Question

The Einstein field equations may be written as Rμν−12Rgμν=8πGTμν. At a very large distance from massive bodies one can neglect Tμν and linearize the rest of the equation. Then it follows that a GW exists, which propagates at the speed of light when the amplitude is small. Both requirements are certainly not met in the vicinity of the source (a binary star or a pulsar).

Question 1: Do we know of a solution to the field equations near large masses?

Question 2: Is the time dependence taken into account because the stars of the binary system move?

Question 3: Can the mass of the Sun be neglected when receiving GW here on Earth? In other words: Does the linear approximation with vGW=c
apply here?

Answer 1

The Einstein field equations describe the behavior of gravity in the presence of matter and energy. Near large masses, the linear approximation is not valid due to the presence of matter and energy. Time dependence and mass cannot be neglected in the field equations.

Step-by-step explanation:

The Einstein field equations describe the behavior of gravity in the presence of matter and energy. At large distances from massive bodies, the effects of matter and energy can be neglected, and the equations can be linearized. However, in the vicinity of the source, such as a binary star or a pulsar, the linear approximation is not valid and the presence of matter and energy cannot be neglected.

Regarding the questions:

1. 
   
3. There are known solutions to the field equations near large masses, such as the Schwarzschild solution for a stationary non-rotating black hole.
4. 
   
6. Yes, the time dependence is taken into account in the field equations, especially when considering systems like binary stars that are in motion.
7. 
   
9. No, the mass of the Sun cannot be neglected when receiving gravitational waves on Earth. The linear approximation with the speed of propagation of gravitational waves, which is the speed of light, only applies in the far-field region where the effects of matter and energy can be neglected.