{"schemaVersion":1,"publication":{"id":"local-horizon-thermodynamics","title":"Local Horizon Thermodynamics and Einstein Gravity in a Source–Readout Architecture","subtitle":"Heat, temperature and area readouts of a shrinking null pencil recover the Einstein equation under the stated thermodynamic and conservation assumptions. A finite generator segment and finite transverse width pose different questions.","description":"Heat, temperature and area readouts of a shrinking null pencil recover the Einstein equation under the stated thermodynamic and conservation assumptions. A finite generator segment and finite transverse width pose different questions.","doi":"10.5281/zenodo.24029166","date":"2026-11-07","url":"/source-readout/local-horizon-thermodynamics","pdfUrl":"/publications/gravity/local-horizon-thermodynamics/paper.pdf","markdownUrl":"/publications/gravity/local-horizon-thermodynamics/complete.md","manifestUrl":"/source-readout/local-horizon-thermodynamics/manifest.json","paperSlug":"local-horizon-thermodynamics","headline":"One null pencil, three readouts.","author":"Jeremy Rodgers","programme":"source-readout","series":"gravity-holography","supplementUrl":"/publications/gravity/local-horizon-thermodynamics/Jacobson_Verification_24029166.zip","previousDoi":"10.5281/zenodo.24016009","supplementDescription":"Full verification suite with errata checks"},"kind":"complete-translated-web-edition","chapters":[{"paperId":"local-horizon-thermodynamics","slug":"01-common-preparation","title":"One prepared horizon, three readouts","description":"Put heat, temperature and entropy on the same null pencil, and normalize the boost before comparing them.","order":1,"url":"/source-readout/local-horizon-thermodynamics/01-common-preparation","sourcePath":"content/paper-integrations/local-horizon-thermodynamics/01-common-preparation.mdx","sections":[{"id":"introduction","title":"1. Where the field equation enters"},{"id":"common-source","title":"2. Prepare the null pencil"},{"id":"three-readouts","title":"Three projections of one preparation"},{"id":"boost-temperature","title":"3. Fix the boost and temperature together"}],"anchors":["overview","introduction","common-source","three-readouts","boost-temperature"],"words":910},{"paperId":"local-horizon-thermodynamics","slug":"02-clausius-and-directions","title":"The Clausius coefficient and the directions that determine it","description":"Derive the leading field equation in both directions, reconstruct its trace-free part from nine null directions, and exhibit the kernel of a circle.","order":2,"url":"/source-readout/local-horizon-thermodynamics/02-clausius-and-directions","sourcePath":"content/paper-integrations/local-horizon-thermodynamics/02-clausius-and-directions.mdx","sections":[{"id":"leading-coefficient","title":"4. Extract the leading Clausius coefficient"},{"id":"theorem-4-1","title":"Theorem 4.1. Leading equivalence"},{"id":"determining-directions","title":"5. Determine the tensor from null directions"},{"id":"nine-direction-inversion","title":"Reconstruct from nine evaluations"},{"id":"circle-kernel","title":"What a circle misses"}],"anchors":["leading-coefficient","eq-1","theorem-4-1","coupling-and-units","determining-directions","nine-direction-inversion","circle-kernel"],"words":684},{"paperId":"local-horizon-thermodynamics","slug":"03-finite-length","title":"The first finite-length correction","description":"Track the cubic residual along one generator, the width estimate needed to transfer it, and the separate weighted expansion prescription.","order":3,"url":"/source-readout/local-horizon-thermodynamics/03-finite-length","sourcePath":"content/paper-integrations/local-horizon-thermodynamics/03-finite-length.mdx","sections":[{"id":"finite-length","title":"6. Follow the residual beyond leading order"},{"id":"finite-width","title":"Transfer to a pencil of finite transverse width"},{"id":"weighted-prescription","title":"A separate weighted expansion prescription"}],"anchors":["finite-length","eq-2","flrw-example","finite-width","weighted-prescription"],"words":475},{"paperId":"local-horizon-thermodynamics","slug":"04-assumptions-and-references","title":"Preparation, assumptions and verification","description":"Separate pointwise equilibrium from stronger screen conditions, state the physical inputs, and check what the construction establishes.","order":4,"url":"/source-readout/local-horizon-thermodynamics/04-assumptions-and-references","sourcePath":"content/paper-integrations/local-horizon-thermodynamics/04-assumptions-and-references.mdx","sections":[{"id":"preparation-assumptions","title":"7. Preparation, assumptions and verification"},{"id":"codazzi-obstruction","title":"When the Codazzi obstruction vanishes"},{"id":"physical-inputs","title":"What the derivation assumes"},{"id":"verification","title":"What the research calculations checked"},{"id":"conclusion","title":"8. What the construction establishes"},{"id":"funding","title":"Funding"},{"id":"verification-materials","title":"Verification materials for this edition"},{"id":"references","title":"References"}],"anchors":["preparation-assumptions","codazzi-obstruction","physical-inputs","verification","conclusion","funding","verification-materials","references","ref-1","ref-2","ref-3","ref-4","ref-5","ref-6","ref-7"],"words":722}],"completeMarkdown":"/publications/gravity/local-horizon-thermodynamics/complete.md","originalPdf":"/publications/gravity/local-horizon-thermodynamics/paper.pdf"}