# Tidal forces in accelerating frames

## Main Question or Discussion Point

Let's say I'm floating in space in a spaceship, and there are some stars around.

Now I turn on powerful spaceship engines. This causes a huge acceleration, which causes the brightness of some stars to increase a lot. (Those stars that are up in the pseudo gravity well become bright)

Does tidal force from a star increase as much as its brightness?

If the star is able to shine brightly, it contains a lot of energy, so it exerts a large gravitational force on those observers that say that it's a bright star, right?

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PeterDonis
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Now I turn on powerful spaceship engines. This causes a huge acceleration, which causes the brightness of some stars to increase a lot. (Those stars that are up in the pseudo gravity well become bright)
Not immediately. They will only become brighter as your ship's velocity relative to them increases. This is an example of how the equivalence principle only works locally: in a small patch of spacetime, you can equate acceleration with being at rest in a gravitational field, but globally, you can't.

Does tidal force from a star increase as much as its brightness?
The brightness does not increase at once, as above. The tidal force from the star doesn't increase at once, either; it will increase gradually as you get closer to the star. Also, your acceleration has no effect on the tidal force you experience from the star.

If the star is able to shine brightly, it contains a lot of energy, so it exerts a large gravitational force on those observers that say that it's a bright star, right?
The brightness of the star is a function of its luminosity and your distance from it. There is a relationship between mass and luminosity, but it's not the simple one you appear to be implicitly assuming; brighter stars are more massive in some cases, but not all.

Not immediately. They will only become brighter as your ship's velocity relative to them increases. This is an example of how the equivalence principle only works locally: in a small patch of spacetime, you can equate acceleration with being at rest in a gravitational field, but globally, you can't.
Oh yes. Gradual change of brightness seems to spoil my simple idea.

The brightness does not increase at once, as above. The tidal force from the star doesn't increase at once, either; it will increase gradually as you get closer to the star. Also, your acceleration has no effect on the tidal force you experience from the star.
I would like to eliminate the effect of the change of distance. If observer's clock becomes quickly time dilated, then the observer will say that the gradual brightening of the star happens quickly, and the star does not have time to move much during that time. This is the situation when the acceleration is sufficiently high.

The brightness of the star is a function of its luminosity and your distance from it. There is a relationship between mass and luminosity, but it's not the simple one you appear to be implicitly assuming; brighter stars are more massive in some cases, but not all.
I just want to assume that the star gains potential energy when I start to accelerate, and I can feel the gravitational force of that extra energy.

andrewkirk
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Gold Member
If the star is able to shine brightly, it contains a lot of energy, so it exerts a large gravitational force on those observers that say that it's a bright star, right?
If the increased brightness is a consequence of the star moving towards the observer in the observer's rest frame then presumably the star dims by the same amount in the opposite direction in that frame. If so then the amount of energy being emitted by the star, measured in the observer's rest frame, may not have changed, and hence there is no reason to expect observer to perceive the gravitation of the star as having increased.

But a cleaner way to look at it is that the 'gravitational pull' of the star is a function of the stress-energy tensor, which is a coordinate-independent item, not of a coordinate-dependent measurement of mass-energy. So the observer's perception of the gravitation of the star via phenomena such as tidal effects cannot be affected by the observer's velocity relative to the star.

PeterDonis
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2019 Award
If observer's clock becomes quickly time dilated,
It doesn't.

I just want to assume that the star gains potential energy when I start to accelerate, and I can feel the gravitational force of that extra energy.
You may want to assume this, but that doesn't mean it's correct. It isn't.

Once again: the EP only works locally. Your scenario is not local; it covers a large patch of spacetime, including your ship and the star. A "pseudo-gravity" field due to acceleration is not equivalent to a real gravitational field over this large patch of spacetime; suddenly accelerating your ship does not instantly create the effects you are talking about.