Waves and null congruences in a draining bathtub

Dempsey, David; Dolan, Sam R.

doi:10.1142/s0218271816410042

Cited by 7 publications

(5 citation statements)

References 40 publications

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“…In the 2D setting, the Raychaudhuri equation is 'missing' the factor of 1/2 in front of ϑ 2 , and the shear tensor vanishes identically. In addition, geodesics are hypersurface orthogonal (k µ is a gradient) and so the vorticity tensor vanishes as well [30]. Hence Eq.…”

Section: Appendix A: Raychauduri's Equation and Ricci Tensormentioning

confidence: 98%

Wave focusing by submerged islands and gravitational analogues

Torres¹,

Lloyd²,

Dolan³

et al. 2022

Preprint

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We study water waves propagating over a smooth obstacle in a fluid of varying depth, motivated by the observation that submerged islands in the ocean act as effective lenses that increase the amplitude and destructive power of tsunami waves near focal points. We show that islands of substantial height (compared to the water depth) lead to strong focusing in their immediate vicinity, and generate caustics of either cusp or butterfly type. We highlight similarities and differences with focusing of (high-frequency) gravitational waves by a neutron star. In the linear regime, the comparison is made precise through an effective-spacetime description of the island-fluid system. This description is then put to practical use: we identify caustics by solving the Raychaudhuri equation (a transport equation) along rays of the effective metric. Next, the islandfluid scattering processes are examined in detail (i.e. deflection angle, phase shifts, scattering amplitudes) using numerical simulations and analytical techniques, including the eikonal approximation and its generalisation in the form of the Gaussian beam approximation. We show that the techniques capture the key features of the simulations. Finally, we extend the eikonal approximation to the dispersive regime, demonstrating that the essential features are robust in dispersive settings. This paves the way for future exploration in a controlled laboratory set-up.

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Section: Appendix A: Raychauduri's Equation and Ricci Tensormentioning

confidence: 98%

Wave focusing by submerged islands and gravitational analogues

Torres¹,

Lloyd²,

Dolan³

et al. 2022

Preprint

Self Cite

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“…Radially directed photons have no angular momentum so p ϕ = 0. Then, normalizing the time component to p t = −1 [50] leads equation (68) to give the radial momentum that reproduces the wave vector used by Chen and Kantowski [33].…”

Section: Dispersive Media In Physical Spacetimementioning

confidence: 99%

“…The photon energy can always be normalized to k t = −1 by adjusting the affine parameter by a constant factor [50]. For such a radially directed ray, the complex eikonal is…”

Section: Opacity In the Schwarzschild Spacetimementioning

confidence: 99%

Ray tracing through absorbing dielectric media in the Schwarzschild spacetime

Rogers

2024

Class. Quantum Grav.

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General Relativity describes the trajectories of light-rays through curved spacetime near a massive object. In addition to gravitational lensing, we include an absorbing dielectric medium given by a complex refractive index known as the Drude model. When absorption is included the eikonal becomes complex, with the imaginary part related to the absorption along a ray between emission and observation points. We extend results from the literature to include dispersion in the index of refraction. The complex Hamiltonian splits into a real part that describes the equations of motion and a constraint equation that governs the momentum loss in the system. We work in coordinates which are fully real, with a real metric in physical spacetime. We assume the dust and plasma distributions of the Drude matter to coincide and vary as a power-law $1/r^h$. We find that transmission requires $h>1$, otherwise exponential absorption occurs along ray paths. We use ray-tracing through strongly absorbing matter near the surface of the compact star, as well as specializing to a point-lens in the weak-field limit with weakly absorbing matter to generate potentially observable light curves for distant observers. In the appropriate limits, our theory reproduces results from the literature.

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“…Moreover, wave scattering around a draining bathtub vortex has been extensively studied [66][67][68][69][70]. Under the influence of the effective acoustic metric from the draining bathtub vortex, the waves can display the analogue Aharonov-Bohm effect, superradiance effect, and orbiting oscillations in the scattering length [66,68,70].…”

Section: Analogue Gravitational Lensingmentioning

confidence: 99%

Analogue Gravitational Lensing in Bose-Einstein Condensates

Ma,

Jia,

Solano

et al. 2023

Universe

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We consider the propagation of phonons in the presence of a particle sink with radial flow in a Bose–Einstein condensate. Because the particle sink can be used to simulate a static acoustic black hole, the phonon would experience a considerable spacetime curvature at appreciable distance from the sink. The trajectory of the phonons is bended after passing by the particle sink, which can be used as a simulation of the gravitational lensing effect in a Bose–Einstein condensate. Possible experimental implementations are discussed.

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Waves and null congruences in a draining bathtub

Cited by 7 publications

References 40 publications

Wave focusing by submerged islands and gravitational analogues

Wave focusing by submerged islands and gravitational analogues

Ray tracing through absorbing dielectric media in the Schwarzschild spacetime

Analogue Gravitational Lensing in Bose-Einstein Condensates

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