The space-time structure of an untouchable naked singularity in superstrings theory

Abstract

According to the Cosmic Censorship Conjecture, naked singularities are believed to be forbidden in nature and must remain hidden by an event horizon. In this work, we present the causal structure of an exact solution to the Einstein-Maxwell-Dilaton equations with five parameters: mass, angular momentum, electric and magnetic charges, and a scale, satisfying constraint equations. For one of the constraints, the solution represents a wormhole (WH), and for the other, a black hole (BH), both with an untouchable ring singularity causally disconnected from the rest of the universe. After topologically defining the concept of Wormhole Cosmic Censorship (WCC), we analyze its metric functions in Papapetrou coordinates to verify metric analyticity in spacetime, construct the Carter-Penrose diagram, and use Boyer-Linquist coordinates to visualize the cladding of the ring singularity by the throat. We conclude that the ring singularity in this WH is clad by the throat, similarly to how the event horizon clads the ring singularity in the Kerr-Newman black hole, thus satisfying the WCC Conjecture. In this work, we show that the topology of the WH throat is such that the two sides of the throat are separated by the singularity but topologically identified, resulting in an instantaneous connection between these two regions. These results are applicable to various theories, including Kaluza-Klein and superstring theory. We provide a rigorous proof that, in the black hole case, the domain of outer communication includes a chronology-violating region and thus supports the existence of closed timelike curves outside the event horizon.

Figures (4)

• Figure 1: The black outer layer signifies the event horizon, while the inner black layer denotes the Cauchy surface, the blue torus symbolizes the ring singularity, while the yellow layer indicates a surface singularity and the orange signifies another one. This figure is a schematically Cosmic Censorship illustration.
• Figure 2: This figure illustrates the numerical schematic of the WCCC employing the parameters $\lambda_0=10^{-3}$, $(L_{+}=1)$, and $k_0=3/4$ (in the context of Superstrings theory with a dilatonic field). The royal blue line denotes the throat ($x=0$) under the condition $y \notin [-45\lambda_0, 45\lambda_0]$. The outermost sky blue line signifies the deformed throat within the region $y \in [-45\lambda_0, 45\lambda_0]$, characterized by the conditions $\frac{d \, \text{Areal}}{d r}|_{x_G}=0$ and $\frac{d^2 \, \text{Areal}}{d x^2}|_{x_G}>0$. The dashed gray line depicts the throat in the equatorial plane ($y_0=0$), where it is found that $x_G \approx 0.02941> x_v \approx \lambda_0$. Furthermore, the yellow point signifies the ring singularity, while the two black circles represent the boundaries where Closed Timelike Curves (CTCs) emerge, indicating that CTCs are present within these two circles.
• Figure 3: Carter–Penrose diagrams corresponding to each universe at the equatorial plane $y_0=0$.
• Figure 4: Carter-Penrose diagram at the equatorial plane $y_0=0$, representing the WH ring. The dashed lines represent throats topologically connecting $R_G$ to $-R_G$, which cover the singularity of the ring and the chronology-violation region $x<x_*(0)$.

Theorems & Definitions (15)

• Definition 2.1: Topological enclosure by the throat
• Proposition 2.1: Operational enclosure criterion in meridional variables ($x,y$)
• proof
• Remark 2.1: Horizon inclusion
• Conjecture 2.1: Wormhole Cosmic Censorship Conjecture, topological form
• Remark 2.2: Causal reading
• Remark 2.3: What WCCC does not claim
• Lemma 3.1: Exponential domination
• proof
• Proposition 3.1: Existence of a real outer root $x_v(y)>1$