Gravitational Waves from a Black Hole Falling into a Traversable Wormhole ✦
The gravitational-wave signal from the radial infall of a stellar-mass black hole into a traversable thin-shell Schwarzschild wormhole is computed. In the test-particle approximation, analytical expressions for the waveform including contributions from the mass quadrupole and higher multipoles are derived. The resulting signal exhibits a characteristic 'pulse—pause' structure due to multiple throat crossings. The amplitude spectral density is calculated, and for optimal source orientation, it falls within the sensitivity band of ground-based detectors for distances on the order of 500 Mpc. The results point to the possibility of detecting traversable wormholes in gravitational-wave observational data.
Context
The direct detection of gravitational waves from mergers of black holes and neutron stars by the LIGO/Virgo collaboration opened a new window into astrophysics. But beyond standard sources, gravitational waves can carry the imprint of exotic objects predicted by general relativity and quantum theories of gravity. One of the most intriguing hypothetical objects remains traversable wormholes — 'tunnels' in spacetime, first proposed by Kip Thorne and colleague Morris. In the strong fields of such objects, extreme time dilation occurs, and the propagation of gravitational waves themselves happens at the speed of light. Detecting them would be a breakthrough in understanding the quantum structure of spacetime, since wormholes require exotic matter that violates classical energy conditions.
Methods
The authors modeled the wormhole using the Visser method, gluing two Schwarzschild spacetimes together along a thin shell with exotic matter at the throat. A black hole of 5 solar masses, treated as a test particle, falls radially into a wormhole of 200 solar masses. Its motion is described by geodesics in curved spacetime, including time dilation effects. Gravitational radiation was computed analytically using quadrupole and octupole approximations, with the cross-polarization vanishing due to symmetry. The mass quadrupole moment plays a key role, and the constant speed of light enters the signal amplitude, linking to Earth-based detectors.
Results
The resulting gravitational-wave signal exhibits a characteristic structure: repeated bursts in 'our' universe and complete dropouts when the black hole is behind the wormhole throat. The amplitude grows as it nears the throat and cuts off abruptly at the transition. The amplitude spectral density (ASD) reaches ~10⁻²² Hz⁻¹/² at 500 Mpc, intersecting the LIGO sensitivity curves in the 10–100 Hz band. This means existing ground-based interferometers could potentially detect such events under optimal orientation. The observed signal modulation carries information about the geometry of curved spacetime near the throat, and time dilation effects distort the burst timing. The gravitational waves themselves travel at the speed of light, encoding the delay.
Implications
Detecting such a signal would directly confirm the existence of wormholes — objects that violate classical energy conditions and require a quantum description of gravity. It would provide an observational foundation for theories beyond general relativity and allow the study of topologically nontrivial solutions to Einstein's equations in curved spacetime. Indirect evidence of exotic matter would revolutionize our understanding of the vacuum and fundamental fields, and would connect black holes with quantum effects.
Future development
Further research will include rotating wormholes (Kerr solutions) and non-zero angular momentum of the black hole, which will generate more complex gravitational-wave patterns. For realistic predictions, full-scale numerical simulations will be needed, accounting for radiation back-reaction on the orbit and nonlinear gravity effects. Such simulations will form the basis for constructing templates suitable for searching signals in data from future gravitational-wave detectors.
Impact
The results will influence search strategies for non-traditional sources of gravitational waves in astrophysics, the development of quantum gravity theories, and the interpretation of data from LIGO and planned observatories like the Einstein Telescope.
Next steps
Immediate next steps include applying matched-filtering techniques to archival LIGO data to search for bursting signals with the characteristic modulation, and analytically extending the model to non-zero eccentricities and tidal effects.
Key open problems
The research directly addresses the fundamental problem of energy condition violation in wormholes and the need for a quantum description of gravity to explain their structure. It also touches on the stability of spacetime tunnels in curved spacetime and their connection to the black hole information paradox.
🎯 For the system considered, the wormhole throat area is about 3600 times larger than the black hole's horizon area. It falls in like a basketball into a huge tunnel, barely disturbing the geometry. Due to the negative energy density of exotic matter, the black hole doesn't swallow it; instead it gets repelled, preventing the wormhole from collapsing.
🎬 The idea of a traversable wormhole was featured in the film 'Interstellar' (with [scientist:Kip Thorne]Kip Thorne[/scientist] as scientific consultant), where astronauts make an interstellar journey through such a tunnel. The signatures proposed in the paper offer a real chance to 'hear' a black hole diving into a wormhole, turning science fiction into observational science.
Key numbers
- Wormhole mass: 200 M☉
- Black hole mass: 5 M☉
- Distance to source: 500 Mpc
- Throat radius: 3 r_Sch (M_WH)
- Typical burst duration: about 0.1 s