Observational and theoretical aspects of Superspinars

TL;DR

The paper argues that superspinars with scalar‑regular interiors (SR‑superspinars) avoid the naked singularities and causality issues of classical Kerr superspinars by choosing mass functions $M(r)$ with $M(0)=M'(0)=M''(0)=0$, enabling a topologically trivial, horizonless spacetime. It employs a Gürses–Gürsey Kerr–Schild metric to model rotating SR objects and analyzes the inner Planckian region as a nonellipsoidal Planckian pseudotorus with major radius ~$|a|$ and minor radii of order a few $l_P$, with a potentially visible boundary for distant observers. The study derives conditions for null geodesics reaching $r=0$, showing that SR cases permit geodesics to access the ring from non-equatorial directions, unlike Kerr, and predicts distinctive silhouettes consisting of an unstable‑orbit arc and an observable ring ellipse without a dark shadow. It also discusses the effective energy–momentum content and the stability of circular orbits, noting that some SR models may be stable while others could exhibit nonlinear instabilities, and highlighting the observational potential to test quantum gravity effects via high-curvature interiors. Overall, the work provides a framework where quantum‑gravity‑regulated interiors yield observationally distinguishable signatures from black holes and classical superspinars, with implications for future high-resolution imaging and tests of strong gravity.

Abstract

This article delves into the observational signatures and theoretical underpinnings of rotating astrophysical objects, with a particular focus on superspinars -exotic objects characterized by the absence of event horizons due to their high angular momentum. While solutions within General Relativity (Kerr superspinars) predict such objects, their classical forms harbor naked singularities, violate causality, and exhibit problematic repulsive gravitational effects. These characteristics render classical superspinars theoretically objectionable, leading to the consideration of them as physically implausible. On the other hand, the incompatibility between General Relativity and Quantum Mechanics suggests the exploration of alternative models, particularly those in which Quantum Gravity dominates the core and prevents the formation of scalar curvature singularities. This work demonstrates that superspinars without scalar curvature singularities can avoid all the complications associated with Kerr superspinars. Moreover, from a phenomenological standpoint, it is shown that the silhouettes of these superspinars could be markedly distinct from those of black holes and classical Kerr superspinars. To substantiate these differences, we perform a comprehensive analysis of inner null geodesics and investigate the structure of the Planckian region within superspinars without scalar curvature singularities. Our study reveals that only these superspinars provide the potential for distant observers to directly observe the extremely high curvature regions within their interiors.

Figures (13)

• Figure 1: Left: Penrose diagram for Kerr's superspinar. The spacetime is extended through $r=0$ to an asymptotically flat region with negative values for $r$. (Note that the diagram is valid for $\theta\neq \pi/2$. The diagram with $\theta= \pi/2$ will require drawing the ring singularity). Right: Penrose diagram for a topologically trivial SR superspinar. (Note that, since there are no singularities, the diagram is valid for all $\theta$).
• Figure 2: A plot of the behaviour of the toroidal coordinates with the (SR) ring ($\rho=0$) highlighted in black.
• Figure 3: Polar plot of $\tilde{\mu}\equiv \mu/(6 m_3)$ and (minus) $\tilde{p}_x\equiv p_x/(3 m_3)$ around the ring for the case $\mathcal{M}(r)\sim r^3$ around $r=0$.
• Figure 4: An example of the region with planckian densities ($\mu\sim \mu_{Planck}$) in BL coordinates (dark region). Note that the region has a maximum minor radius of the order of a few $l_P$ and that it is concentrated around $\theta=\pi/2$ (i.e., the equatorial plane). In this example it has not been necessary to plot the region with $0\leq\theta\leq 1.53$ since it does not have planckian densities. We have specifically used the BR model. However, the results are qualitatively similar for all SR models under the assumptions in subsection \ref{['secRegu']}.
• Figure 6: A light-like geodesic (red) with non-null angular momentum ($\xi\neq 0$) crossing the disk of an SR-superspinar from the region with $z>0$ to the region with $z<0$. The planckian region is represented by a pseudotorus. As required in order to cross the disk, Carter's constant is negative $\eta<0$ and the parameters have been chosen among the required conditions for these geodesics. Specifically, $\eta=-10$, $\xi=1$ and $E=1$. On the other hand, the BR superspinar is defined by the parameters $M=100$, $a=100$, $l=1$ and $L=100$ that, as required for superspinars, avoid the formation of horizons since $\Delta\neq 0$. In this topologically trivial SR-superspinar, once the geodesic crosses the disk, $r$ monotonically increases along it.

Theorems & Definitions (2)

• Theorem 1
• Theorem 2