{"id":1288,"date":"2025-08-08T13:20:46","date_gmt":"2025-08-08T13:20:46","guid":{"rendered":"https:\/\/projects.ift.uam-csic.es\/master\/?p=1288"},"modified":"2026-07-17T10:36:27","modified_gmt":"2026-07-17T10:36:27","slug":"gravitation","status":"publish","type":"post","link":"https:\/\/projects.ift.uam-csic.es\/master\/gravitation\/","title":{"rendered":"Gravitation (GRA)"},"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-52-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (52)&#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:\/\/www.yashar-akrami.com&#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><strong>Type: Compulsory\u2013 PEC&amp;AC Track \u2013 1stTrimester<\/strong><\/p>\n<p>This course offers an in-depth study of gravity as described by Einstein\u2019s General Theory of Relativity. Students will explore gravity as a geometric property of spacetime, learn to derive and interpret exact solutions to Einstein\u2019s equations, and understand their cosmological and astrophysical relevance.<\/p>\n<p><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>Foundations of General Relativity: equivalence principles, covariance, and differential geometry.<\/li>\n<li>Einstein\u2019s field equations: vacuum and matter solutions, weak field limits, and exact metrics like Schwarzschild, Reissner-Nordstr\u00f6m, and Kerr.<\/li>\n<li>Experimental tests of General Relativity and classical Solar System tests.<\/li>\n<li>Introduction to black hole physics, including singularities, event horizons, and black hole mechanics.<\/li>\n<li>Gravitational waves: theory, emission, and modern detection methods.<\/li>\n<li>Astrophysical applications: black hole mergers and supermassive black holes in galaxies.<\/li>\n<\/ul>\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;]<strong>Skills Acquired<\/strong>[\/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>Understand gravity as a geometric effect on spacetime structure.<\/li>\n<li>Derive and analyze key exact solutions of Einstein\u2019s equations.<\/li>\n<li>Relate theory with experimental and observational tests.<\/li>\n<li>Gain insight into current research topics like gravitational waves and black hole astrophysics.<\/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>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><i>Lecture Notes on General Relativity<\/i> by Daniel Baumann (all sections except Section 7 on Cosmology).<\/li>\n<\/ul>\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;]<strong>Additional Recommended Books:<\/strong>[\/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>Sean M. Carroll, <em>Spacetime and Geometry<\/em><\/li>\n<li>James Hartle, <em>Gravity<\/em><\/li>\n<li>Bernard Schutz, <em>A First Course in Relativity<\/em><\/li>\n<li>Ray d\u2019Inverno, <em>Introducing Einstein\u2019s Relativity<\/em><\/li>\n<li>M. P. Hobson et al., <em>General Relativity<\/em><\/li>\n<li>Anthony Zee, <em>Einstein Gravity in a Nutshell<\/em><\/li>\n<li>Robert M. Wald, <em>General Relativity<\/em><\/li>\n<li>Steven Weinberg, <em>Gravitation and Cosmology<\/em><\/li>\n<li>P. A. M. Dirac, <em>General Theory of Relativity<\/em><\/li>\n<li>Misner, Thorne &amp; Wheeler, <em>Gravitation<\/em><\/li>\n<li>Eric Poisson &amp; Clifford Will, <em>Gravity<\/em><\/li>\n<li>Yvonne Choquey-Bruhat, <em>Introduction to General Relativity<\/em><\/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>Course Outline<\/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>Special Relativity: Lorentz transformations, spacetime, relativistic kinematics and dynamics<\/li>\n<li>Gravity as Geometry: equivalence principle, curved spacetime<\/li>\n<li>Differential Geometry basics: manifolds, tensors, metric<\/li>\n<li>Geodesics: equations, Newtonian limit, applications (Mercury precession, light bending)<\/li>\n<li>Spacetime Curvature: covariant derivatives, Riemann tensor, geodesic deviation<\/li>\n<li>Einstein Equations: field equations, matter, cosmological constant, vacuum solutions<\/li>\n<li>Gravitational Waves: linearized gravity, wave creation<\/li>\n<li>Black Holes: Schwarzschild, charged, rotating<\/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>Course Outline<\/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\/1GRsd97HworGbTlQUQeCwq7Axa9nYR0KZ\/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; url=&#8221;https:\/\/drive.google.com\/file\/d\/1_ZLp9FeMflqhARSW4FcRfi8DNcU4JbqH\/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_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Academic TeamCourse ContentType: Compulsory\u2013 PEC&amp;AC Track \u2013 1stTrimester This course offers an in-depth study of gravity as described by Einstein\u2019s General Theory of Relativity. Students will explore gravity as a geometric property of spacetime, learn to derive and interpret exact solutions to Einstein\u2019s equations, and understand their cosmological and astrophysical relevance. Main Topics Foundations of [&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\":1526,\"sizeSlug\":\"large\",\"linkDestination\":\"custom\"} -->\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.yashar-akrami.com\/\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-52-1024x576.png\" alt=\"\" class=\"wp-image-1526\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><strong>Course Content<\/strong><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p><strong>Type: Compulsory\u2013 PEC&amp;AC Track \u2013 1stTrimeste<\/strong>r<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>This course offers an in-depth study of gravity as described by Einstein\u2019s General Theory of Relativity. Students will explore gravity as a geometric property of spacetime, learn to derive and interpret exact solutions to Einstein\u2019s equations, and understand their cosmological and astrophysical relevance.