New answers tagged gravity
5
votes
Can perfectly stable orbits exist in GR?
In the 1979 paper "Time without end", Freeman Dyson calculates a time in the order of 1020 years until the earth would fall into the sun due to gravitational decay alone, based on the ...
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8
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Can perfectly stable orbits exist in GR?
As you say, GR implies that all orbits lose energy (very slowly) over time, due to gravitational waves. Also the vacuum of space is not true vacuum and there is some drag from the intergalactic medium ...
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8
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Can perfectly stable orbits exist in GR?
In the literature, the orbits you are looking for a called “floating orbits”. Floating orbits are not possible in plain GR (See e.g. 1302.1016).
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0
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How exactly does curved space-time describe the force of gravity?
If we ... use a fictional device to cancel all the inertia of the
particle, it is obvious that the curve of space-time is towards the
star but what is not obvious is what would make the particle begin ...
- 6,104
1
vote
Accepted
Cause of Coordinate Acceleration in Free Fall
The acceleration on a particle following a geodesic is defined by the Christoffel symbols which are in turn defined in terms of the metric.
More properly, all inertially-moving objects not affected by ...
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0
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Do you always experience the gravitational influence of other mass as you see them in your frame?
These are excellent questions! They involve the interrelation of various physics concepts. And we would expect physics to be internally consistent, generally speaking. But since your insights are not ...
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1
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What is the gravitational field of a hole in an infinite perfect crystal?
... overdensity attracts underdensity and underdensity repels overdensity ...
Yes, in an empty universe a pair of matched positive and negative masses initially at rest would be self-accelerating ...
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2
votes
What is the gravitational field of a hole in an infinite perfect crystal?
The equations that govern gravitational fields and matter simply don't make sense when you apply them to an "infinite" volume of matter. Mathematically, we have $\nabla^2 \phi = 4 \pi G \...
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2
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What is the gravitational field of a hole in an infinite perfect crystal?
If you put overdensity next to underdensity, overdensity attracts underdensity and underdensity repels overdensity. They chase each other forever with runaway acceleration.
Not true. A volume with ...
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16
votes
Accepted
Areas with anti-parallel gravity in classical physics
If we let the $y$-axis point upwards then OP's 2D gravitational field is
$$\vec{g}~=~ \begin{pmatrix} 0 \cr g~{\rm sgn}(x)\end{pmatrix}.$$
It has a non-zero curl $$(\vec{\nabla}\times \vec{g})_z~=~2g\...
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5
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Areas with anti-parallel gravity in classical physics
The potential that yields your provided force field is discontinuous. One possible choice would be $$V(x,y) = \begin{cases} gy & x\leq 0 \\ -gy & x>0 \end{cases},$$ which has a dicontinuity ...
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0
votes
Accepted
Confused about Weinberg's result of gravitational time dilation
I think the confusion comes from my misunderstandings of coordinate time $dt$ and proper time $\Delta t$. Actually the reading on the stationary clock is the proper time. Therefore, to compare two ...
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1
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Confused about Weinberg's result of gravitational time dilation
That the clock rate for a stationary clock deeper in the potential well is slower can easily be established from the Schwarzschild metric with $dr= d\theta = d\phi= 0$ for two clocks at different ...
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0
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Why does angular momentum shorten the Schwarzschild Radius of a black hole?
Black holes aside, adding the freedom of rotation within the 3 standard volumetric dimensions essentially increases dimensionality. Rotation is a place to store momentum and energy without ...
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0
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How to derive the surface gravity in terms of redshift factor in static spacetime?
Unfortunately, I do not know how to continue this approach, but I can suggest a different way.
One can start by considering the expression
$$\sqrt{\nabla_\mu V \nabla^\mu V}$$
By plugging in the ...
3
votes
Do you always experience the gravitational influence of other mass as you see them in your frame?
An easy way to see why this would not work: if you are moving rapidly, aberration makes most of the mass content of the Universe appear to lie in front of you. If gravity were based on apparent ...
- 6,404
1
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Do you always experience the gravitational influence of other mass as you see them in your frame?
The answer to the question in the title is "No." For a mass moving with constant velocity, the Newtonian approximation for gravity points toward the current position of the mass, not where ...
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1
vote
Accepted
How to properly combine kinetic and gravitational time dilation effect?
Simply multiply the gravitional time dilation with the kinematic time dilation for both the earth and the GPS and then divide the earth's total by the GPS's. Of course on the poles the v on the ...
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0
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Tug of war between observers in frames with different rate of time
How the force changes along the rope depends not just on the relative redshift but also on the specific matter model for the rope.
