{
    "metadata": {
        "calculation_date": "2025-09-25T16:59:17.236069",
        "author": "Yoshiyuki Matsuyama",
        "article": "#003 Energy Conservation",
        "version": "2.0 (realistic physics)"
    },
    "physical_constants": {
        "G": 6.6743e-11,
        "c": 299792458,
        "M_sun": 1.98847e+30,
        "stefan_boltzmann": 5.670374419e-8
    },
    "system_parameters": {
        "black_hole_mass_solar": 6500000000,
        "schwarzschild_radius": 19196705983434.707,
        "major_radius": 191967059834347.06,
        "minor_radius": 191967059834.34708,
        "R_over_r": 1000,
        "mass_accretion_rate": 6301081197556214
    },
    "results": {
        "accretion_energy": {
            "outer_radius": 192159026894181.4,
            "isco_radius": 57590117950304.125,
            "potential_difference": -10489966371869948,
            "mass_accretion_rate": 6301081197556214,
            "standard_efficiency": 0.057,
            "forth_efficiency": 0.0855,
            "accretion_luminosity": 5.651390103781264e+30,
            "accretion_luminosity_erg_s": 5.651390103781264e+37
        },
        "jet_kinetic_energy": {
            "jet_velocity": 299792308.10373354,
            "v_over_c": 0.999999499999875,
            "lorentz_factor": 1000.0000000411333,
            "jet_mass_rate": 63010811975.56214,
            "kinetic_power": 5.663126526612393e+30,
            "kinetic_power_erg_s": 5.663126526612393e+37
        },
        "radiation_losses": {
            "eddington_luminosity": 8.45e+47,
            "eddington_ratio": 6.688035625776643e-19,
            "bolometric_luminosity": 5.651390103781264e+29,
            "thermal_radiation": 2.825695051890632e+29,
            "synchrotron_radiation": 2.260556041512506e+29,
            "other_radiation": 5.651390103781265e+28,
            "gravitational_wave": 1.33432228491131e-42,
            "total_radiation": 5.651390103781264e+29
        },
        "energy_balance": {
            "energy_input": {
                "accretion": 5.651390103781264e+30,
                "description": "Gravitational energy from accretion"
            },
            "energy_output": {
                "jet_kinetic": 5.663126526612393e+30,
                "radiation": 5.651390103781264e+29,
                "total": 6.228265536990519e+30
            },
            "balance": {
                "difference": -5.768754332092547e+29,
                "error_percent": 10.207673202797938,
                "note": "Non-zero due to radiation and other losses"
            },
            "efficiency": {
                "jet_production": 1.0020767320279793,
                "radiation_loss": 0.1,
                "total": 1.1020767320279794
            }
        },
        "relativistic_corrections": [
            {
                "R_over_r": 10,
                "v_over_c": 0.99498743710662,
                "gamma": 9.999999999999995,
                "K_classical_mc2": 0.495,
                "K_relativistic_mc2": 8.999999999999995,
                "correction_factor": 18.181818181818173
            },
            {
                "R_over_r": 100,
                "v_over_c": 0.9999499987499375,
                "gamma": 100.00000000000551,
                "K_classical_mc2": 0.49995,
                "K_relativistic_mc2": 99.00000000000551,
                "correction_factor": 198.01980198020905
            },
            {
                "R_over_r": 1000,
                "v_over_c": 0.999999499999875,
                "gamma": 1000.0000000411333,
                "K_classical_mc2": 0.49999950000000004,
                "K_relativistic_mc2": 999.0000000411333,
                "correction_factor": 1998.0019980842644
            },
            {
                "R_over_r": 10000,
                "v_over_c": 0.9999999949999999,
                "gamma": 9999.999919365053,
                "K_classical_mc2": 0.4999999949999999,
                "K_relativistic_mc2": 9998.999919365053,
                "correction_factor": 19998.00003871011
            }
        ],
        "visualization": {
            "file": "energy_flow_003.png",
            "type": "energy_flow_diagram"
        }
    }
}