Baran Thermal Metric: A Spacetime Metric for Black Holes Surrounded by Thermal Radiation

The Schwarzschild metric describes empty spacetime around a black hole. The Reissner-Nordström metric extends this by including the energy of the electric field surrounding a charged black hole this field energy curves spacetime and enters the metric as an additional r_Q²/r² term.By the same physical reasoning, a black hole is surrounded by thermal radiation (Hawking radiation and accretion disk radiation), which also carries energy. This energy should curve the surrounding spacetime in the same way.This work presents the Baran Thermal Metric, a conjecture for the spacetime metric around a black hole in the presence of thermal radiation: ds² = −(1 − 2GM/c²r + 32πGσT₀⁴/c⁷r²)c²dt² + (...)⁻¹dr² + r²dΩ² The thermal length scale r_T² = 32πGσT₀⁴/c⁷ is derived by matching the G_tt component of the Einstein field equations with the energy-momentum tensor of blackbody radiation, assuming T(r) = T₀/r. The structural parallel with the Reissner-Nordström metric is exact.This is presented as a conjecture and priority record. All ideas and physical intuitions belong to Abdullah Baran. Typeset by Claude (Anthropic) acting as amanuensis.