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In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime.As a consequence, linearized gravity is an effective method for modeling the effects of gravity when the gravitational field is weak.
- Adding Forces
- The Building Blocks of Newtonian Gravity
- Linearity
- The Building Blocks of Electrodynamics
- Goodbye to The Building Blocks: Energy as A Source of Gravity
- General Relativity: A Theory with Non-Linear Laws
Imagine that we are in deep space, far away from all sizeable masses such as planets or stars. In front of us, there is a sphere drifting in space. We can chart the gravitational influence which this sphere exerts on other masses in its vicinity (in physics-speak, the sphere’s gravitational field) by keeping a record of its influence on a small tes...
In this way, the description of the gravitational force becomes a matter of building blocks. Once you have an elementary building block – the force exerted by a small mass in a tiny region of space – you can build up the gravitational influence of more complex configuration simply by dividing it into smaller masses and adding up all the different p...
The building block property – the possibility of calculating the total gravitational force by adding up different contributions – is also known as linearity. The property of “combinability by mere addition”, of being able to construct electromagnetic or gravitational influences in more complex situation by combining simpler building blocks, is call...
For completeness, it should be noted that this linearity also applies to electrodynamics, where the electric and magnetic forces produced by different electric charges or currentsadd up, as well. However, in some respects the situation is more complicated – notably, the force felt by a test particle does not result from where the other electric cha...
While linearity has great practical advantages – reality, which closely follows the laws set down by general relativity, works in a different way. With some basic knowledge in classical physics as well as (special) relativity, it is straightforward to see why. The crucial fact is that, in relativity, mass and energy are equivalent – the mass associ...
Let us approach general relativity step by step, starting with situations in which gravity is comparatively weak. In such situations, the predictions of general relativity differ only by very little from those of Newtonian gravity. Physicists describe such situations using what are called post-Newtonianapproximations, which systematically add gener...
call nearly Lorenz coordinates. Such a coordinate system is as close to a globally inertial coordinate system as is possible to make. There are other coordinate choices we could make. So for instance, you're working in a system like that. This basically boils down to coordinates that are Cartesian like on their spatial slices. You could work in ...
The resulting Newton–Cartan theory is a geometric formulation of Newtonian gravity using only covariant concepts, i.e. a description which is valid in any desired coordinate system. [30] In this geometric description, tidal effects —the relative acceleration of bodies in free fall—are related to the derivative of the connection, showing how the modified geometry is caused by the presence ...
Description: Solving the Einstein field equation by linearizing around a flat background. We treat spacetime as the metric of special relativity plus a perturbation, examine how quantities transform infinitesimal coordinate transformations (which turn out to be equivalent to gauge transformations in electrodynamics), and develop the Einstein field equation in this limit.
Newtonian gravity, as well as a few extensions thereof. In addition to its importance in e.g. the solar system, our study of linearized gravity will prepare us for the discussion of some of the weak-field experimental tests of GR (Lecture XI). It will also illustrate some of the issues that arise in solving the field equations.
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Our modern understanding of gravity comes from Albert Einstein’s theory of general relativity, which stands as one of the best-tested theories in science. General relativity predicted many phenomena years before they were observed, including black holes, gravitational waves, gravitational lensing, the expansion of the universe, and the different rates clocks run in a gravitational field.
