{"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":"2025-09-03T14:17:31","modified_gmt":"2025-09-03T14:17:31","slug":"gravitation","status":"publish","type":"post","link":"https:\/\/projects.ift.uam-csic.es\/master\/gravitation\/","title":{"rendered":"Gravitation (GRA)"},"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:\/\/www.yashar-akrami.com\/\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-52-1024x576.png\" alt=\"\" class=\"wp-image-1526\" srcset=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-52-1024x576.png 1024w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-52-300x169.png 300w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-52-768x432.png 768w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-52-1536x864.png 1536w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-52-2048x1152.png 2048w, https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-52-1200x675.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\"><strong>Course Content<\/strong><\/h2>\n\n\n\n<p><strong>Type: Compulsory\u2013 PEC&amp;AC Track \u2013 1stTrimeste<\/strong>r<\/p>\n\n\n\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\n\n\n<p><strong>Main Topics<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Foundations of General Relativity: equivalence principles, covariance, and differential geometry.<\/li>\n\n\n\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\n\n\n<li>Experimental tests of General Relativity and classical Solar System tests.<\/li>\n\n\n\n<li>Introduction to black hole physics, including singularities, event horizons, and black hole mechanics.<\/li>\n\n\n\n<li>Gravitational waves: theory, emission, and modern detection methods.<\/li>\n\n\n\n<li>Astrophysical applications: black hole mergers and supermassive black holes in galaxies.<\/li>\n<\/ul>\n\n\n\n<p><strong>Skills Acquired<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Understand gravity as a geometric effect on spacetime structure.<\/li>\n\n\n\n<li>Derive and analyze key exact solutions of Einstein\u2019s equations.<\/li>\n\n\n\n<li>Relate theory with experimental and observational tests.<\/li>\n\n\n\n<li>Gain insight into current research topics like gravitational waves and black hole astrophysics.<\/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>Lecture Notes on General Relativity<\/em> by Daniel Baumann (all sections except Section 7 on Cosmology).<\/li>\n<\/ul>\n\n\n\n<p><strong>Additional Recommended Books:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sean M. Carroll, <em>Spacetime and Geometry<\/em><\/li>\n\n\n\n<li>James Hartle, <em>Gravity<\/em><\/li>\n\n\n\n<li>Bernard Schutz, <em>A First Course in Relativity<\/em><\/li>\n\n\n\n<li>Ray d\u2019Inverno, <em>Introducing Einstein\u2019s Relativity<\/em><\/li>\n\n\n\n<li>M. P. Hobson et al., <em>General Relativity<\/em><\/li>\n\n\n\n<li>Anthony Zee, <em>Einstein Gravity in a Nutshell<\/em><\/li>\n\n\n\n<li>Robert M. Wald, <em>General Relativity<\/em><\/li>\n\n\n\n<li>Steven Weinberg, <em>Gravitation and Cosmology<\/em><\/li>\n\n\n\n<li>P. A. M. Dirac, <em>General Theory of Relativity<\/em><\/li>\n\n\n\n<li>Misner, Thorne &amp; Wheeler, <em>Gravitation<\/em><\/li>\n\n\n\n<li>Eric Poisson &amp; Clifford Will, <em>Gravity<\/em><\/li>\n\n\n\n<li>Yvonne Choquey-Bruhat, <em>Introduction to General Relativity<\/em><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Course Outline:<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Special Relativity: Lorentz transformations, spacetime, relativistic kinematics and dynamics<\/li>\n\n\n\n<li>Gravity as Geometry: equivalence principle, curved spacetime<\/li>\n\n\n\n<li>Differential Geometry basics: manifolds, tensors, metric<\/li>\n\n\n\n<li>Geodesics: equations, Newtonian limit, applications (Mercury precession, light bending)<\/li>\n\n\n\n<li>Spacetime Curvature: covariant derivatives, Riemann tensor, geodesic deviation<\/li>\n\n\n\n<li>Einstein Equations: field equations, matter, cosmological constant, vacuum solutions<\/li>\n\n\n\n<li>Gravitational Waves: linearized gravity, wave creation<\/li>\n\n\n\n<li>Black Holes: Schwarzschild, charged, rotating<\/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\/1GRsd97HworGbTlQUQeCwq7Axa9nYR0KZ\/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:365px;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\"><a href=\"https:\/\/drive.google.com\/file\/d\/1_ZLp9FeMflqhARSW4FcRfi8DNcU4JbqH\/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-20-4-1024x576.png\" alt=\"\" class=\"wp-image-1471\" style=\"width:407px;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\" \/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Academic Team Course Content Type: 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 &hellip; <a href=\"https:\/\/projects.ift.uam-csic.es\/master\/gravitation\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Gravitation (GRA)&#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-1288","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\/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":10,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1288\/revisions"}],"predecessor-version":[{"id":1587,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1288\/revisions\/1587"}],"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}]}}