Sine-Gordon soliton as a model for Hawking radiation of moving black holes and quantum soliton evaporation

Villari, Leone Di Mauro; Marcucci, Giulia; Braidotti, Maria Chiara; Conti, Claudio

doi:10.1088/2399-6528/aac340

Cited by 14 publications

(10 citation statements)

References 39 publications

(52 reference statements)

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“…where Hamiltonian H = 8/ √ 1 − v 2 and momentum P = 8v/ √ 1 − v 2 , which are energy and momentum of a relativistic particle of mass M = 8 in terms of a unit 'speed of light'. The right hand side of (20) should be interpreted as a heat term in line with the known result that the sine-Gordon kink radiates at temperature T H = v/(2π) [38]. This first law thus gives an entropy linked to momentum as dS = 2πdP or S = 2πP , again showing the 2π dependence of the entropy on a soliton parameter in two dimensions.…”

Section: Sine-gordon Kink Thermodynamicssupporting

confidence: 58%

“…All of the relevant formulas, including AKNS matrices and coordinate transformations leading to a Schwarzschild form of the metric can be found in Ref. [38]. We include this result here to contrast with our NLSE soliton Hawking temperature found in the previous section.…”

Section: The Case Of the Kdv Soliton And Sine-gordon Kinkmentioning

confidence: 93%

“…This equation has found uses in differential geometry, relativistic field theory and Josephson junction theory, amongst other places [35]. Its IST-induced geometry has been studied before by Gegenberg [34] and later in great detail by one of the authors [36] and was found to describe a 2D black hole with Hawking temperature T H =v/(2π) where v is the velocity of the kink. All of the relevant formulas, including AKNS matrices and coordinate transformations leading to a Schwarzschild form of the metric can be found in [36].…”

Section: The Case Of the Kdv Soliton And Sine-gordon Kinkmentioning

confidence: 99%

“…Its IST-induced geometry has been studied before by Gegenberg [34] and later in great detail by one of the authors [36] and was found to describe a 2D black hole with Hawking temperature T H =v/(2π) where v is the velocity of the kink. All of the relevant formulas, including AKNS matrices and coordinate transformations leading to a Schwarzschild form of the metric can be found in [36]. We include this result here to contrast with our NLSE soliton Hawking temperature found in the previous section.…”

Section: The Case Of the Kdv Soliton And Sine-gordon Kinkmentioning

confidence: 99%

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Universal quantum Hawking evaporation of integrable two-dimensional solitons

2019

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We show that any soliton solution of an arbitrary two-dimensional integrable equation has the potential to eventually evaporate and emit the exact analogue of Hawking radiation from black holes. From the AKNS matrix formulation of integrability, we show that it is possible to associate a real spacetime metric tensor which defines a curved surface, perceived by the classical and quantum fluctuations propagating on the soliton. By defining proper scalar invariants of the associated Riemannian geometry, and introducing the conformal anomaly, we are able to determine the Hawking temperatures and entropies of the fundamental solitons of the nonlinear Schrödinger, KdV and sine-Gordon equations. The mechanism advanced here is simple, completely universal and can be applied to all integrable equations in two dimensions, and is easily applicable to a large class of black holes of any dimensionality, opening up totally new windows on the quantum mechanics of solitons and their deep connections with black hole physics. their energy and mass is radiated away. This outward flux of radiation can be measured at infinity with a characteristic temperature known as the Hawking temperature [4]. Since Hawking's seminal work other thermodynamical properties of black holes have been described in detail, perhaps most significantly the entropy, which in four dimensions turns out to be proportional to the black hole surface area, an observation due to Bekenstein which predates Hawking's work [5]. This result has had major implications for modern physics, and as its study requires a combination of general relativity, quantum field theory, thermodynamics and information theory, it is considered a promising route towards a deeper understanding of quantum gravity [6].Much literature has been devoted, experimentally and theoretically [7][8][9][10][11], to the possible detection of Hawking radiation in classical or semiclassical analogue systems (typically optical, hydrodynamical or based on quantum condensates), due to the considerable (and probably insurmountable) difficulty of detecting it in a real astrophysical setting. In light of Salam and Strathdee's conjecture about the equivalence between solitons and black holes, it is suggestive to imagine that the exact analogue of Hawking radiation can be directly seen in the physics of solitons. It is however important to establish a precise, unambiguous mathematical and physical connection between the two objects, something that we shall do in the present paper for the first time.In this paper, following Salam's steps, we push the analogy between black holes and solitons to a new level. We show that any soliton solution of a two-dimensional integrable nonlinear evolution equation potentially possesses a Hawking temperature which is determined solely by the geometrical properties of an internal surface connected to the specific soliton, called the integrable surface. The curvature of this surface is turned into Hawking radiation due to the existence of a quantum anomaly, well-known in two-dimens...

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Section: Sine-gordon Kink Thermodynamicssupporting

confidence: 58%

Section: The Case Of the Kdv Soliton And Sine-gordon Kinkmentioning

confidence: 93%

Section: The Case Of the Kdv Soliton And Sine-gordon Kinkmentioning

confidence: 99%

Section: The Case Of the Kdv Soliton And Sine-gordon Kinkmentioning

confidence: 99%

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Universal quantum Hawking evaporation of integrable two-dimensional solitons

2019

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“…Another example of a solitonic black hole analogue comes from the sine-Gordon equation u ξξ + u τ τ = sin(u), which has an interesting solution, known as a kink, moving with velocity v [34,35]. This solution is described by u = 4tan −1 e γ(ξ−vτ ) , where γ ≡ 1 + v 2 −1/2 .…”

Section: B Solitons As Analogue Black Holesmentioning

confidence: 99%

Topological nature of the Hawking temperature of black holes

2019

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In this work we determine that the Hawking temperature of black holes possesses a purely topological nature. We find a very simple but powerful formula, based on a topological invariant known as the Euler characteristic, which is able to provide the exact Hawking temperature of any twodimensional black hole -and in fact of any metric that can be dimensionally reduced to two dimensions -in any given coordinate system, introducing a covariant way to determine the temperature only using virtually trivial computations. We apply the topological temperature formula to several known black hole systems as well as to the Hawking emission of solitons of integrable equations.

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