Inertial frames vs velocity vectors

[Vanir]

Hi all. I was trying to imagine gravitation as a causal effect of time dilation and have relatively little schooling so...

With frames of reference obviously a high degree of time dilation is attained with a relative velocity close to c. however I understand a large stellar object such as a planet also has a frame of reference, not simply for its relative velocity vector but also due to its inertial frame, thus as I imagined its impact upon spatial topography is quite intense.

Fast traveling small objects get a bit of inertia going up around c. too, I've been told they also generate some amount of gravitation/regional spatial topography.

So my questions are:

what is the math (fairly simple version) for calculating the "gravitational effect" of a small object (say...10 tons) traveling a relative velocity close to c. (say...0.98c or lambda=5/is this correct way to express?) ?

secondly how is an inertial frame which is relative to rest mass (M_o ?) described in math? Is there a simple equation like the Lorentz transformation for that? Does it describe the factor of time dilation and degree of gravitational influence?

 

[Dale]

what is the math (fairly simple version) for calculating the "gravitational effect" of a small object (say...10 tons) traveling a relative velocity close to c. (say...0.98c or lambda=5/is this correct way to express?) ?

Is ~0 simple enough? I feel like a broken record. This is the third time this week that this same question has come up. A fast-moving object does not have more gravity.

 

[Vanir]

Whilst certainly I do appreciate the hand waving : P , the impression was gleaned from a PhD physicist so perhaps I had simply misunderstood something.

At any rate, as to the second question? I'll try describing what it is I'm after in a variety of ways and get back to you on the first.

How is spacetime curvature calculated for a mass body?
How is time dilation calculated for "areas of high gravity" ?
What exactly is meant by the literal term "inertial frame" ?

I apolegise for my borish lack of educational background on these subjects.

 

[Dale]

How is spacetime curvature calculated for a mass body?

The spacetime curvature is not related to the mass. The http://en.wikipedia.org/wiki/Einstein_field_equations" , not the mass. The misconception that mass is the source of gravity in GR leads to a lot of mistaken conclusions, particularly when combined with the idea of relativistic mass.

How is time dilation calculated for "areas of high gravity" ?

You can always calculate gravitational time dilation by calculating the Doppler shift between two relatively stationary observers.

What exactly is meant by the literal term "inertial frame" ?

There is more than one definition, but my favorite is that an inertial frame is any frame where an ideal accelerometer at rest anywhere in the frame always measures 0 proper acceleration.

 

[Naty1]

Dale:
I don't get:

The spacetime curvature is not related to the mass. The Einstein field equations relate the curvature of spacetime to the stress energy tensor, not the mass.

The misconception that mass is the source of gravity in GR leads to a lot of mistaken conclusions, particularly when combined with the idea of relativistic mass.

What are the sources of gravity, if not mass? Do you prefer using the term momentum instead of mass?

If mass has nothing to do with gravity, I'm surprised since "mass tells space how to curve and space tells mass how to move" or something pretty close to that. I thought Einstein included the affects of mass, energy and pressure in general Relativity...and that each contributed to gravitational effects...

 

[Dale]

I thought Einstein included the affects of mass, energy and pressure in general Relativity...and that each contributed to gravitational effects...

Exactly, all of those and more terms contribute to the stress energy tensor, which is the source of gravitation. None of them, by themselves, are the source of gravity, only all of them together. Any time you consider only one term in the stress energy tensor and neglect the others you are likely to make erroneous conclusions as we have seen over and over this week.

 

[Vanir]

Thankyou so much, Dale. This helps clear up quite a bit of confusion.
I do believe it was Naty's point which was being presented, and the erroneous conclusion you mention is one I had too easily outlined.

However whilst yours a clearer term to understand literal GR it is Naty's kind of point which directly led to the train of thought I was most interested in. This (wild abstract) was initially discluded by your response, yet finally no longer disallowed by it.

And it was an interesting thought. Don't worry I'm not a pseudoscientist, it was just for a sci-fi book I've started working on. The subject is also quite interesting enough for at least some further research.

Thanks again.

 

[Dale]

This (wild abstract) was initially discluded by your response, yet finally no longer disallowed by it.

Please don't misunderstand my last comment. An increase in gravity due to an increase in "relativistic mass" is disallowed by GR. I am sorry if my last comment conveyed any impression to the contrary.

it was just for a sci-fi book I've started working on.

However, if it is for a sci-fi book you are writing then I wouldn't worry about it if it is important to the plot. The vast majority of your audience won't know it's wrong and the few that will are so used to such mistakes that they won't care. It is much more important to have a good plot and compelling characters; don't let science get in the way of a good story.

 

[Vanir]

Please don't misunderstand my last comment. An increase in gravity due to an increase in "relativistic mass" is disallowed by GR. I am sorry if my last comment conveyed any impression to the contrary.

No it's okay. I was rather curious about this at first, but my root concern was actually showing some kind of inverse relationship between gravitation and time dilation, which is somewhat important to the plot.
Fortunately many elements of the plot are still formative. It is more inspiring to have some kind of logical process at work.

 

[Vanir]

I have a new question, apolegies if double posting is not allowed.

Is it accurate to describe gravitation as non-relativistic time dilation, am I totally off on this, or is such a perspective completely irrelevent?

I was considering what curves spacetime and thought of myself as a photon. An area to my right has slowed time, the area to my left faster time. I would bend to the right. As a physical object, doesn't everything have a velocity vector? And as a mass body of hydrogen gas, couldn't conservation of energy play a role in gravitational collapse?

 

[Dale]

I don't even have a good guess as to what you mean by "non-relativistic time dilation". Time dilation is not Newtonian, it only occurs in relativity.

 

[Vanir]

Sorry. I mean time dilation as related to gravity as distinct from that which is related to relative velocity.