Gravitational waves from a black hole orbiting in a wormhole geometry

Current ground-based gravitational wave detectors are tuned to observe compact object mergers from stellar mass black holes and neutron stars; $\sim 50$ such events have been published to date. More exotic compact objects may exist, collisions of which would also generate copious gravitational waves. We model a stellar mass black hole inspiral into a stable, nonspinning, traversable wormhole, and find a characteristic waveform—an antichirp and/or burst—as the black hole outspirals into our region of the Universe. This is a characteristic signature which can be useful in wormhole searches in gravitational wave data or used to constrain wormhole geometries.

Figure 1

We show an embedding diagram depicting a wormhole that connects two different universes, where the upper branch is Universe 1 and the lower is Universe 2. The throat is a thin shell of “exotic material” and there is no spacetime within the “hole.”

Figure 2

We show the embedding diagram for an orbit following Diemer and Smolarek [45] for a BH with mass $5M_{\odot }$ around and through a WH with an effective mass $200M_{\odot }$. Without GWs this would be a bound, circular orbit in Universe 1 (top half). The initial position is at the top of the hyperboloid; the inspiral of the BH can be seen. As it passes the throat into Universe 2 (bottom half), we indicate orbits in Universe 2 with dashed lines. Five “passes” or “petals” are shown, three in Universe 1 and two (dashed) in Universe 2.

Figure 3

We show the orbits of the BH in Fig. 2 from above. The orbit starts in Universe 1 and traverses to 2, then back in 1, etc. The black circle marks the initial position and the circulation of the orbits are counterclockwise. The solid gray circle is approximately the WH throat—the center of the WH executes the small orbit indicated by the black dot around the origin. Orbits in Universe 2 are shown dashed.

Figure 4

Shown is the dimensionless gravitational strain measured for the WH-BH binary shown in Fig. 3 at a distance of 500 Mpc and at $\phi =\pi /4$ and $\theta =\pi /4$ relative to the binary orbital plane. The WH mass is $200M_{\odot }$ and the BH is $5M_{\odot }$. The estimated GW frequency of this example is approximately 9 Hz near $t=0$.

Figure 5

Shown here is the dimensionless gravitational strain of Fig. 4 showing the gaps at the late times when the BH is passing back and forth between universes. We display only waves for Universe 1.