{"uid":"cap_0aVGLGvVJyy-Vp4jf_bwq","slug":"schwarzschild-null-scattering-ray-bending-coordinate-time-field-ledger-af6bb8ed","name":"Schwarzschild Null-Scattering Ray Bending Coordinate Time Field Ledger","description":"Recover a complete bounded relativistic light-scattering artifact from an explicit spherical spacetime model.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B012/schwarzschild-null-scattering-ray-bending-coordinate-time-field-ledger?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["schwarzschild"],"properties":{"schwarzschild":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["mass_parameter","periapsis_radius","sample_radii"],"properties":{"sample_radii":{"type":"array","items":{"type":"number","maximum":20000,"minimum":0.0301},"maxItems":24,"minItems":1},"mass_parameter":{"type":"number","maximum":10,"minimum":0.01},"periapsis_radius":{"type":"number","maximum":1000,"minimum":0.0301}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_lYC_NDeUTVS5kP-Yilatn","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes relativistic light-scattering (ray bending) artifacts in Schwarzschild spacetime geometry, returning a complete bounded null-geodesic coordinate-time field ledger for given mass, periapsis, and radial sample points.","exampleAgentPrompt":"Calculate the full null-geodesic ray bending coordinate-time ledger for a Schwarzschild black hole with mass parameter 1.5, periapsis radius 0.5, sampled at radii [0.5, 1.0, 2.5, 5.0, 10.0].","exampleUseCases":[{"title":"Gravitational lensing photon trajectory simulation","prompt":"I need to simulate how light bends near a compact object — give me the full Schwarzschild null-scattering coordinate-time field ledger for mass parameter 2.0, periapsis radius 0.1, and sample radii at [0.1, 0.5, 1.0, 3.0, 8.0, 15.0]."},{"title":"Black hole shadow ray bending research","prompt":"For my astrophysics research, compute the ray bending artifact in Schwarzschild spacetime with mass parameter 0.5 and periapsis radius 0.08, sampled at radii [0.08, 0.2, 0.6, 1.5, 4.0, 10.0, 18.0]."},{"title":"Relativistic photon path around neutron star","prompt":"Model the null-geodesic light scattering for a neutron star with mass parameter 0.05 and periapsis of 0.04, sampling radii at [0.04, 0.1, 0.5, 2.0, 7.0] — I need the full coordinate-time field ledger output."}],"resultDescription":"Returns a complete bounded relativistic light-scattering artifact record: a coordinate-time field ledger capturing the null-geodesic ray bending trajectory through Schwarzschild spacetime, computed at each specified sample radius given the mass parameter and periapsis. The response includes the structured artifact with scattering data points and associated metadata.","failureModes":["Invalid mass_parameter outside [0.01, 10] returns validation error","periapsis_radius below 0.0301 (inside photon sphere) may cause unphysical results or error","sample_radii values below periapsis_radius may be rejected as unphysical","Exceeding 24 sample radii returns a schema validation error","Missing required fields (mass_parameter, periapsis_radius, sample_radii) returns 400 Bad Request","Payment not provided or insufficient USDC balance returns 402 Payment Required"],"whenToPreferThis":"Choose this endpoint when you need precise, general-relativistic null-geodesic ray bending computations in Schwarzschild spacetime — particularly for gravitational lensing studies, black hole shadow modeling, or photon orbit analysis. It is well-suited for research or simulation workflows that require coordinate-time field data at multiple radii for a specified mass and periapsis. Prefer this over Newtonian or approximate deflection-angle calculators when full GR accuracy and a structured ledger output are required.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:38:25.454Z","isFirstParty":false,"canonicalSlug":"schwarzschild-null-scattering-ray-bending-coordinate-time-field-ledger-af6bb8ed"}