{"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":"2026-07-17T10:40:02","modified_gmt":"2026-07-17T10:40:02","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":"<p>[et_pb_section fb_built=&#8221;1&#8243; _builder_version=&#8221;4.27.4&#8243; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row _builder_version=&#8221;4.16&#8243; background_size=&#8221;initial&#8221; background_position=&#8221;top_left&#8221; background_repeat=&#8221;repeat&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.16&#8243; custom_padding=&#8221;|||&#8221; global_colors_info=&#8221;{}&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Academic Team<\/h2>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-47-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (47)&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; hover_enabled=&#8221;0&#8243; global_colors_info=&#8221;{}&#8221; url=&#8221;https:\/\/members.ift.uam-csic.es\/ortin\/&#8221; url_new_window=&#8221;on&#8221; sticky_enabled=&#8221;0&#8243;][\/et_pb_image][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Course Content<\/h2>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<p class=\"wp-block-paragraph\"><strong>Type: Optional\u2013 PEC&amp;AC Track \u2013 3rd Trimeste<\/strong>r<\/p>\n<p class=\"wp-block-paragraph\">This course covers advanced mathematical and theoretical tools for modern gravitational physics. It combines in-depth study of<span>\u00a0<\/span><strong>differential geometry<\/strong>,<span>\u00a0<\/span><strong>Hamiltonian formulations of General Relativity<\/strong>, and<span>\u00a0<\/span><strong>black hole thermodynamics<\/strong>, with an introduction to extensions of Einstein\u2019s theory.<\/p>\n<p class=\"wp-block-paragraph\"><strong>Main Topics<\/strong><\/p>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<ul>\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<li>Hamiltonian formalism of GR: ADM mass, time, and conserved quantities.<\/li>\n<li>Conserved charges in gauge and gravitational theories: Komar integrals, Abbott\u2013Deser approach, Witten\u2019s positive mass theorem.<\/li>\n<li>Black hole thermodynamics: laws of black hole mechanics, cosmic censorship, singularity theorems, horizon topology, and no-hair results.<\/li>\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<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Reading List<\/h2>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<ul>\n<li><em>Spacetime and Geometry<\/em>, Carroll, Cambridge University Press (2019)<\/li>\n<li><em>Gravitation<\/em>; Misner, Thorne, Wheeler, and Freeman (1970)<\/li>\n<li><em>General Relativity<\/em>; Wald, The University Chicago Press (1984)<\/li>\n<li><em>Gravitation and Cosmology<\/em>; Weinberg, Addison Wesley (1978)<\/li>\n<li><em>Gravity: Newtonian, Post Newtonian, Relativistic<\/em>; Poisson and Will, Cambridge University Press (2014)<\/li>\n<li><em>The large scale structure of spacetime<\/em>; Hawking and Ellis, Cambridge University Press (1973)<\/li>\n<\/ul>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2> Teaching Plan Information<\/h2>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (21)&#8221; url=&#8221;https:\/\/drive.google.com\/file\/d\/15bzpArb-iXVJvsNzciwZeRyjay69zMPu\/view&#8221; url_new_window=&#8221;on&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; width=&#8221;50%&#8221; max_width=&#8221;50%&#8221; module_alignment=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; custom_margin=&#8221;50px||||false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Course Schedule<\/h2>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (20)&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; width=&#8221;50%&#8221; max_width=&#8221;50%&#8221; module_alignment=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Academic TeamCourse ContentType: 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\u00a0differential geometry,\u00a0Hamiltonian formulations of General Relativity, and\u00a0black hole thermodynamics, with an introduction to extensions of Einstein\u2019s theory. Main Topics Advanced differential geometry: differential forms, Lie groups and algebras, Yang\u2013Mills fields, [&hellip;]<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Academic Team<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"lightbox\":{\"enabled\":false},\"id\":1508,\"sizeSlug\":\"large\",\"linkDestination\":\"custom\"} -->\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/members.ift.uam-csic.es\/ortin\/\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-47-1024x576.png\" alt=\"\" class=\"wp-image-1508\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Content Course<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p><strong>Type: Optional\u2013 PEC&amp;AC Track \u2013 3rd Trimeste<\/strong>r<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\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<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p><strong>Main Topics<\/strong><\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:list -->\n<ul class=\"wp-block-list\"><!-- wp:list-item -->\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<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Hamiltonian formalism of GR: ADM mass, time, and conserved quantities.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Conserved charges in gauge and gravitational theories: Komar integrals, Abbott\u2013Deser approach, Witten\u2019s positive mass theorem.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Black hole thermodynamics: laws of black hole mechanics, cosmic censorship, singularity theorems, horizon topology, and no-hair results.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Extensions of GR: scalar\u2013tensor theories, f(R)f(R)f(R) gravity, Lovelock theories, topological terms, and 3D gravity.<\/li>\n<!-- \/wp:list-item --><\/ul>\n<!-- \/wp:list -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Reading List<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:list -->\n<ul class=\"wp-block-list\"><!-- wp:list-item -->\n<li><em>Spacetime and Geometry<\/em>, Carroll, Cambridge University Press (2019)<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>Gravitation<\/em>; Misner, Thorne, Wheeler, and Freeman (1970)<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>General Relativity<\/em>; Wald, The University Chicago Press (1984)<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>Gravitation and Cosmology<\/em>; Weinberg, Addison Wesley (1978)<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>Gravity: Newtonian, Post Newtonian, Relativistic<\/em>; Poisson and Will, Cambridge University Press (2014)<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>The large scale structure of spacetime<\/em>; Hawking and Ellis, Cambridge University Press (1973)<\/li>\n<!-- \/wp:list-item --><\/ul>\n<!-- \/wp:list -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Teaching Plan Information<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"lightbox\":{\"enabled\":false},\"id\":1470,\"width\":\"343px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"custom\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><a href=\"https:\/\/drive.google.com\/file\/d\/15bzpArb-iXVJvsNzciwZeRyjay69zMPu\/view?usp=drive_link\"><img 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\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Course Schedule<br><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"id\":1471,\"width\":\"353px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img 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\"\/><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p><a href=\"https:\/\/drive.google.com\/file\/d\/1A9sAQdsDmyDm9nx3G7N9ZQEJW9CKE9Uf\/view?usp=drive_link\"><\/a><\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p><\/p>\n<!-- \/wp:paragraph -->","_et_gb_content_width":"1080","footnotes":""},"categories":[20,18],"tags":[],"class_list":["post-1315","post","type-post","status-publish","format-standard","hentry","category-common-courses","category-optional"],"_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":9,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1315\/revisions"}],"predecessor-version":[{"id":2367,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1315\/revisions\/2367"}],"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}]}}