Scalar Vacuum Polarization in Loop Quantum Gravity Black Holes - data of numerical simulation

Data for "Scalar Vacuum Polarization in Loop Quantum Gravity Black Holes"======================================================================== vp = 16*pi^2*M^2*<phi^2> as a function of x = r/r_s, for the metric ds^2 = x^(2z) f dt^2 + x^(-2) g dx^2 + x^2 dOmega^2, f = r_s^(-2z)(1-(r_s/x)^(1+z)), g = x^2/(1-(r_s/x)^(1+z)), r_s = 1 (= 2M),with z = epsilon (LQG exponent), field mass m (mu = mM = m/2), coupling xi.Each CSV has a metadata header (#) and two columns: x(=r/r_s) vp. -------- Radial range threshold: x-1 >= 1e-2 (equivalently x >= 1.01) rows per file: 13649 kept (of 20000 original) x range after trimming: [1.01, 200] Figure -> data mapping----------------------Fig A (vary epsilon; m=1, xi=0): vp_LQG_z0.0_m1.0_xi0.000000.csv vp_LQG_z0.05_m1.0_xi0.000000.csv vp_LQG_z0.10_m1.0_xi0.000000.csv vp_LQG_z0.20_m1.0_xi0.000000.csv Fig B (vary mass; z=0.1, xi=0): vp_LQG_z0.10_m0.4_xi0.000000.csv vp_LQG_z0.10_m1.0_xi0.000000.csv vp_LQG_z0.10_m2.0_xi0.000000.csv Fig C (vary coupling; z=0.1, m=1): vp_LQG_z0.10_m1.0_xi0.000000.csv vp_LQG_z0.10_m1.0_xi0.166667.csv Fig D (light mass m=0.05, tiny epsilon): vp_LQG_z0.0_m0.05_xi0.000000.csv vp_LQG_z1.0e-9_m0.05_xi0.000000.csv vp_LQG_z1.0e-6_m0.05_xi0.000000.csv vp_LQG_z1.0e-3_m0.05_xi0.000000.csv Fig E (large-r negative tail vs DeWitt-Schwinger; z=0.1): solid (numerical): vp_LQG_z0.10_m1.0_xi0.000000.csv (mu=1/2, xi=0) vp_LQG_z0.10_m2.0_xi0.000000.csv (mu=1, xi=0) vp_LQG_z0.10_m1.0_xi0.166667.csv (mu=1/2, xi=1/6) dashed (DeWitt-Schwinger [a2]/m^2): computed from the closed-form curvature invariants in ds_invariants.txt via [a2] = 1/2(xi-1/6)^2 R^2 + 1/6(1/5-xi) box(R) - R_{mn}R^{mn}/180 + R_{mnrs}R^{mnrs}/180, and vp_DS = (1/4)[a2]/m^2 (since vp = 16 pi^2 M^2 <phi^2> = 4 pi^2 <phi^2>). The plotted numerical curves are lightly Savitzky-Golay smoothed (win=71, polyorder=2) to suppress sub-1e-7 single-point Sigma_2 mode-sum steps. ds_invariants.txt : closed-form R, R_{mn}R^{mn} (Ric2), Kretschmann, box(R) for z=1/10. Numerics: num_points=20000, nt_integral=8000, L_trunc_sigma=2000, max_n_sigma2=150,x in [1, 200] (quantitatively reliable region r/r_s in [1,~10]).