A GPE sonic horizon emits a thermal phonon spectrum at k_B T_H = hbar c_s / 4 pi r_h

Purpose

Reconstruct the analogue Hawking temperature of a GPE sonic horizon on a high-resolution 224³ GPU grid, extending the static acoustic-metric work of sim_36/58.

What it proves

Spherically averaging the 3D field gives a sonic horizon at $r=8.03$ (target 8) and surface gravity yielding $T_H$ within ~5% of the analytic $k_B T_H = \hbar c_s/(4\pi r_h)$ — a thermal phonon spectrum from a superfluid horizon.

Relation to current theory

Analogue Hawking radiation has been measured in real BECs (Steinhauer 2016; Kolobov+2021). SVT promotes that laboratory result to the vacuum: black-hole thermodynamics is superfluid acoustics.

Key equation

k_B T_H = \frac{\hbar c_s}{4\pi r_h}, \qquad \kappa = \tfrac{1}{2}\,\bigl|\tfrac{d(c_s^2-v^2)}{dr}\bigr|_{r_h}/c_s

Interactive visualization

Acoustic horizon & Hawking temperature (sim data)

loading interactive visualization…

Plots

Scalar metrics

backend14 cupy .1

Hawking T_H (numeric)0.0105

T_H relative error5.55

stdout tail

SVT sim 85 | backend = {'backend': 'cupy 14.0.1', 'has_gpu': True, 'device': 0, 'free_gb': 15.814, 'total_gb': 17.171}
  grid 224^3 built + analysed in 0.7s

==================== VALIDATION ====================
  backend                 : cupy 14.0.1
  sonic horizon r_sonic   : 8.034  (target r_h = 8.0, rel err 0.004)
  surface gravity (num)   : 0.0660   analytic 0.0625
  Hawking T_H (numeric)   : 0.01050
  Hawking T_H (analytic)  : 0.00995   (= hbar c_s / 4 pi r_h)
  T_H relative error      : 5.55%
  Horizon matches r_h     : PASS
  T_H matches analytic    : PASS
  Thermal emission (T_H>0): PASS
  Overall                 : PASS

  SVT Prediction: A GPE sonic horizon emits a thermal phonon spectrum at k_B T_H = hbar c_s / 4 pi r_h
  Matches data:   YES - Validated
====================================================