{"id":1315,"date":"2025-08-08T14:43:07","date_gmt":"2025-08-08T14:43:07","guid":{"rendered":"https:\/\/projects.ift.uam-csic.es\/master\/?p=1315"},"modified":"2025-09-03T14:17:10","modified_gmt":"2025-09-03T14:17:10","slug":"advanced-gravitation-graav","status":"publish","type":"post","link":"https:\/\/projects.ift.uam-csic.es\/master\/advanced-gravitation-graav\/","title":{"rendered":"Advanced Gravitation (GRAAv)"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Academic Team<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/members.ift.uam-csic.es\/ortin\/\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-47-1024x576.png\" alt=\"\" class=\"wp-image-1508\" srcset=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-47-1024x576.png 1024w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-47-300x169.png 300w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-47-768x432.png 768w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-47-1536x864.png 1536w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-47-2048x1152.png 2048w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-47-1200x675.png 1200w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/a><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Content Course<\/h2>\n\n\n\n<p><strong>Type: Optional\u2013 PEC&amp;AC Track \u2013 3rd Trimeste<\/strong>r<\/p>\n\n\n\n<p>This course covers advanced mathematical and theoretical tools for modern gravitational physics. It combines in-depth study of <strong>differential geometry<\/strong>, <strong>Hamiltonian formulations of General Relativity<\/strong>, and <strong>black hole thermodynamics<\/strong>, with an introduction to extensions of Einstein\u2019s theory.<\/p>\n\n\n\n<p><strong>Main Topics<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Advanced differential geometry: differential forms, Lie groups and algebras, Yang\u2013Mills fields, spinors in curved space, first-order formalism of General Relativity, and elements of supergravity.<\/li>\n\n\n\n<li>Hamiltonian formalism of GR: ADM mass, time, and conserved quantities.<\/li>\n\n\n\n<li>Conserved charges in gauge and gravitational theories: Komar integrals, Abbott\u2013Deser approach, Witten\u2019s positive mass theorem.<\/li>\n\n\n\n<li>Black hole thermodynamics: laws of black hole mechanics, cosmic censorship, singularity theorems, horizon topology, and no-hair results.<\/li>\n\n\n\n<li>Extensions of GR: scalar\u2013tensor theories, f(R)f(R)f(R) gravity, Lovelock theories, topological terms, and 3D gravity.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Reading List<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>Spacetime and Geometry<\/em>, Carroll, Cambridge University Press (2019)<\/li>\n\n\n\n<li><em>Gravitation<\/em>; Misner, Thorne, Wheeler, and Freeman (1970)<\/li>\n\n\n\n<li><em>General Relativity<\/em>; Wald, The University Chicago Press (1984)<\/li>\n\n\n\n<li><em>Gravitation and Cosmology<\/em>; Weinberg, Addison Wesley (1978)<\/li>\n\n\n\n<li><em>Gravity: Newtonian, Post Newtonian, Relativistic<\/em>; Poisson and Will, Cambridge University Press (2014)<\/li>\n\n\n\n<li><em>The large scale structure of spacetime<\/em>; Hawking and Ellis, Cambridge University Press (1973)<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Teaching Plan Information<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><a href=\"https:\/\/drive.google.com\/file\/d\/15bzpArb-iXVJvsNzciwZeRyjay69zMPu\/view?usp=drive_link\"><img decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-1024x576.png\" alt=\"\" class=\"wp-image-1470\" style=\"width:343px;height:auto\" srcset=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-1024x576.png 1024w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-300x169.png 300w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-768x432.png 768w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-1536x864.png 1536w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-2048x1152.png 2048w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-1200x675.png 1200w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/a><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\">Course Schedule<br><\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-1024x576.png\" alt=\"\" class=\"wp-image-1471\" style=\"width:353px;height:auto\" srcset=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-1024x576.png 1024w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-300x169.png 300w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-768x432.png 768w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-1536x864.png 1536w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-2048x1152.png 2048w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-1200x675.png 1200w\" sizes=\"(max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/figure>\n<\/div>\n\n\n<p><a href=\"https:\/\/drive.google.com\/file\/d\/1A9sAQdsDmyDm9nx3G7N9ZQEJW9CKE9Uf\/view?usp=drive_link\"><\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Academic Team Content Course Type: Optional\u2013 PEC&amp;AC Track \u2013 3rd Trimester This course covers advanced mathematical and theoretical tools for modern gravitational physics. It combines in-depth study of differential geometry, Hamiltonian formulations of General Relativity, and black hole thermodynamics, with an introduction to extensions of Einstein\u2019s theory. Main Topics Reading List Teaching Plan Information Course &hellip; <a href=\"https:\/\/projects.ift.uam-csic.es\/master\/advanced-gravitation-graav\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Advanced Gravitation (GRAAv)&#8221;<\/span><\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1315","post","type-post","status-publish","format-standard","hentry","category-sin-categoria"],"_links":{"self":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1315","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/comments?post=1315"}],"version-history":[{"count":5,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1315\/revisions"}],"predecessor-version":[{"id":1591,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1315\/revisions\/1591"}],"wp:attachment":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/media?parent=1315"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/categories?post=1315"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/tags?post=1315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}