The equation that governs forces along the rope stems from ...
- 15.8k
0
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Do you always experience the gravitational influence of other mass as you see them in your frame?
The contraction of distance and the contraction of the gravity field cancel out. The additional energy quite obviously causes additional force. I do not know how much additional force exactly.
Force ...
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10
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Do you always experience the gravitational influence of other mass as you see them in your frame?
Unfortunately the whole premise of your questions is wrong. You seem to be trying to apply Newtonian gravity in a relativistic context, and that just doesn't work. You need general relativity to ...
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5
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How much time does it take for an object to fall from space?
If the body has no angular momentum (no tangential speed with respect to Earth), what you want to solve is Newton's second law in this form:
$$m \frac{\mathrm d^2h(t)}{\mathrm dt^2}=-\frac{GMm}{(R_{\...
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2
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How much time does it take for an object to fall from space?
Assuming the fall is purely radial and neglecting any fancy rotation and coriolis effects, you would obtain a single differential equation:
$$\frac{GM_e}{(R+h)^2} = -\frac{\mathrm{d}^2 h}{\mathrm{d}t^...
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3
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How much time does it take for an object to fall from space?
The solution can be found on Wikipedia, the time $\rm t$ to fall from $\rm r_0$ to $\rm r_1$ is
$$\rm t=\left(\sqrt{\frac{{r_1} \left(1-\frac{{r_1}}{{r_0}}\right)}{{r_0}}}+arccos\left(\sqrt{\frac{{r_1}...
- 12.4k
1
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Tug of war between observers in frames with different rate of time
I will address only question (a). Assuming sufficient distance that the gravitational pull on B is negligible (and, as stated in the question, that the gravitational pull on the rope is negligible), ...
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-1
votes
Does time dilation cause gravity as explained in this video?
Space reduction/shrinkage is concurrent with time dilation in mass fields.
Time dilation is insufficient to and functionally ancillary/independent to/of gravitational effects.
It is byenlarge the ...
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0
votes
Why does rotation make black holes smaller?
@Yukterez: the area $A=16\pi\mathcal{M}^2$ comes from the expression $A=\int \sqrt{|\gamma|} d\theta d\phi$ (being $\gamma_{\mu\nu}$ the induced metric on the event horizon), which describes exactly ...
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0
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Confusion over what constitutes a uniform gravitational field in relativity
a. The Rindler coordinates are sometimes referred to as a "uniform gravitational field" because they have the property of not exhibiting any tidal-forces, like a classical uniform ...
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3
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Do clocks tick faster when gravitational forces are weaker?
Pop sci (e.g., YouTube) regularly says gravitational fields slow clocks, and then the comments are flooded with Flat Space Timers claiming acceleration changes how clocks function, not time itself. Ug....
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7
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Do clocks tick faster when gravitational forces are weaker?
The (relative) rate of clocks depends on the gravitational potential not force. For example, a clock at the center of the Earth would experience no acceleration due to gravity, but would tick slower ...
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0
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Do clocks tick faster when gravitational forces are weaker?
Yes, this is a well-known effect referred to as gravitational time dilation: https://en.wikipedia.org/wiki/Gravitational_time_dilation
0
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What is the weight equation through general relativity?
Little late but I'll try anyway.
I thought I'd put this here because it doesn't require world-lines or Christoffel symbols or spacetime curvature to get to.
The equivalence principle tells us that ...
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2
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Does Matter Cause Curvature or Vice-Versa
I am puzzled by the last paragraph--it's been a while since grammar class, but is that subjunctive mood? There is no need to speculate on the density of Earth's core: it's more dense than the planet's ...
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3
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Does Matter Cause Curvature or Vice-Versa
The actual physics is expressed in math, not words. The equations of general relativity (the Einstein field equations) give a precise relationship between the curvature of spacetime and the stress-...
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1
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Does Matter Cause Curvature or Vice-Versa
There are two problems with this idea:
First, you claim that celestial mechanics in your system would be indistinguishable from the celestial mechanics we observe. This is not necessarily true: If you ...
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-2
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Does time dilation cause gravity as explained in this video?
Dilation Theory by Roy D Herbert suggests it does.
Abstract;
Conservational geometric symmetries apply to all emergent phenomena independently of scale, providing geometric unity and a greater ...
4
votes
Binary black hole merging condition
The critical impact parameter $b_{\rm crit}(v)$ depends on the highly non-linear general relativistic interaction of the two black holes. The only way we currently have to address this question is ...
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