<\/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>Foundations of General Relativity: equivalence principles, covariance, and differential geometry.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Einstein\u2019s field equations: vacuum and matter solutions, weak field limits, and exact metrics like Schwarzschild, Reissner-Nordstr\u00f6m, and Kerr.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Experimental tests of General Relativity and classical Solar System tests.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Introduction to black hole physics, including singularities, event horizons, and black hole mechanics.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Gravitational waves: theory, emission, and modern detection methods.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Astrophysical applications: black hole mergers and supermassive black holes in galaxies.<\/li>\n<!-- \/wp:list-item --><\/ul>\n<!-- \/wp:list -->\n\n<!-- wp:paragraph -->\n<p><strong>Skills Acquired<\/strong><\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:list -->\n<ul class=\"wp-block-list\"><!-- wp:list-item -->\n<li>Understand gravity as a geometric effect on spacetime structure.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Derive and analyze key exact solutions of Einstein\u2019s equations.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Relate theory with experimental and observational tests.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Gain insight into current research topics like gravitational waves and black hole astrophysics.<\/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>Lecture Notes on General Relativity<\/em> by Daniel Baumann (all sections except Section 7 on Cosmology).<\/li>\n<!-- \/wp:list-item --><\/ul>\n<!-- \/wp:list -->\n\n<!-- wp:paragraph -->\n<p><strong>Additional Recommended Books:<\/strong><\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:list -->\n<ul class=\"wp-block-list\"><!-- wp:list-item -->\n<li>Sean M. Carroll, <em>Spacetime and Geometry<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>James Hartle, <em>Gravity<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Bernard Schutz, <em>A First Course in Relativity<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Ray d\u2019Inverno, <em>Introducing Einstein\u2019s Relativity<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>M. P. Hobson et al., <em>General Relativity<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Anthony Zee, <em>Einstein Gravity in a Nutshell<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Robert M. Wald, <em>General Relativity<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Steven Weinberg, <em>Gravitation and Cosmology<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>P. A. M. Dirac, <em>General Theory of Relativity<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Misner, Thorne &amp; Wheeler, <em>Gravitation<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Eric Poisson &amp; Clifford Will, <em>Gravity<\/em><\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Yvonne Choquey-Bruhat, <em>Introduction to General Relativity<\/em><\/li>\n<!-- \/wp:list-item --><\/ul>\n<!-- \/wp:list -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\"><strong>Course Outline:<\/strong><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:list -->\n<ul class=\"wp-block-list\"><!-- wp:list-item -->\n<li>Special Relativity: Lorentz transformations, spacetime, relativistic kinematics and dynamics<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Gravity as Geometry: equivalence principle, curved spacetime<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Differential Geometry basics: manifolds, tensors, metric<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Geodesics: equations, Newtonian limit, applications (Mercury precession, light bending)<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Spacetime Curvature: covariant derivatives, Riemann tensor, geodesic deviation<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Einstein Equations: field equations, matter, cosmological constant, vacuum solutions<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Gravitational Waves: linearized gravity, wave creation<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>Black Holes: Schwarzschild, charged, rotating<\/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\":\"365px\",\"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\/1GRsd97HworGbTlQUQeCwq7Axa9nYR0KZ\/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:365px;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 {\"lightbox\":{\"enabled\":false},\"id\":1471,\"width\":\"407px\",\"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\/1_ZLp9FeMflqhARSW4FcRfi8DNcU4JbqH\/view?usp=drive_link\"><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:407px;height:auto\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p><\/p>\n<!-- \/wp:paragraph -->","_et_gb_content_width":"1080","footnotes":""},"categories":[20,16],"tags":[],"class_list":["post-1288","post","type-post","status-publish","format-standard","hentry","category-common-courses","category-compulsory"],"_links":{"self":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1288","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=1288"}],"version-history":[{"count":17,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1288\/revisions"}],"predecessor-version":[{"id":2363,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1288\/revisions\/2363"}],"wp:attachment":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/media?parent=1288"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/categories?post=1288"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/tags?post=1288"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}