1 / 59

Acoustic Black Holes

Acoustic Black Holes. ーブラックホール物理を実験室で検証するー. 京都大学大学院　人間・環境学研究科 宇宙論・重力グループ M2 奥住　聡 共同研究者：阪上雅昭（京大　人・環） , 吉田英生（京大　工）. Outline. Introduction: “What is an Acoustic Black Hole”? “Acoustic BH Experiment Project” Application I: Hawking Radiation (classical analogue)

suelita-ypina
Télécharger la présentation

Acoustic Black Holes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Acoustic Black Holes ーブラックホール物理を実験室で検証するー 京都大学大学院　人間・環境学研究科 宇宙論・重力グループM2 奥住　聡 共同研究者：阪上雅昭（京大　人・環）, 吉田英生（京大　工）

  2. Outline • Introduction: “What is an Acoustic Black Hole”? • “Acoustic BH Experiment Project” • Application I: Hawking Radiation (classical analogue) • Application II: Quasinormal Ringing

  3. Introduction: • “What is an Acoustic Black Hole?”

  4. Interest and Difficulty in Black Hole Physics Black holes are the most fascinating objects in GR. Numerous quantum / classical phenomena have been predicted. For example, Hawking radiation (quantum) : thermal emission from BHs Quasinormal Ringing (classical) : characteristic oscillation of BHs However, many of them are difficult to observe. To examine them, an alternative way is nessesary!

  5. What is an Acoustic Black Hole? Acoustic BH region “effective” sound velocity in the lab “Acoustic BH” = Transonic Flow sonic point = sonic horizon down up In the supersonic region, sound waves cannotpropagate against the flow →“Acoustic Black Hole”

  6. Sound Waves in Inhomogeneous Fluid Flow Perturbation: -- wave eq. for velocity potential perturbation

  7. “Acoustic Metric”: Metric for Sound Waves Unruh, Phys. Rev. Lett. 46, 1351 (1981) This is precisely the eq. for a massless scalar field in a geometry with metric Furthermore, setting “Acoustic Metric”

  8. “Acoustic Metric”: Metric for Sound Waves Unruh, Phys. Rev. Lett. 46, 1351 (1981) “Acoustic Metric” Schwarzschild Metric sonic point horizon

  9. 2. Acoustic BH Experiment Project: Black Holes in Laval nozzles

  10. “Laval Nozzle”:Convergent-Divergent Nozzle throat

  11. Two Types of Steady Flow in Laval Nozzles Pressure difference pu/ pd determines the flow in the nozzle: Subsonic flow : max M at throat, but M<1 everywhere. Transonic flow : M=1 at throat; supersonic region exists. (may have a steady shock downstream) pd pu throat throat flow flow

  12. Acoustic BH Experiment Project at Kyoto Univ. THEORY Graduate School of H&E Studies EXPERIMENT Graduate School of Engineering numerical Planckian fit • TARGETS • Hawking Radiation • Quasinormal Ringing

  13. Configuration compressor mass flow meter settling chamber Laval nozzle flow 20cm

  14. Form of our Laval Nozzle R=200mm throat 61.6mm 61.6mm x=0 x b=8mm 100mm 100mm

  15. Preliminary Experiment: Acoustic Black Hole Formation subsonic transonic Acoustic BH is materialized in our experiments!!

  16. 3. Application I: Classical Analogue of Hawking Radiation

  17. Properties of Hawking Radiation Thermal emission from BHs. : “surface gravity” Quantum phenomenon; derived from QFT in curved ST. ( mixing of positive & negative freq. modes) Too weak to observe in the case of astrophysical BHs!

  18. How can we study Hawking Radiation? Hawking radiation of phonon in airflow: impossible!! (possible for BEC transonic flow ? [Garay et al., 2000] ) Nevertheless, some classical phenomena in acoustic BHs will shed light on quantum aspects of Hawking radiation. “classical counterpert of Hawking radiation”

  19. Positive & Negative Frequency Mode Mixing collapse BH exponential redshift horizon quantization negative freq. part appears! Particle Creation!! Nonstationary evolution of ST  Change of vacuum state surfacre gravity positive freq. mode (CLASSICAL) deformed observer star before collapse infinity

  20. Classical Counterpart of Hawking Radiation (Nouri-Zunoz & Padmanabhan, 1998) Inner product (Fourier tr.): negative freq. mode from infinity positive freq. mode for an observer Planck distribution!!

  21. Experimental Setting Step 1: subsonic background flow ( no horizon ). Send sinusoidal sound wave against the flow. Step 2: transonic background flow ( horizon present ). Observe the waveform at upstream region.

