Relativistic acoustic geometry

We study spherical and nonspherical linear acoustic perturbations of the Michel flow, which describes the steady radial accretion of a perfect fluid into a nonrotating black hole. The dynamics of such perturbations are governed by a scalar wave equation on an effective curved background geometry determined by the acoustic metric, which is constructed from the spacetime metric and the particle density and four-velocity of the fluid. For the problem under consideration in this article the acoustic metric has the same qualitative features as an asymptotically flat, static and spherically symmetric black hole, and thus it represents a natural astrophysical analogue black hole.As for the case of a scalar field propagating on a Schwarzschild background, we show that acoustic perturbations of the Michel flow exhibit quasi-normal oscillations. Based on a new numerical method for determining the solutions of the radial mode equation, we compute the associated frequencies and analyze their dependency on the mass of the black hole, the radius of the sonic horizon and the angular momentum number. Our results for the fundamental frequencies are compared to those obtained from an independent numerical Cauchy evolution, finding good agreement between the two approaches. When the radius of the sonic horizon is large compared to the event horizon radius, we find that the quasi-normal frequencies scale approximately like the surface gravity associated with the sonic horizon.

show abstract

“…(18), which will play an important role later, can be computed using Eqs. (11) and (13). The result is…”

Section: Quasi-normal Oscillations From a Mode Analysismentioning

confidence: 94%

“…In [11] we proved that the branch corresponding to the global solution for n(r) extending from the horizon to infinity is the one with the + sign in Eq. (13).…”

Section: Review Of Michel Flow and Its Relevant Propertiesmentioning

confidence: 99%

Quasinormal acoustic oscillations in the Michel flow

2015

View full text Add to dashboard Cite

show abstract

“…In general, a 4-velocity can be expressed in terms of the 3-velocity components [7,8] u µ = γ 1 √ g 00 − g 0j v j g 00 ; v i , (2.1)…”

Section: Relativistic Kinematics Of the Flowmentioning

confidence: 99%

“…The analogue surface gravity κ may be calculated with help of the Killing field χ µ that is null on the horizon. We start from the expression [8,10] …”

Section: Surface Gravity and Hawking Temperaturementioning

confidence: 99%

Acoustic horizons in axially symmetric relativistic accretion

Abraham

Bilić

Das

2006

Class. Quantum Grav.

View full text Add to dashboard Cite

Transonic accretion onto astrophysical objects is a unique example of analogue black hole realized in nature. In the framework of acoustic geometry we study axially symmetric accretion and wind of a rotating astrophysical black hole or of a neutron star assuming isentropic flow of a fluid described by a polytropic equation of state. In particular we analyze the causal structure of multitransonic configurations with two sonic points and a shock. Retarded and advanced null curves clearly demonstrate the presence of the acoustic black hole at regular sonic points and of the white hole at the shock. We calculate the analogue surface gravity and the Hawking temperature for the inner and outer acoustic horizons.

show abstract

“…Energy is added to extrinsic topological systems to break time reversal symmetry [15][16][17][18][19][20]. A common example of an extrinsic approach is that of time-reversal symmetry breaking of acoustic waves by moving fluids [21][22][23][24][25][26][27][28][29]. Recently, extrinsic topological phononic crystals have demonstrated the astonishing property of non-reciprocity and backscattering-immune edge states and bulk states establishing classical equivalents of topological electronic insulators.…”

Section: Introductionmentioning

confidence: 99%

One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology

Deymier

Runge

2016

Crystals

View full text Add to dashboard Cite

There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.

show abstract

Relativistic acoustic geometry

Cited by 113 publications

References 15 publications

Quasinormal acoustic oscillations in the Michel flow

Quasinormal acoustic oscillations in the Michel flow

Acoustic horizons in axially symmetric relativistic accretion

One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology

Contact Info

Product

Resources

About