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- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.02%3A__Spacetime_GeometryWe begin our exploration of physics in an expanding spacetime with a spacetime with just one spatial dimension that is not expanding: a 1+1-dimensional Minkowski spacetime. We then generalize it sligh...We begin our exploration of physics in an expanding spacetime with a spacetime with just one spatial dimension that is not expanding: a 1+1-dimensional Minkowski spacetime. We then generalize it slightly so that the spatial dimension is expanding. After introduction of notions of age and "past horizon," we go on to calculate these quantities for some special cases.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/13%3A_Gravitation/13.08%3A_Einstein's_Theory_of_GravityAccording to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy. The principle of equivalence states that that both mass and acceleration d...According to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy. The principle of equivalence states that that both mass and acceleration distort space-time and are indistinguishable in comparable circumstances. Black holes, the result of gravitational collapse, are singularities with an event horizon that is proportional to their mass.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC_%3A_Physics_213_-_Modern_Physics/01%3A__Relativity/1.06%3A_The_Lorentz_TransformationRelativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativ...Relativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativistic phenomena in terms of space-time diagrams supports the conclusion that these phenomena result from properties of space and time itself, rather than from the laws of electromagnetism.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/05%3A__Relativity/5.06%3A_The_Lorentz_TransformationRelativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativ...Relativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativistic phenomena in terms of space-time diagrams supports the conclusion that these phenomena result from properties of space and time itself, rather than from the laws of electromagnetism.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.36%3A__The_Simplest_Expanding_SpacetimeWe begin our exploration of physics in an expanding spacetime with a spacetime with just one spatial dimension that is not expanding: a 1+1-dimensional Minkowski spacetime. We then generalize it sligh...We begin our exploration of physics in an expanding spacetime with a spacetime with just one spatial dimension that is not expanding: a 1+1-dimensional Minkowski spacetime. We then generalize it slightly so that the spatial dimension is expanding. After introduction of notions of age and "past horizon," we go on to calculate these quantities for some special cases.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/13%3A_Gravitation/13.08%3A_Einstein's_Theory_of_GravityAccording to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy. The principle of equivalence states that that both mass and acceleration d...According to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy. The principle of equivalence states that that both mass and acceleration distort space-time and are indistinguishable in comparable circumstances. Black holes, the result of gravitational collapse, are singularities with an event horizon that is proportional to their mass.
- https://phys.libretexts.org/Workbench/PH_245_Textbook_V2/13%3A_Gravitation/13.08%3A_Einstein's_Theory_of_GravityAccording to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy. The principle of equivalence states that that both mass and acceleration d...According to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy. The principle of equivalence states that that both mass and acceleration distort space-time and are indistinguishable in comparable circumstances. Black holes, the result of gravitational collapse, are singularities with an event horizon that is proportional to their mass.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Big_Ideas_in_Cosmology_(Coble_et_al.)/09%3A_Special_Relativity/9.04%3A_The_Geometry_of_Special_Relativity-_SpacetimeYou will recall the mathematical concepts of coordinate systems and the Pythagorean theorem. You will be able to draw/interpret spacetime diagrams for a variety of scenarios.
- https://phys.libretexts.org/Bookshelves/Modern_Physics/Book%3A_Spiral_Modern_Physics_(D'Alessandris)/3%3A_Spacetime_and_General_Relativity/3.1%3A_Minkowski_MetricHermann Minkowski discovered that if the temporal (dt) and spatial (dx, dy, dz) separation between two events are combined appropriately, the resulting quantity, the spacetime interval, is the same f...Hermann Minkowski discovered that if the temporal (dt) and spatial (dx, dy, dz) separation between two events are combined appropriately, the resulting quantity, the spacetime interval, is the same for all observers. This result is the metric of the four-dimensional flat spacetime that obeys Special Relativity. This metric is referred to as the Minkowski metric.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/05%3A__Relativity/5.06%3A_The_Lorentz_TransformationRelativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativ...Relativistic phenomena can be explained in terms of the geometrical properties of four-dimensional space-time, in which Lorentz transformations correspond to rotations of axes. The analysis of relativistic phenomena in terms of space-time diagrams supports the conclusion that these phenomena result from properties of space and time itself, rather than from the laws of electromagnetism.
