Logarithmic catastrophes and Stokes's phenomenon in waves at horizons
arXiv:2209.11148 · doi:10.1088/1751-8121/acb29e
Abstract
Waves propagating near an event horizon display interesting features including logarithmic phase singularities and caustics. We consider an acoustic horizon in a flowing Bose-Einstein condensate where the elementary excitations obey the Bogoliubov dispersion relation. In the hamiltonian ray theory the solutions undergo a broken pitchfork bifurcation near the horizon and one might therefore expect the associated wave structure to be given by a Pearcey function, this being the universal wave function that dresses catastrophes with two control parameters. However, the wave function is in fact an Airy-type function supplemented by a logarithmic phase term, a novel type of wave catastrophe. Similar wave functions arise in aeroacoustic flows from jet engines and also gravitational horizons if dispersion which violates Lorentz symmetry in the UV is included. The approach we take differs from previous authors in that we analyze the behaviour of the integral representation of the wave function using exponential coordinates. This allows for a different treatment of the branches that gives rise to an analysis based purely on saddlepoint expansions, which resolve the multiple real and complex waves that interact at the horizon and its companion caustic. We find that the horizon is a physical manifestation of a Stokes surface, marking the place where a wave is born, and that the horizon and the caustic do not in general coincide: the finite spatial region between them delineates a broadened horizon.
arXiv comment34 pages, 12 figures
References in corpus (46)
- Fiber-optical analogue of the event horizon
- Dumb Holes and the Effects of High Frequencies on Black Hole Evaporation
- Sonic analog of gravitational black holes in Bose-Einstein condensates
- Observation of quantum Hawking radiation and its entanglement in an analogue black hole
- Measurement of stimulated Hawking emission in an analogue system
- Hawking Spectrum and High Frequency Dispersion
- Observation of self-amplifying Hawking radiation in an analog black hole laser
- Observation of thermal Hawking radiation at the Hawking temperature in an analogue black hole
- Hawking radiation from ultrashort laser pulse filaments
- Realization of a sonic black hole analogue in a Bose-Einstein condensate
- Sonic black holes in dilute Bose-Einstein condensates
- Numerical observation of Hawking radiation from acoustic black holes in atomic Bose-Einstein condensates
- Observation of negative-frequency waves in a water tank: A classical analogue to the Hawking effect?
- Gravity wave analogs of black holes
- Hawking Radiation Without Transplanckian Frequencies
- Observation of Stimulated Hawking Radiation in Optics
- Non-local density correlations as signal of Hawking radiation in BEC acoustic black holes
- Computing the spectrum of black hole radiation in the presence of high frequency dispersion: an analytical approach
- Black-hole radiation in Bose-Einstein condensates
- Observation of noise correlated by the Hawking effect in a water tank
- The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
- On the Universality of the Hawking Effect
- Bogoliubov Theory of acoustic Hawking radiation in Bose-Einstein Condensates
- Observation of stationary spontaneous Hawking radiation and the time evolution of an analogue black hole
- Quantum catastrophe of slow light
- The asymptotic quasinormal mode spectrum of non-rotating black holes
- Quantum fluctuations around black hole horizons in Bose-Einstein condensates
- Horizon effects with surface waves on moving water
- Black hole radiation with short distance dispersion, an analytical S-matrix approach
- Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate
- Acoustic white holes in flowing atomic Bose-Einstein condensates
- Generalization of the model of Hawking radiation with modified high frequency dispersion relation
- Scattering of co-current surface waves on an analogue black hole
- Undulations from amplified low frequency surface waves
- Short-distance contribution to the spectrum of Hawking radiation
- Hawking radiation with dispersion: The broadened horizon paradigm
- The trans-Planckian problem as a guiding principle
- An analytic evaluation of gravitational particle production of fermions via Stokes phenomenon
- Birth of a quasi-stationary black hole in an outcoupled Bose-Einstein condensate
- Black hole radiance, short distances, and TeV gravity
- Globally exact asymptotics for integrals with arbitrary order saddles
- Stokes phenomenon and Hawking Radiation
- Confirmation of stimulated Hawking radiation, but not of black hole lasing
- Oscillatory path integrals for radio astronomy
- Towards a classification of wave catastrophes
- Non-linear Processes and Stimulated Hawking Radiation in Hydrodynamics for Decelerating Subcritical Free Surface Flows with a Subluminal Dispersion Relation
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