Geodesic structure of naked singularities in AdS3 spacetime

Abstract

We present a complete study of the geodesics around naked singularities in AdS 3 , the three-dimensional anti-de Sitter spacetime. These stationary spacetimes, characterized by two conserved charges -mass and angular momentum-, are obtained through identifications along spacelike Killing vectors with a fixed point. They are interpreted as massive spinning point particles, and can be viewed as three-dimensional analogues of cosmic strings in four spacetime dimensions. The geodesic equations are completely integrated and the solutions are expressed in terms of elementary functions. We classify different geodesics in terms of their radial bounds, which depend on the constants of motion. Null and spacelike geodesics approach the naked singularity from infinity and either fall into the singularity or wind around and go back to infinity, depending on the values of these constants, except for the extremal and massless cases for which a null geodesic could have a circular orbit. Timelike geodesics never escape to infinity and do not always fall into the singularity, namely, they can be permanently bounded between two radii. The spatial projections of the geodesics (orbits) exhibit self-intersections, whose number is particularly simple for null geodesics. As a particular application, we also compute the lengths of fixed-time spacelike geodesics of the static naked singularity using two different regularizations.

Overspinning naked singularities in AdS$_3$ spacetime

“…3, a review of general features of the geodesics -timelike, spacelike and null-for the metric (1.1) is presented. The analysis considers generic and circular geodesics which complements the results presented in [7] for M > |J| (black holes), and in [8] for M < −|J| (conical singularities). This section also includes general properties of the geodesics for the remaining case |M | < |J| (overspinning singularities).…”

“…Equations (3.8) to (3.10) are the same for all BTZ spacetimes [7,8]. Although the radial motion is easily determined for each BTZ geometry, the behavior of t(λ) and θ(λ) is strongly dependent on the type of zeros of R(u) in the denominators of (3.8) and (3.9).…”

Shadows and precession of orbits in rotating Janis-Newman-Winicour spacetime

“…T µν = ρ e u µ u ν + P r e µ r e ν r + P θ e µ θ e ν θ + P φ e µ φ e ν φ (59) where, ρ e is the energy density, and P i (i → r, θ, φ) are the principal pressure components. The Einstein field equation in the form G µν = T µν requires…”

“…The relativistic orbital precession in the Schwarzschild spacetime is discussed in [58]. There are large number of literature where the nature of the orbit precession is extensively studied in various spacetime geometry [59][60][61][62][63][64][65][66][67][68][69][70][71]. In [64,65], the periastron precession of particles orbit in static JMN1, JMN2, JNW, and Bertrand (BST) naked singularity spacetimes are studied, and the results obtained are compared with that of the Schwarzschild spacetime.…”

Shadows and precession of orbits in rotating Janis–Newman–Winicour spacetime

“…The relativistic orbital precession in the Schwarzschild spacetime is discussed in [58]. There are large number of literature where the nature of the orbit precession is extensively studied in various spacetime geometry [59][60][61][62][63][64][65][66][67][68][69][70][71]. In [64,65], the periastron precession of particles orbit in static JMN1, JMN2, JNW, and Bertrand (BST) naked singularity spacetimes are studied, and the results obtained are compared with that of the Schwarzschild spacetime.…”