Molecular analogue for scalar dynamics in a tachyonic metric

TL;DR

The paper investigates scalar dynamics in the tachyonic AII spacetime by solving the Klein-Gordon equation, obtaining angular solutions in terms of associated Legendre functions and radial solutions via confluent Heun functions, which yield complex energy eigenvalues and quasi-normal modes. It then computes the Hawking spectrum and temperature for the tachyon horizon using the Damour–Ruffini–Sannan framework and identifies a discrete set of QNM frequencies. To bridge theory and experiment, the authors propose a concrete analogue model using the hydrogen molecular ion H2+ with a carefully engineered external potential, deriving explicit mappings between target and laboratory parameters and showing the radial and angular dynamics can be reproduced. This work broadens the analogue gravity program by providing a tangible, tunable platform to explore dynamics in extreme gravitational fields.

Abstract

Tachyons are hypothetical particles that propagate faster than light, yet they have never been observed in nature or in the laboratory. In this work, we introduce the hydrogen molecule ion as an analogue for the dynamics of a spinless test particle interacting with the gravitational field generated by a tachyon. The tachyonic spacetime is modeled using an AII metric, and the problem is analyzed through the Klein-Gordon equation for a scalar field in this background. We compute the quasinormal modes and the Hawking radiation spectrum associated with the system. By introducing an external potential, we demonstrate that both the radial and angular components of the test particles wave function can be effectively reproduced by the electron dynamics in the hydrogen molecule ion, thus proposing a molecular analogue model for an extreme gravitational system.

Figures (1)

• Figure 1: Hawking radiation spectrum $N$ as a function of the complex energy $\sigma$, given by \ref{['radiacaohawking']}, for the mass parameter $b=1/2$ and considering that the energy $\sigma \in \mathbb{C}$. We observe that there are poles whenever $\sigma = i n/(2b)$, where $n$ is an integer.