Particle production, absorption, scattering, and geodesics in a Schwarzschild--Hernquist black hole

TL;DR

This work analyzes a Schwarzschild black hole embedded in a Hernquist dark matter halo via an exact static metric $f(r)=1-rac{2M}{r}-rac{4πρ_s r_s^{3}}{r+r_s}$, enabling a unified treatment of quantum and classical observables. Hawking radiation is obtained both from Bogoliubov transformations and a tunneling approach with energy conservation, yielding an effective temperature $T$ that depends on halo parameters and showing halo-induced suppression of particle occupation numbers. In the high-frequency limit, evaporation slows down due to the halo, with a remnant mass $M_{rem}$ set by $ρ_s$ and $r_s$, while absorption and scattering are computed through partial waves, revealing that the halo scale $r_s$ more strongly modulates high-frequency cross sections and photon-sphere properties. The analysis of null and timelike geodesics demonstrates that the Hernquist halo enhances light bending and alters massive particle dynamics, indicating discernible environmental imprints on shadows, lensing, and orbital structure. Overall, the Hernquist environment leaves a tangible fingerprint on quantum emission, greybody factors, and classical trajectories, motivating further studies of information-theoretic aspects and neutrino oscillations in halo-embedded black hole spacetimes.

Abstract

We investigate quantum and classical signatures of a Schwarzschild black hole embedded in a Hernquist dark matter halo. Starting from the exact spherically symmetric solution describing this composite system, we analyze particle production for both bosonic and fermionic fields using semiclassical techniques. Hawking radiation is derived through Bogoliubov transformations and independently via the tunneling method with energy conservation, allowing us to identify the effective temperature, emission spectrum, and the role of dark matter parameters in suppressing particle creation. The evaporation process is examined in the high-frequency regime, leading to modified evaporation times and emission rates relative to the vacuum Schwarzschild case. We further study absorption and scattering of massless scalar waves employing a partial-wave analysis, computing phase shifts, partial and total cross sections, and assessing the impact of the Hernquist scale radius and density on these observables. Finally, null and timelike geodesics are explored to characterize light propagation and particle motion in the presence of the dark matter halo.

Figures (13)

• Figure 1: Frequency dependence of the bosonic number density $n$ for different choices of the parameter $\rho_{\text{s}}$, evaluated at $M=1$ and $r_{\text{s}}=0.7$.
• Figure 2: Frequency dependence of the fermionic number density $n_{\psi}$ for several choices of the parameter $\rho_{\text{s}}$, evaluated at $M=1$ and $r_{\text{s}}=0.7$.
• Figure 3: Energy flux as a function of the frequency $\omega$. The left panel shows configurations with $M=1$ and fixed $r_{\text{s}}=0.1$, while the right panel corresponds to fixed $\rho_{\text{s}}=0.1$ and varying $r_{\text{s}}$.
• Figure 4: Particle emission rate as a function of the frequency $\omega$. The left panel corresponds to the case $M=1$ with $r_{\text{s}}=0.1$ held fixed, whereas the right panel is obtained by fixing $\rho_{\text{s}}=0.1$ and varying $r_{\text{s}}$.
• Figure 5: Partial absorption cross sections with respect to $M\omega$, for $\ell=0,1,2$. In the left panel, ${r_\text{s}}/M = 0.1$ and various Hernquist parameter ${\rho_\text{s}}M^2$ vary from $0.0$ to $0.6$. In the right panel, ${\rho_\text{s}}M^2$ is fixed at $0.1$ and different Hernquist parameter ${r_\text{s}}/M$ have been considered.