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int64 0
400k
| black_hole
dict | observer
dict | metrics
dict | raw_parameters
dict | notes
stringlengths 47
47
|
---|---|---|---|---|---|
0 | {
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} | Spin=0.025, Time dilation=0.955, Redshift=0.047 |
1 | {
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} | Spin=0.890, Time dilation=0.849, Redshift=0.177 |
2 | {
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} | Spin=0.504, Time dilation=0.772, Redshift=0.296 |
3 | {
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} | Spin=0.220, Time dilation=0.994, Redshift=0.006 |
4 | {
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} | Spin=0.697, Time dilation=0.970, Redshift=0.031 |
5 | {
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} | Spin=0.093, Time dilation=0.859, Redshift=0.164 |
6 | {
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7 | {
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8 | {
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} | Spin=0.046, Time dilation=0.940, Redshift=0.064 |
9 | {
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} | {
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} | Spin=0.101, Time dilation=0.956, Redshift=0.046 |
10 | {
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} | {
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13 | {
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14 | {
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15 | {
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16 | {
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17 | {
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18 | {
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19 | {
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20 | {
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22 | {
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23 | {
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24 | {
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25 | {
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27 | {
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28 | {
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29 | {
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30 | {
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59 | {
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60 | {
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"gr_metric_type": "Kerr"
} | {
"mass_kg": 2.7291130596403148e+31,
"radius_m": 454599.137006,
"theta_rad": 1.004397,
"phi_rad": 3.393877,
"spin": 0.285157,
"rs_m": 40533.661947,
"event_horizon_m": 39692.201617
} | Spin=0.285, Time dilation=0.954, Redshift=0.048 |
93 | {
"mass_solar": 45.338443,
"spin": 0.230799,
"type": "Kerr"
} | {
"r_km": 20288.25392,
"theta_rad": 2.219281,
"phi_rad": 0.403562,
"v_r_km_s": 0,
"v_theta_rad_s": 0,
"v_phi_rad_s": 17220.84375
} | {
"schwarzschild_radius_km": 133.89981,
"time_dilation": 0.996695,
"redshift": 0.003316,
"frame_dragging": false,
"orbital_period_s": 7.402359,
"extremeness_score": 1.006633,
"is_near_horizon": false,
"frame_drag_value": -0.002852082,
"metric_tensor": [
[
-0.9934,
0,
0,
-64.779178
],
[
0,
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],
[
0,
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],
[
-64.779178,
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]
],
"r_m": 20288253.91968,
"rs_m": 133899.809507,
"event_horizon_m": 132092.259839,
"theta_rad": 2.219281,
"omega_rad_s": 0.848808527,
"v_phi_m_s": 17220844,
"gamma_time_dilation": 0.996694624,
"redshift_z": 0.003316283,
"frame_drag_flag": false,
"a_spin_m": 15451.968173,
"delta": 408896892537656.6,
