Abstract
Analogue systems are used to test Hawking radiation, which is hard to observe in actual black holes. One such system is the electrical transmission line, but it suffers the inevitable issue of excess heat that collapses the successfully generated analogue black holes. Soliton provides a possible solution to this problem due to its stable propagation without unnecessary energy dissipation in nonlinear transmission lines. In this work, we propose analogue Hawking radiation in a nonlinear LC transmission line including nonlinear capacitors with a third-order nonlinearity in voltage. We show that this line supports voltage soliton that obeys the nonlinear Schrödinger equation by using the discrete reductive perturbation method. The voltage soliton spatially modifies the velocity of the electromagnetic wave through the Kerr effect, resulting in an event horizon where the velocity of the electromagnetic wave is equal to the soliton velocity. Therefore, Hawking radiation bears soliton characteristics, which significantly contribute to distinguishing it from other radiation.
Highlights
We have proposed the analogue black hole in LC transmission lines with nonlinear capacitors and shown that the voltage dark soliton obeying a nonlinear Schrödinger equation exists in the LC transmission lines by using discrete reductive perturbation methods
The voltage soliton can propagate through the transmission line without causing any unnecessary heat generation, and it spatially modifies the capacitance owing to the nonlinearity of the capacitor, leading to the spatial change of the electromagnetic-wave velocity in the transmission line
These spatial changes in the electromagnetic-wave velocity lead to the generation of the analogue black holes. This analogue black hole is dual to the one in Josephson transmission lines with nonlinear inductors [8], where the velocity of electromagnetic waves is spatially modulated through the nonlinear Josephson inductance
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In 1981, Unruh [2] opened the possibility of observing analogue Hawking radiation in the laboratory by using a sonic horizon that separates a subsonic and a supersonic current in a moving fluid Inspired by his seminal work, there have been proposals to test predictions of gravity and cosmology in various systems with analogies, such as liquid helium [3], Bose–Einstein condensates [4], and optical fibers [5]. Schützhold and Unruh [6] proposed an analogue black hole in electric circuits for the first time In their method, the velocity of the electromagnetic waves in LC transmission lines is modulated through the changes in capacitance by applying the laser light along the waveguide at a fixed velocity. We derive the Hawking temperature to evaluate whether Hawking radiation is detectable in our system
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