If the pressure vanishes, we recover as interior geometries Gödel like metrics defined on causally well behaved domains, but with unphysical values of the mass to angular momentum ratio. The introduction of pressure in the sources cures the latter problem and leads to physically more relevant models.

Static circularly symmetric perfect fluid solutions with an exterior BTZ metric

“…This showed that the geometrical condition find in (9) yields to the condition to pressure zero at r = a. So, it allow us to write N (r ) in the following form…”

“…Lubo et al have showed in [9], that the equality of the induced metric on the junction surface implies the continuity of the interior and exterior metric, i.e., g in µν | r =a = g ext µν | r =a , where µ, ν ∈ (t, r, θ). The equality of the extrinsic curvature with respect to the two spacetime geometries reduces to require the continuity of some of the metric component derivatives, i. e., [∂ r g in µν ] r =a = [∂ r g ext µν ] r =a , where µ, ν ∈ (t, θ).…”

Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole

“…On the other hand, since the method depends only on the asymptotic behavior of the metric, it also gives an entropy (3.2.8) for a "star" [82,83], a circularly symmetric, horizonless lump of matter whose exterior is described by the BTZ metric. I shall return to this issue in section 6.…”

Boson stars with negative cosmological constant

“…Many other types of 3D regular and black hole solutions with a negative cosmological constant have also been found by coupling matter fields to gravity in different way. (2+1)-dimensional stars with negative cosmological constant have been studied in [44,45]. We notice also the existence of interesting BTZ-like solutions in a class of 3D gravity models in which the cosmological constant is induced [46].…”