Have you noticed that no matter what the sun's revolution speed is, GR tells us that the sun's gravitational force on the surrounding space is the same. GR is a static gravity model.
The gravity model under the influence of gravitational waves can explain everything that GR can explain.
Gravitational waves caused by the revolution of the sun will affect the surrounding gravity. In the same way, the rotation of the sun will also cause gravitational waves, but it will be much smaller.
https://www.researchgate.net/publication/350617258_Gravitational_Fields_and_Gravitational_Waves
The gravity model under the influence of gravitational waves can explain everything that GR can explain.
Gravitational waves caused by the revolution of the sun will affect the surrounding gravity. In the same way, the rotation of the sun will also cause gravitational waves, but it will be much smaller.
https://www.researchgate.net/publication/350617258_Gravitational_Fields_and_Gravitational_Waves