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quantum123
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For a 2 body problem in GR, will the metric be that due to one body, or both bodies?
cesiumfrog said:If one body isn't very massive, you use the metric due to the other body, and just have to integrate the geodesic equation for the first.
quantum123 said:You mean in GR, we need to consider the metric of the two body in order to derive the geodesic of anyone body?
Chris Hillman said:There is an axisymmetric "double Kerr vacuum solution" (two bodies) which can be written down (using a lot of space) in closed form, but its interpretation is trickier than the Kerr vacuum solution (one body).
Chris Hillman said:4. the problem of determing the motion of a test particle orbiting an isolated object is not the same as the problem of finding an exact solution describing two objects forming a gravitationally bound isolated system
Jheriko said:Just out of curioisity, is this because even a zero mass particle will effect the gravitational field?
quantum123 said:In classical electrodynamics, when we have 2 electric charge, we consider the motion of one charge due to the electric field of another and not the resultant field of both of them, otherwise we will be using the "self" field.
You mean in GR, we need to consider the metric of the two body in order to derive the geodesic of anyone body?
The 2-body problem in general relativity is a theoretical framework used to study the gravitational interactions between two massive objects in the context of Einstein's theory of general relativity. It takes into account the curvature of spacetime caused by the masses of the two objects, and how this curvature affects their motion.
In classical mechanics, the gravitational force between two objects is described by Newton's law of universal gravitation, which assumes that gravity is a force acting instantaneously at a distance. In general relativity, gravity is described as the curvature of spacetime caused by the masses of the objects, and this curvature affects the motion of the objects in a more complex way than Newton's law.
Studying the 2-body problem in general relativity has important applications in astrophysics and cosmology. It can help us understand the motion of planets and other celestial objects in our solar system, as well as the behavior of binary star systems. It is also crucial for accurately predicting the motion of objects in the strong gravitational fields of black holes and neutron stars.
No, the 2-body problem in general relativity is still an active area of research and there are ongoing efforts to find exact solutions for different scenarios. While there are some approximate solutions and numerical methods that can be used, finding exact solutions for the equations of motion in general relativity is a challenging task.
The 2-body problem in general relativity is closely related to the study of gravitational waves, which are ripples in spacetime caused by the acceleration of massive objects. The motion of two massive objects in a binary system can produce gravitational waves, and studying the 2-body problem is crucial for accurately predicting the properties of these waves and detecting them with gravitational wave detectors.