"rho_squared": 411613334208178.06,
"velocity_vector_m_s": [
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0,
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],
"coordinate_position_m": [
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],
"horizon_proximity_ratio": 153.591542,
"gr_metric_type": "Kerr"
} | {
"mass_kg": 9.015413393605573e+31,
"radius_m": 20288253.91968,
"theta_rad": 2.219281,
"phi_rad": 0.403562,
"spin": 0.230799,
"rs_m": 133899.809507,
"event_horizon_m": 132092.259839
} | Spin=0.231, Time dilation=0.997, Redshift=0.003 |
94 | {
"mass_solar": 8933.90354,
"spin": 0.541526,
"type": "Kerr"
} | {
"r_km": 719326.619649,
"theta_rad": 0.649789,
"phi_rad": 2.63984,
"v_r_km_s": 0,
"v_theta_rad_s": 0,
"v_phi_rad_s": 40544.902344
} | {
"schwarzschild_radius_km": 26384.84916,
"time_dilation": 0.981489,
"redshift": 0.01886,
"frame_dragging": false,
"orbital_period_s": 111.473013,
"extremeness_score": 1.037721,
"is_near_horizon": false,
"frame_drag_value": -0.001140304,
"metric_tensor": [
[
-0.963322,
0,
0,
-95914.184894
],
[
0,
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0,
0
],
[
0,
0,
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0
],
[
-95914.184894,
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]
],
"r_m": 719326619.648914,
"rs_m": 26384849.159561,
"event_horizon_m": 24283085.567352,
"theta_rad": 0.649789,
"omega_rad_s": 0.05636508,
"v_phi_m_s": 40544904,
"gamma_time_dilation": 0.981488705,
"redshift_z": 0.018860459,
"frame_drag_flag": false,
"a_spin_m": 7144039.834152,
"delta": 498502498684791700,
"rho_squared": 517463140954006900,
"velocity_vector_m_s": [
0,
0,
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],
"coordinate_position_m": [
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],
"horizon_proximity_ratio": 29.622538,
"gr_metric_type": "Kerr"
} | {
"mass_kg": 1.7764799171707084e+34,
"radius_m": 719326619.648914,
"theta_rad": 0.649789,
"phi_rad": 2.63984,
"spin": 0.541526,
"rs_m": 26384849.159561,
"event_horizon_m": 24283085.567352
} | Spin=0.542, Time dilation=0.981, Redshift=0.019 |
95 | {
"mass_solar": 154507615.329418,
"spin": 0.582911,
"type": "Kerr"
} | {
"r_km": 69813686968.06926,
"theta_rad": 2.691503,
"phi_rad": 4.810373,
"v_r_km_s": 0,
"v_theta_rad_s": 0,
"v_phi_rad_s": 17136.404297
} | {
"schwarzschild_radius_km": 456313425.181611,
"time_dilation": 0.996727,
"redshift": 0.003284,
"frame_dragging": false,
"orbital_period_s": 25597688.293178,
"extremeness_score": 1.006568,
"is_near_horizon": false,
"frame_drag_value": -1e-9,
"metric_tensor": [
[
-0.993464,
0,
0,
-164523468.362753
],
[
0,
1.006578,
0,
0
],
[
0,
0,
4.8739653674422525e+27,
0
],
[
-164523468.362753,
0,
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]
],
"r_m": 69813686968069.26,
"rs_m": 456313425181.6106,
"event_horizon_m": 413542215488.32556,
"theta_rad": 2.691503,
"omega_rad_s": 2.45e-7,
"v_phi_m_s": 17136404,
"gamma_time_dilation": 0.996726573,
"redshift_z": 0.003284216,
"frame_drag_flag": false,
"a_spin_m": 132995115758.72571,
"delta": 4.8421116531514225e+27,
"rho_squared": 4.8739652281100955e+27,
"velocity_vector_m_s": [
0,
0,
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],
"coordinate_position_m": [
69813686968069.26,
2.691503,
4.810373
],
"horizon_proximity_ratio": 168.818767,
"gr_metric_type": "Kerr"
} | {
"mass_kg": 3.07233757854088e+38,
"radius_m": 69813686968069.26,
"theta_rad": 2.691503,
"phi_rad": 4.810373,
"spin": 0.582911,
"rs_m": 456313425181.6106,
"event_horizon_m": 413542215488.32556
} | Spin=0.583, Time dilation=0.997, Redshift=0.003 |
96 | {
"mass_solar": 5236.759645,
"spin": 0.005884,
"type": "Kerr"
} | {
"r_km": 284137.285655,
"theta_rad": 2.367112,
"phi_rad": 5.362372,
"v_r_km_s": 0,
