Search
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/05%3A_CurvatureGeneral relativity describes gravitation as a curvature of spacetime, with matter acting as the source of the curvature in the same way that electric charge acts as the source of electric fields. Our ...General relativity describes gravitation as a curvature of spacetime, with matter acting as the source of the curvature in the same way that electric charge acts as the source of electric fields. Our goal is to arrive at Einstein’s field equations, which relate the local intrinsic curvature to the locally ambient matter in the same way that Gauss’s law relates the local divergence of the electric field to the charge density.
- https://phys.libretexts.org/Courses/Chicago_State_University/PH_S_1150%3A_Basic_Astronomy/10%3A_General_Relativity/10.03%3A_What_is_CurvatureFigure \(\PageIndex{9}\): (Left) If we wanted to measure the distance between two points on a cylindrical surface we would have to know the size of the cylinder in addition to the (x,y) coordinates of...Figure \(\PageIndex{9}\): (Left) If we wanted to measure the distance between two points on a cylindrical surface we would have to know the size of the cylinder in addition to the (x,y) coordinates of the individual points. (Right) Despite having a radius and looking curved, by our definition the cylinder has a flat geometry because it can be unrolled onto a flat surface Credit: NASA/SSU/Aurore Simonnet
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Fowler)/03%3A_Mostly_1-D_Quantum_Mechanics/3.01%3A_1-D_Schrodinger_Equation_-_Example_SystemsRather, the lowest energy state must have the minimal amount of bending of the wavefunction necessary for it to be zero at both walls but nonzero in between -- this corresponds to half a period of a s...Rather, the lowest energy state must have the minimal amount of bending of the wavefunction necessary for it to be zero at both walls but nonzero in between -- this corresponds to half a period of a sine or cosine (depending on the choice of origin), these functions being the solutions of Schrödinger’s equation in the zero potential region between the walls.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Big_Ideas_in_Cosmology_(Coble_et_al.)/10%3A_General_Relativity/10.03%3A_What_is_CurvatureThe distortion of spacetime is more complicated in general relativity. We say that spacetime is flat and static in special relativity. In contrast, spacetime is curved and dynamic in general relativit...The distortion of spacetime is more complicated in general relativity. We say that spacetime is flat and static in special relativity. In contrast, spacetime is curved and dynamic in general relativity. What is meant by flat and curved? In this section you will explore the meaning of these words in some detail in order to help you better understand what Einstein’s view of gravity is really all about.
- https://phys.libretexts.org/Courses/Chicago_State_University/PH_S_1150%3A_Basic_Astronomy/10%3A_General_Relativity/10.02%3A_Gravity_and_CurvatureThe difference in velocity of the rocket between the time the light is emitted at the source and when it is detected is due only to the acceleration of the rocket over the time the light is in transit...The difference in velocity of the rocket between the time the light is emitted at the source and when it is detected is due only to the acceleration of the rocket over the time the light is in transit. And just as in the case of the rocket, the velocity we attain downward is very small in the short time needed for the light to reach the top of the tower: this means that the frame of the top of the tower is only moving slowly relative to the free-falling frame of the light.
- https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156%3A_A_Cosmology_Workbook/01%3A_Workbook/1.33%3A_CurvatureWe introduce the notion of "curvature'' in an attempt to loosen up your understanding of the nature of space, to have you better prepared to think about the expansion of space.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Big_Ideas_in_Cosmology_(Coble_et_al.)/10%3A_General_Relativity/10.02%3A_Gravity_and_CurvatureIn this section we will explore some of the consequences of the weak equivalence principle. Let us again consider a rocket ship far away from any source of gravity. Earlier, we imagined the motions of...In this section we will explore some of the consequences of the weak equivalence principle. Let us again consider a rocket ship far away from any source of gravity. Earlier, we imagined the motions of material objects. Now we will consider what happens when light passes through the rocket ship under these same conditions.