  22. Numerical Waveform (quasi-stationary flow, geometric acoustics limit) incident freq:15kHz Redshift due to surface gravity horizon formed

  23. Numerical Waveform (quasi-stationary flow, geometric acoustics limit) incident freq:15kHz Redshift due to surface gravity horizon formed

  24. Numerical Spectrum (quasi-stationary flow, geometric acoustics limit) incident freq:15kHz sinusoidal wave(t<0) (next slide)

  25. Numerical Spectrum (quasi-stationary flow, geometric acoustics limit) penetrates into positive frequency range! (next slide)

  26. Numerical Spectrum (quasi-stationary flow, geometric acoustics limit) 7 - ｴ 5 10 Numerical Planckian fit 7 - ｴ 4 10 7 - ｴ 3 10 S 7 - ｴ 2 10 7 - ｴ 1 10 500 1000 1500 2000 2500 3000 f Hz

  27. Observation in a Laboratory Signal is buried in noise. However, output of LIA implies that redshift occurs.

  28. Classical Counterpart of HR: Discussion Recently, full order calculation has been performed. Furuhashi, Nambu and Saida, CQG 23, 5417 (2006) Their results agree with our calculation. Planckian distr. seems to be robust. How about the effect of high frequency dispersion? Does the thermal emission of phonon really occur in quantum fluids (BEC / superfluid) ?

  29. 3. Application II: Quasinormal Ringing Okuzumi & Sakagami “Quasionormal Ringing of Acoustic Black Holes in Laval Nozzles” in preparation

  30. Quasinormal Ringing “Characteristic ‘sound’ of BHs (and NSs)” Arises when the geometry around a BH is perturbed and settles down into its stationary state. e.g. after BH formation / test particle infall Described as a superposition of acountably infinite number of damped sinusoids (QuasiNormal Modes, QNMs). QNM frequencies contain the information on (M,J) of BHs.

  31. Quasinormal Ringing of a BH NS-NS marger to a BH (Shibata & Taniguchi, 2006) inspiral phase marger phase QN ringing

  32. Mathematical Description of QNMs In general, QNMs are defined as solutions of .. Schrodinger-type Eq. with outgoing B.C. V(x): effective potential barrier

  33. Examples of Schroedinger-type Equation (1) Schwarzschild Black Hole

  34. Examples of Schroedinger-type Equation (1) Schwarzschild Black Hole horizon spatial infinity

  35. Examples of Schroedinger-type Equation (2) Acoustic Black Hole in a Laval Nozzle cs0: sound speed at stagnation points

  36. Potential Barrier for Different Laval Nozzles Consider two-parameter family of Laval nozzle. nozzle radius K : integer : radius of the throat 1.0 tank 1 nozzle tank 2 flow

  37. Potential Barrier for Different Laval Nozzles sonic horizon 3.92 1.04 flow 11.4 sonic horizon 1.19 flow

  38. QNM Frequencies of Different Laval Nozzle easier to observe Re/Im ~ 4 (WKB approx. is not good) (the least-damped (n=0) mode; 3rd WKB value)

  39. Numerical Simulation of Acoustic QN Ringing We perform two types of simulations: “Acoustic BH Formation” initial state: no flow set sufficiently large pressure difference final state: transonic flow “Weak Shock Infall” initial state: transonic flow ‘shoot’ a weak shock into the flow final state: transonic flow ~ BH formation ~ test particle infall

  40. Example of Transonic Flow sonic horizon supersonic subsonic flow

  41. Result 1: Weak Shock Infall QN ringing weak shock gif horizon steady shock

  42. Result 2: Acoustic BH Formation observed waveform numerical QNM fit nonlinear phase ringdown phase

  43. Result 2: Acoustic BH Formation observed waveform numerical QNM fit nonlinear phase ringdown phase

  44. Numerical Simulation: Summary In both types of simulations, QNMs are actually excited. The results agree with WKB analysis well ( for K >1 ). Typical values in laboratories:  similar to values for astrophysical BHs cf. Schwarzschild, l = 2 , least-damped mode

  45. Numerical Simulation: Discussion For future experiments, larger Q-value is wanted. However, Q is at most ~ 2 for planar wave modes. QNMs for non-planar waves QNMs of an Acoustic BH surrounded by a “half-mirror” (contact surface) Can matched filtering be used in our experiments ?

  46. Summary “Acoustic BH” = Transonic Flow wave eq. for sound in perfect fluid  wawe eq. for a massless scalar field in curved ST sonic point  event horizon of a BH Results of numerical simulations strongly suggest that classical counterpart of HR and QN ringing can be realized in a laboratory.

  47. Appendix

  48. Standard Procedure for Calculating QNM Freq’s Calculate the “S-matrix” for the potential barrierV(x): : “S-matrix” Then, impose the outgoing B.C. , and obtain k’s that meet the boundary condition.

  49. WKB Approach 1st order: Schutz & Will, 1985 3rd order: Iyer & Will, 1987 6th order: Konoplya, 2004 ExpandV(x) in a Taylor series about the maximum pointx0: Region (I) & (III): WKB solutions for truncatedV(x) Aroundx0 : exact solution for truncatedV(x) Matching (I) (II) (III) k2 matching regions x12 x0 x23

  50. WKB Approach: S-Matrix where Here, n is related to k by (1st WKB)

More Related