"v_theta_rad_s": 0,
"v_phi_rad_s": 49455.902344
} | {
"schwarzschild_radius_km": 15465.928495,
"time_dilation": 0.972404,
"redshift": 0.02838,
"frame_dragging": false,
"orbital_period_s": 36.098567,
"extremeness_score": 1.056759,
"is_near_horizon": false,
"frame_drag_value": -0.004944354,
"metric_tensor": [
[
-0.945569,
0,
0,
-1211.353546
],
[
0,
1.057564,
0,
0
],
[
0,
0,
80733994911531000,
0
],
[
-1211.353546,
0,
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]
],
"r_m": 284137285.655168,
"rs_m": 15465928.494565,
"event_horizon_m": 15465794.616905,
"theta_rad": 2.367112,
"omega_rad_s": 0.174056366,
"v_phi_m_s": 49455904,
"gamma_time_dilation": 0.972403646,
"redshift_z": 0.02837956,
"frame_drag_flag": false,
"a_spin_m": 45503.015147,
"delta": 76339552227428220,
"rho_squared": 80733998157351600,
"velocity_vector_m_s": [
0,
0,
49455904
],
"coordinate_position_m": [
284137285.655168,
2.367112,
5.362372
],
"horizon_proximity_ratio": 18.371981,
"gr_metric_type": "Kerr"
} | {
"mass_kg": 1.041313945167542e+34,
"radius_m": 284137285.655168,
"theta_rad": 2.367112,
"phi_rad": 5.362372,
"spin": 0.005884,
"rs_m": 15465928.494565,
"event_horizon_m": 15465794.616905
} | Spin=0.006, Time dilation=0.972, Redshift=0.028 |
97 | {
"mass_solar": 400952034.563529,
"spin": 0.418183,
"type": "Kerr"
} | {
"r_km": 249636513364.702,
"theta_rad": 1.715725,
"phi_rad": 3.790348,
"v_r_km_s": 0,
"v_theta_rad_s": 0,
"v_phi_rad_s": 14599.351562
} | {
"schwarzschild_radius_km": 1184147433.99631,
"time_dilation": 0.997625,
"redshift": 0.00238,
"frame_dragging": false,
"orbital_period_s": 107437135.927746,
"extremeness_score": 1.00476,
"is_near_horizon": false,
"frame_drag_value": 0,
"metric_tensor": [
[
-0.995257,
0,
0,
-1149968304.153959
],
[
0,
1.004765,
0,
0
],
[
0,
0,
6.231838817026844e+28,
0
],
[
-1149968304.153959,
0,
0,
6.10186276490178e+28
]
],
"r_m": 249636513364702,
"rs_m": 1184147433996.3103,
"event_horizon_m": 1129891391622.078,
"theta_rad": 1.715725,
"omega_rad_s": 5.8e-8,
"v_phi_m_s": 14599352,
"gamma_time_dilation": 0.99762547,
"redshift_z": 0.002380133,
"frame_drag_flag": false,
"a_spin_m": 247595305331.35718,
"delta": 6.202284367158767e+28,
"rho_squared": 6.231839008353634e+28,
"velocity_vector_m_s": [
0,
0,
14599352
],
"coordinate_position_m": [
249636513364702,
1.715725,
3.790348
],
"horizon_proximity_ratio": 220.938504,
"gr_metric_type": "Kerr"
} | {
"mass_kg": 7.972810921685404e+38,
"radius_m": 249636513364702,
"theta_rad": 1.715725,
"phi_rad": 3.790348,
"spin": 0.418183,
"rs_m": 1184147433996.3103,
"event_horizon_m": 1129891391622.078
} | Spin=0.418, Time dilation=0.998, Redshift=0.002 |
98 | {
"mass_solar": 227.376619,
"spin": 0.218983,
"type": "Kerr"
} | {
"r_km": 20718.181043,
"theta_rad": 0.091184,
"phi_rad": 2.111964,
"v_r_km_s": 0,
"v_theta_rad_s": 0,
"v_phi_rad_s": 38147.257812
} | {
"schwarzschild_radius_km": 671.520324,
"time_dilation": 0.98366,
"redshift": 0.016611,
"frame_dragging": false,
"orbital_period_s": 3.412465,
"extremeness_score": 1.033222,
"is_near_horizon": false,
"frame_drag_value": -0.031430483,
"metric_tensor": [
[
-0.967588,
0,
0,
-19.759507
],
[
0,
1.033497,
0,
0
],
[
0,
0,
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0
],
[
-19.759507,
0,
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]
],
"r_m": 20718181.043493,
"rs_m": 671520.324497,
"event_horizon_m": 663370.995941,
"theta_rad": 0.091184,
"omega_rad_s": 1.841245413,
"v_phi_m_s": 38147256,
"gamma_time_dilation": 0.98366046,
"redshift_z": 0.01661098,
"frame_drag_flag": false,
"a_spin_m": 73525.697554,
"delta": 415335752121844.2,
"rho_squared": 429248386954906.75,
"velocity_vector_m_s": [
0,
0,
38147256
],
"coordinate_position_m": [
20718181.043493,
0.091184,
2.111964
],
