- #1
Devin
- 24
- 1
Let a mass oscillate with relativistic acceleration (sinusoidal) by means which are irrelevant. What does the gravitational field look like a distance R away?
What if perhaps we had a mechanism that made it such that the mass oscillates with constant /omegapervect said:If one considers a sinusoidal mass oscillating in isolation, one finds that ##\nabla_a T^{ab}## is not equal to zero, while ##\nabla_a G^{ab} = 0##. As a consequence one cannot satisfy Einstein's field equations ##T^{ab} = 8 \pi G^{ab}## as taking the covariant derivative of each side yields the result that ##\nabla_a T^{ab} = \nabla_a G^{ab}##, but this is not possible.
Thus one is lead to the conclusion that the means by which the mass is made to osscilate cannot be ignored.. Another way of saying this that may be simpler - one needs the source to conserve energy-momentum (the precise mathematical statement of this idea is that ##\nabla_a T^{ab} = 0## ) in order to be able to apply Einstein's field equations in the first place. And an oscillating mass doesn't do that by itself, it needs help.
Relativistic mass oscillation refers to the concept in physics where the mass of an object changes due to its motion and energy. This phenomenon is described by Einstein's theory of relativity, where mass and energy are considered interchangeable.
Relativistic mass oscillation is related to gravitational fields because the presence of a gravitational field can cause a change in the energy of an object, which in turn affects its mass. This is known as gravitational redshift, where the energy of an object decreases as it moves away from a strong gravitational field, resulting in a decrease in its mass.
R is a variable used in equations to represent the distance between two objects. In the context of relativistic mass oscillation and gravitational fields, R represents the distance between a massive object (such as a planet or star) and a smaller object (such as a satellite or particle) that is affected by its gravitational field.
The strength of a gravitational field can affect relativistic mass oscillation by causing a larger change in the energy of an object, resulting in a larger change in its mass. This effect is more significant in strong gravitational fields, such as those near massive objects like black holes.
Yes, relativistic mass oscillation can be observed in everyday life through various phenomena such as the redshift of light from distant galaxies, the time dilation of atomic clocks on GPS satellites, and the gravitational lensing of light by massive objects. However, these effects are often very small and require precise measurements to be detected.