About: Metric tensor (general relativity)

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In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational potential of Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past.

Attributes	Values
rdf:type	yago:WikicatMetricTensors yago:WikicatTensorsInGeneralRelativity yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Quantity105855125 yago:Tensor105864481 yago:Variable105857459
rdfs:label	موتر متري (ar) Metric tensor (general relativity) (en) Метрика пространства-времени (ru) Метрика простору-часу (uk)
rdfs:comment	في النسبية العامة، يعد الموتر المتري (أو التنسور المتري أو ببساطة المترية) الكائن الأساسي في الدراسة. يمكن اعتباره بصورة عمومية رخوة على أنه معلوم من جاذبية نيوتن. يتضمن التنسور كل الهندسة الفراغية و من الزمكان، المستخدمة في تعريفات مثل المسافة، الحجم، الانحناء، الزاوية، المستقبل، والماضي. العلامات والاصطلاحات: في هذا المقال نتناول والتي تكون غالباً موجبة (− + + +); طالع . جرت العادة في النسبية، يتم اعتماد حيث تكون سرعة الضوء c = 1. سيبقى ثابت الجذب العام G سيبقى مصرحا به. ، سيتم توظيفه حيثما تكررت عمليات جمع الفهرسة. (ar) In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational potential of Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past. (en) Ме́трика про́стору-ча́су — 4-тензор, який визначає властивості простору-часу в загальній теорії відносності. (uk) Метрика пространства-времени — 4-тензор, который определяет свойства пространства-времени в общей теории относительности. Как правило, обозначается символом . В инерциальной системе отсчёта матрица метрического тензора пространства-времени имеет вид . В неинерциальных системах отсчёта вид метрики пространства-времени изменяется и в общем зависит от точки пространства и момента времени. Пространственно-временной интервал выражается через метрику пространства-времени формулой . Так как метрика задаёт превращения координат, то её называют также метрическим тензором. . (ru)
dcterms:subject	Tensors in general relativity Time in physics
Wikipage page ID	2145168 (xsd:integer)
Wikipage revision ID	1117722426 (xsd:integer)
Link from a Wikipage to another Wikipage	Proper time Scalar curvature Schwarzschild metric Non-singular matrix De Sitter space Deriving the Schwarzschild solution Determinant Region (mathematics) Ricci calculus Rindler coordinates Volume form Light cone Proper length Connection (mathematics) Covariance and contravariance of vectors Mass Symmetric matrix Reissner–Nordström metric Christoffel symbols Einstein field equations Energy Fundamental theorem of Riemannian geometry General relativity Gradient Gravitational potential Gravity Minkowski metric Minkowski space Anti-de Sitter space Lemaître–Tolman metric Levi-Civita connection Lorentzian manifold Sign convention Stress–energy tensor Friedmann–Lemaître–Robertson–Walker metric Kerr–Newman metric Kruskal–Szekeres coordinates Tangent space Mathematics of general relativity 2-sphere Weyl−Lewis−Papapetrou coordinates Line element Local coordinates Curvature Eddington–Finkelstein coordinates Alternatives to general relativity Tensors in general relativity Euclidean space Four-vector Partial differential equation Gravitational singularity Isotropic coordinates Lemaître coordinates Riemann curvature tensor Einstein summation convention Tensor field Gödel metric Covariant derivative Tensor Tensor product Atlas (topology) Abstract index notation Time in physics Kerr metric Symmetric tensor Torsion tensor Symmetric bilinear form Differentiable manifold Dot product Positive definite Spacetime Special relativity Spherical coordinates Exact solutions Gravitation constant Tensor degree Linear form

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