Naked singularity

Abstract: Expansion of supersymmetric string theory suggests that the leading quadratic curvature correction to the Einstein action is the Gauss-Bonnet invariant. We show that this model has both flat and anti-de Sitter space as solutions, but that the cosmological branch is unstable, because the graviton becomes a ghost there: The theory solves its own cosmological problem. The general static spherically symmetric solution is exhibited; it is asymptotically Schwarzschild. The sign of the Gauss-Bonnet coefficient determines whether there is a normal event horizon (for the string-generated sign) or a naked singularity. We discuss the effects of higher-curvature corrections and of an explicit cosmological term on stability.

Abstract: We model massive dark objects in galactic nuclei as spherically symmetric static naked singularities in the Einstein massless scalar field theory and study the resulting gravitational lensing in detail. Based on whether or not a naked singularity is covered within a photon sphere we classify naked singularities into two kinds: weakly naked (those contained within at least one photon sphere) and strongly naked (those not contained within any photon sphere). The qualitative features of gravitational lensing due to a weakly naked singularity are similar to those due to a Schwarzschild black hole (these give rise to one Einstein ring but no radial critical curve). However, the gravitational lensing due to a strongly naked singularity is qualitatively different from that due to a Schwarzschild black hole; a strongly naked singularity gives rise to either two or nil Einstein ring(s) and one radial critical curve. A light ray passing close to a photon sphere of a black hole or a weakly naked singularity goes around its photon sphere once, twice, or many times (before reaching an observer) depending upon the impact parameter and thus gives rise to a sequence of theoretically infinite number of relativistic images, which are highly demagnified. A strongly naked singularity produces no relativistic images.

Abstract: We give analytical arguments and demonstrate numerically the existence of black hole solutions of the 4D effective superstring action in the presence of Gauss-Bonnet quadratic curvature terms. The solutions possess nontrivial dilaton hair. The hair, however, is of "secondary type," in the sense that the dilaton charge is expressed in terms of the black hole mass. Our solutions are not covered by the assumptions of existing proofs of the "no-hair" theorem. We also find some alternative solutions with singular metric behavior, but finite energy. The absence of naked singularities in this system is pointed out.