Surface temperature of an accretion disk around a wormhole Kerr-mimicker

TL;DR

This paper investigates whether Kerr-like wormholes can mimic Kerr black holes in accretion-disk observables. Using a Lagrangian formulation for test-particle orbits and standard thin-disk theory, it shows that equatorial circular-orbit properties (e.g., $\Omega$, $E$, $l$, and Lense-Thirring precession) coincide with Kerr for the same $M$ and $a$ when the spacetime differs only in the radial metric component $g_{rr}$. The key distinguishing feature is a robust suppression of the disk's surface temperature near the wormhole throat due to the altered radial metric, with the effect quantified by $T/\tilde{T}=(\tilde{g}_{rr}/g_{rr})^{1/8}$ and approaching zero at the throat. The suppression is significant for traversable wormholes with moderate to large deviation parameter values (e.g., $\lambda^2\sim 0.1$–1) and can serve as an observational signature, though realistic appearance requires ray-tracing of light paths.

Abstract

It has been suggested that spinning wormholes may mimic Kerr black holes in astronomical sources such as X-ray binaries and supermassive compact objects in centers of galaxies. With recent advances in instrumentation this could be tested if clear differences between wormhole and black hole accretion were identified. We aim to quantitatively determine the extent to which the orbital properties of test particles in the gravity of a spinning wormhole may differ from those of a Kerr black hole. We seek to find an observable related to disk accretion that would be clearly different for Kerr black holes and Kerr-like wormholes. We use the standard Lagrangian approach to derive the orbital properties of test particles from an effective potential. We use standard thin disk theory to infer the disk surface temperature. We find that at a given circumferential radius the physical quantities relating to circular orbits in the equatorial plane are exactly the same for the spinning wormhole and a black hole of the same mass and angular momentum, if only the two space-time metrics differ in the g_rr component alone. However, for a wormhole there are no orbits of radius less than that of its throat. Non-circular orbits, bound or unbound, are affected by the radial distance function; in particular, the angle of apsidal precession in Kerr-like wormholes will differ from that in Kerr black holes. A Kerr-like wormhole is a perfect black hole mimicker in relation to the orbital properties in the equatorial plane. The angular velocity, specific energy, specific angular momentum, and Lense-Thirring precession rate are the same for a Kerr black hole and a Kerr-like wormhole in circular orbits of the same circumference. We find that the area of the (geometrically thin) accretion disk is different, and this yields a visibly suppressed disk temperature for traversable wormholes with a sufficiently wide throat.

Figures (2)

• Figure 1: Ratio of the surface temperatures of an accretion disk around a non-spinning wormhole and around a Schwarzschild black hole. The vertical dashed line indicates the position of the ISCO. Left panel: the traversable wormhole ($\tilde{M} > M$). The curves correspond to fixed values of $\tilde{M}/M$, which increase from left to right. Right panel: a wormhole with an event horizon outside its throat ($\tilde{M} < M$). The curves correspond to fixed values of $\tilde{M}/M$, which increase from top to bottom.
• Figure 2: Ratio of the surface temperature of an accretion disk for a spinning wormhole to that of a Kerr black hole, for spin $a=0.95M$. The ordinate axis is at the photon orbit $r_\textrm{ph} = 1.386 M$. The dashed vertical line marks the radial coordinate of the ISCO. The retrograde photon orbit is at the gray dotted line, and the retrograde ISCO at the dot-dashed line. Left panel: the traversable wormhole ($\tilde{M} > M$). The curves correspond to fixed values of $\tilde{M}/M$, which increase from left to right. Right panel: a wormhole with an event horizon outside its throat ($\tilde{M} < M$). The curves correspond to fixed values of $\tilde{M}/M$, which increase from top to bottom.