Spontaneous particle creation by oscillating compact stars

Abstract

Quantum field theory predicts that dynamical curved spacetimes can spontaneously excite particle pairs from the quantum vacuum, a phenomenon extensively studied in expanding universes and in scenarios involving gravitational collapse. In this article, we explore particle creation driven by radial oscillations of 3+1-dimensional spherically symmetric compact objects, such as neutron stars, using a massless, minimally coupled scalar field as a reference model. We employ a toy model to describe the oscillatory dynamics and its coupling to the field modes, focusing on the resulting effects in the exterior spacetime of the star. The Bogoliubov coefficients relating the in and out vacua are computed non-perturbatively using high-precision numerical methods, without relying on weak-field, small-amplitude or small-velocity expansions. This allows us to determine the full particle spectrum and the total particle number in the strong-field and fully relativistic regime. Our analysis confirms the existence of particle creation in this setting and, crucially, reveals a distinct resonance structure in the spectrum.

Figures (9)

• Figure 1: Switching function $\epsilon(T)$ for some example parameters, its first and second derivatives and the resulting oscillations. The left and right gray bands centered around $T_{\text{on}}$ and $T_{\text{off}}$ have width $\Delta$.
• Figure 2: Eigenvalues and eigenfunctions of the Sturm-Liuiville problem in Eq. \ref{['sl']} obtained with boundary conditions $R_{\omega\ell}(z_0)=0$ and $R_{\omega\ell}(z_N)=0$ for $z_0 = 20/3 \,M$ and $z_N = 2100\,M$. Left: first 20 lowest allowed frequencies $\omega_{n\ell}$ for each $\ell \in [0,20]$. Right: eigenfunctions $R_{n\ell}(z)\equiv R_{\omega_{n\ell}\ell}(z)$ shown for several representative values of $n$ and $\ell$.
• Figure 3: Spacetime diagram in the $(T,z)$ plane showing the deviation of the numerically evolved in radial mode $R^{\rm in}_{n\ell}(T,z)$ from the corresponding freely evolved stationary solution, $|R^{\rm in}_{n\ell}(T,z)-e^{-i\omega_{n\ell}(T-T_0)}R^{\rm in}_{n\ell}(T_0,z)|$, displayed in logarithmic scale. Left: evolution of the stellar radius, showing the switching function $\varepsilon(T)$ (blue) and the full oscillatory profile $\varepsilon(T)\sin(\Omega T)$ (purple) used in the simulation. Center: evolution of the mode $(n,\ell)=(1,0)$, corresponding to the lowest frequency $\omega_{n\ell}$. Right: evolution of the mode $(n,\ell)=(20,1)$, whose frequency $\omega_{n1}$ is closest to $\Omega$. Both panels exhibit a sequence of outward-propagating wave bursts traveling at the speed of light, originating near the stellar surface at the instants of maximal radial compression and expansion.
• Figure 4: Left: Absolute error of the norm of representative in (solid) and out (dashed) modes, computed at different times for selected $(n,\ell)$. Right: Maximum absolute deviation over time of the mode norms as a function of $n$. The inner products are evaluated using Eq. \ref{['eq:inner-prod-oscillating-coords']}. Numerical errors are bounded by $5\times 10^{-9}$, indicating a high degree of numerical stability and accuracy.
• Figure 5: Numerical values of the Bogoliubov coefficients $\beta_{n\ell,n'\ell}$ for $\ell = 0$, $n = 20$ (corresponding to $\omega_{20, 0} = 2.98 \times 10^{-2} \approx \Omega$), and $n' = 1,\dots,90$, shown as a function of time $T$. The time-independence is verified with high accuracy. The colorbar indicates the frequency $\omega'$ of the out modes.