By Ted Jacobson (auth.), Daniele Faccio, Francesco Belgiorno, Sergio Cacciatori, Vittorio Gorini, Stefano Liberati, Ugo Moschella (eds.)
Analogue Gravity Phenomenology is a suite of contributions that disguise an unlimited variety of components in physics, starting from floor wave propagation in fluids to nonlinear optics. The underlying universal element of a lot of these themes, and for that reason the focus and point of view from which they're defined the following, is the try to increase analogue versions for gravitational structures. the unique and major motivation of the sector is the verification and research of Hawking radiation from a horizon: the allowing function is the prospect to generate horizons within the laboratory with quite a lot of actual structures that contain a move of 1 style or one other. The years round 2010 and onwards witnessed a unexpected surge of experimental task during this increasing box of study. even though, construction an services in analogue gravity calls for the researcher to be built with a slightly huge variety of data and pursuits. the purpose of this e-book is to deliver the reader modern with the most recent advancements and supply the elemental historical past required that allows you to enjoy the ambitions, problems, and good fortune tales within the box of analogue gravity.
Each bankruptcy of the publication treats a special subject defined intimately via the main specialists for every particular self-discipline. the 1st chapters provide an summary of black gap spacetimes and Hawking radiation ahead of relocating directly to describe the massive number of analogue spacetimes which have been proposed and are at the moment below research. This introductory half is then by means of an in-depth description of what are at present the 3 such a lot promising analogue spacetime settings, particularly floor waves in flowing fluids, acoustic oscillations in Bose-Einstein condensates and electromagnetic waves in nonlinear optics. either thought and experimental endeavours are defined intimately. the ultimate chapters consult with different elements of analogue gravity past the learn of Hawking radiation, akin to Lorentz invariance violations and Brownian movement in curved spacetimes, prior to concluding with a go back to the origins of the sector and an outline of the on hand observational proof for horizons in astrophysical black holes.
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Extra resources for Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons, from Theory to Experiment
20) has the interesting property that it is conformally invariant. That is, it is unchanged by a conformal rescaling of the metric gab → Ω 2 gab , provided the conformal factor Ω is regular at the horizon . This follows simply because |χ| is rescaled by Ω, while the norm of its gradient is rescaled by Ω −1 , and the contribution from dΩ vanishes since it is multiplied by |χ|H which vanishes. 13) and the Killing vector χ = ∂t we have |χ| = c2 − v 2 , 1/2 which depends on x and not t. Thus κ = (−g xx ∂x |χ|∂x |χ|)H , and the minus sign arises because the gradient is spacelike outside the horizon.
33) Near a horizon x = xH where v = −c we have the expansions v/c = −1 + O(x − xH ) and v 2 /c − c = −2κ(x − xH ) + O[(x − xH )2 ]. 34) whose solutions have the form u ∼ (x − xH )iω/κ = ei(ω/κ) ln(x−xH ) . 35) The logarithmic divergence in the phase justifies the dominance of spatial derivatives of ϕ near the horizon. 12), which we inferred in Sect. 4 using the equation of outgoing lightrays to propagate the phase of the wave in the near horizon region. Now let’s see how to arrive at the same approximate solution using the dispersion relation with the fluid picture.
Positive norm modes that are localized can be recognized as those that have positive frequency in the fluid frame. In the relativistic case, this amounts to positive frequency in any freely falling frame. The time derivative in the fluid frame is (∂t )f = ∂t + v∂x . 35) near the horizon, this is dominated by the second term, and v ≈ −c, hence for such modes positive frequency with respect to t in the fluid frame is the same as positive frequency with respect to x. 35) with logarithmic phase divergence at the horizon can be analytically continued across the horizon to make either a positive or a negative frequency solution.
Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons, from Theory to Experiment by Ted Jacobson (auth.), Daniele Faccio, Francesco Belgiorno, Sergio Cacciatori, Vittorio Gorini, Stefano Liberati, Ugo Moschella (eds.)