{"id":169405,"date":"2023-08-10T08:25:52","date_gmt":"2023-08-10T13:25:52","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2023\/08\/what-is-a-spacelike-surface-in-relativity"},"modified":"2023-08-10T08:25:52","modified_gmt":"2023-08-10T13:25:52","slug":"what-is-a-spacelike-surface-in-relativity","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2023\/08\/what-is-a-spacelike-surface-in-relativity","title":{"rendered":"What is a \u2018spacelike surface\u2019 in relativity?"},"content":{"rendered":"<p><a class=\"blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/what-is-a-spacelike-surface-in-relativity2.jpg\"><\/a><\/p>\n<p>I am studying Noether\u2019s theorem in field theory and I am not understanding what spacelike-surfaces mean. I will reproduce the bit of the argument below that contains the term \u201cspacelike-sufaces\u201d in the context I am not understanding.<\/p>\n<blockquote><p>There will be a conserved ccurrent for each group generator $a$. Each will result in a conserved charge (that is, an integral of motion). <strong>To see this, take in spacetime a volume unbounded in the space-like direction, but limited in time by two space-like surfaces $w_1$ and $w_2$<\/strong>. Integrating $\\partial_{\\mu} J^{\\mu}_a=0$ over this volume, we get an integral over the boundary surface, composed of $w_1$, $w_2$ and the time-like boundaries supposed to be at infinity. If we now suppose the current to be zero at infinity on these boundaries, we remain with.<\/p>\n<p>$$\\int_{w_1}d\\sigma_{\\mu} J^{\\mu}_a=\\int_{w_2}d\\sigma_{\\mu} J^{<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>I am studying Noether\u2019s theorem in field theory and I am not understanding what spacelike-surfaces mean. I will reproduce the bit of the argument below that contains the term \u201cspacelike-sufaces\u201d in the context I am not understanding. There will be a conserved ccurrent for each group generator $a$. Each will result in a conserved charge [\u2026]<\/p>\n","protected":false},"author":661,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-169405","post","type-post","status-publish","format-standard","hentry","category-space"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/169405","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/661"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=169405"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/169405\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=169405"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=169405"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=169405"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}