"horizon_proximity_ratio": 31.231665,
"gr_metric_type": "Kerr"
} | {
"mass_kg": 4.521315862855188e+32,
"radius_m": 20718181.043493,
"theta_rad": 0.091184,
"phi_rad": 2.111964,
"spin": 0.218983,
"rs_m": 671520.324497,
"event_horizon_m": 663370.995941
} | Spin=0.219, Time dilation=0.984, Redshift=0.017 |
99 | {
"mass_solar": 1842320.529763,
"spin": 0.403508,
"type": "Kerr"
} | {
"r_km": 31611961.166443,
"theta_rad": 1.468349,
"phi_rad": 0.801909,
"v_r_km_s": 0,
"v_theta_rad_s": 0,
"v_phi_rad_s": 87059.765625
} | {
"schwarzschild_radius_km": 5440997.77494,
"time_dilation": 0.90988,
"redshift": 0.099046,
"frame_dragging": false,
"orbital_period_s": 2281.465139,
"extremeness_score": 1.198092,
"is_near_horizon": false,
"frame_drag_value": -0.000303608,
"metric_tensor": [
[
-0.827884,
0,
0,
-186963267.29431
],
[
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],
[
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],
"r_m": 31611961166.44309,
"rs_m": 5440997774.940273,
"event_horizon_m": 5209690351.773418,
"theta_rad": 1.468349,
"omega_rad_s": 0.002754013,
"v_phi_m_s": 87059768,
"gamma_time_dilation": 0.909880042,
"redshift_z": 0.099045992,
"frame_drag_flag": false,
"a_spin_m": 1097743162.477424,
"delta": 828520518471356600000,
"rho_squared": 999328691934449500000,
"velocity_vector_m_s": [
0,
0,
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],
"coordinate_position_m": [
31611961166.44309,
1.468349,
0.801909
],
"horizon_proximity_ratio": 6.067916,
"gr_metric_type": "Kerr"
} | {
"mass_kg": 3.663399103818432e+36,
"radius_m": 31611961166.44309,
"theta_rad": 1.468349,
"phi_rad": 0.801909,
"spin": 0.403508,
"rs_m": 5440997774.940273,
"event_horizon_m": 5209690351.773418
} | Spin=0.404, Time dilation=0.910, Redshift=0.099 |
End of preview. Expand
in Data Studio
π³οΈ Black Hole Sim β Randomized Dataset (ProCreations)
ProCreations/black-hole-sim-randomized is a high-fidelity, randomized simulation dataset of relativistic physics near Kerr and Schwarzschild black holes. Designed to train and evaluate AI systems on general relativity, orbital mechanics, and spacetime geometryβwithout any visual dependencies.
π¦ Dataset Overview
- Samples: 400,000+
- Format: JSON Lines (
.jsonl
) - Size: ~583 MB
- Compression: Optionally
.jsonl.gz
- Language/Structure: Pure structured JSON (1 per line)
- Generated on: Apple Silicon (Metal-accelerated)
- Use cases: Pretraining, fine-tuning, RAG, reasoning, QA, simulation
β¨ Features per Sample
Each sample describes a single randomly sampled scenario, containing:
π³οΈ Black Hole
mass_solar
β In solar masses (randomized log-uniform from 3 to 1e9)spin
β Kerr spin parametera
(0.0 to 0.998)type
β"Schwarzschild"
or"Kerr"
ποΈ Observer
- 3D position (
r_km
,theta_rad
,phi_rad
) - Orbital velocity vector in spherical coordinates
- Orbital angular velocity
omega
π Metrics (GR & physics)
time_dilation
,redshift
,gamma
orbital_period_s
,frame_dragging
,extremeness_score
metric_tensor
β Full 4x4 Kerr metric in BoyerβLindquist coordinatesa_spin_m
,event_horizon_m
,delta
,rho_squared
- Velocity vector + coordinate positions
horizon_proximity_ratio
(how close the observer is to Rs)
π§ͺ Raw Parameters
- Ground truth values like
mass_kg
,radius_m
,rs_m
π Example
{
"step": 2,
"black_hole": {
"mass_solar": 219.051486,
"spin": 0.504345,
"type": "Kerr"
},
"observer": {
"r_km": 1600.060345,
"theta_rad": 0.624667,
"phi_rad": 4.083344,
"v_phi_rad_s": 128884.609375
},
"metrics": {
"time_dilation": 0.771804,
"redshift": 0.295665,
"frame_dragging": true,
"metric_tensor": [[...]],
"horizon_proximity_ratio": 2.654,
"gr_metric_type": "Kerr"
},
"notes": "Spin=0.504, Time dilation=0.772, Redshift=0.296"
}
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