Dirty Black Holes, Clean Signals: Near-Horizon vs. Environmental Effects on Grey-Body Factors and Hawking Radiation

Abstract

Grey-body factors are not only essential ingredients for computing the intensity of Hawking radiation, but also serve as characteristics of black hole's geometry that are closely related to their quasinormal modes. Importantly, they tend to be more stable under small deformations of the background spacetime. In this work, we carry out a detailed analysis of grey-body factors and Hawking radiation for a spherically symmetric black hole subject to localized deformations which do not alter the Hawking temperature: near-horizon modifications to simulate possible new physics or matter fields, and far-zone perturbations to model environmental or astrophysical effects. We show that environmental deformations have only a minor impact on the grey-body factors and Hawking radiation--unless the additional potential barrier created by the environment becomes comparable in height to the primary peak associated with the black hole itself, a scenario more relevant to nonlinear dynamics. In contrast, near-horizon deformations significantly affect the Hawking spectrum, particularly in the low-frequency regime.

Figures (13)

• Figure 1: Near-horizon Gaussian bump deformations (top panels: \ref{['eq:Gaussian_bump_typical']}, bottom panels: \ref{['eq:Gaussian_bump_eps']}) of the effective potentials on the Schwarzschild background for various values of the height parameter $\alpha$ and two different values of the width parameter (left and right panels). For reference, we also depict the effective potentials for the electromagnetic field with $l=1$ (blue) and the Dirac field with $l=1/2$ (red) with the dashed curves, while the locations of their peaks are indicated by the dot-dashed lines respectively.
• Figure 2: Top left: Deformation of the electromagnetic effective potential \ref{['eq:Veff_em']} by the Gaussian bump \ref{['eq:Gaussian_bump_eps']} with parameters $(\alpha,r_m,\kappa)=(0.025,1.001,0.001)$, for the first 4 multipole numbers (colored solid curves). In all panels, dashed curves of the same color correspond to the no-bump limits. Top middle: Grey-body factors (GFs). Top right: Difference between the GFs and their no-bump limits. Bottom left: Differential energy-emission rates (EERs), along with their sum (black-dashed curve). Bottom middle: Percentage of absolute relative difference of the EERs from their no-bump limits. Bottom right: Difference between the sum of EERs and their no-bump limit. The total emissivity of the black hole in the electromagnetic channel is enhanced by $\sim 1.1294 \%$.
• Figure 3: When the effective potential \ref{['eq:Veff_em']} is deformed by a Gaussian bump \ref{['eq:Gaussian_bump_eps']} with parameters $(\alpha,r_m,\kappa)=(0.025,1.001,0.01)$, the total emissivity of the black hole in the electromagnetic channel is reduced by $\sim 2.1848 \%$. For details on the contents of panels, see caption of Fig. \ref{['fig:[A0025_rm1001_k0001]']}.
• Figure 4: When the effective potential \ref{['eq:Veff_em']} is deformed by a Gaussian dip \ref{['eq:Gaussian_bump_eps']} with parameters $(\alpha,r_m,\kappa)=(-0.025,1.001,0.01)$, the total emissivity of the black hole in the electromagnetic channel is enhanced by $\sim 1.2899 \%$. For details on the contents of the panels, see caption of Fig. \ref{['fig:[A0025_rm1001_k0001]']}.
• Figure 5: When the effective potential \ref{['eq:Veff_em']} is deformed by a Gaussian bump \ref{['eq:Gaussian_bump_eps']} with parameters $(\alpha,r_m,\kappa)=(-0.025,10,0.01)$, the total emissivity of the black hole in the electromagnetic channel is enhanced by $\sim 0.01679 \%$. For details on the contents of the panels, see caption of Fig. \ref{['fig:[A0025_rm1001_k0001]']}. The inlaid plot in the top-left panel provides a magnified view of the region indicated by the black rectangle in the main plot.