[mad aetherist]

Do you have an example? I can imagine a gravitational field generated by an infinite plane. In that case the field is uniform and there are no tidal forces. But infinite planes were not detected by astronomers until now.

If you looked in MTW you'd see their example. But, sure. See:
http://www.newenglandphysics.org/physics_world/gr/grav_cavity.htm
Comment. I had a look. That link does not refer to an infinite plane or plate. It refers to a hole. And here i am thinking that the equations shown might be wrong because i feel sure that the equations dont explain the well known borehole (gravity) anomaly.

If there are tidal forces, and the Riemann tensor is not zero, some Christoffel symbols must be non zero.

Not true. In a locally inertial frame in a curved spacetime all of the affine connections vanish but the Riemann tensor doesn't. That's because the Riemann tensor is a function of both the Christoffel symbols as well as their derivatives. See "Coordinate expression" at
https://en.wikipedia.org/wiki/Riemann_curvature_tensor

What according to the Einstein text (..non-vanishing of the components of the affine connection...) => gravitational field.

You're making it about Einstein when in fact many others agree with him and its in all of his books. Its simple. How do you tell if there's a gravitational field in your living room? Simple; hold an apple in your hand while its stretched out and then let it go. If it drops to the floor at a rate independent of its mass (drop others with different masses to check this out) then there's a gravitational field in that room.
Comment. I dont agree. If your living room is a part of a rotating artificial g space station with no gravity field then your apple test there would-might give results no different to tests in a living room sitting on Earth.

How do you tell if there are tidal forces? Use sensitive equipment and measure the small changes in the field with height. If they exist then there are tidal forces present.
Comment. I dont understand the concept of tidal forces, why are tidal forces a different thing to plain old gravity forces. A small change in the field with height shows gravity is present -- & gravity gives tidal effects (or can). Have i missed something?

Just remembered. There are two tidal forces. On the Earth's near side to the moon the tidal force is the moon's gravity partly negated by centrifugal force (arising from Earth orbiting the barycenter). On the Earth's far side from the moon the tidal force is a combination of the reduced gravity from the moon plus a largish centrifugal force. In between the near side & the far side we have the in-between bits of the Earth where there is in effect no tidal force, yet in all 3 sections sensitive equipment would find small changes in the field with height. Or am i missing something?

You could read Einstein's gravitational field by Peter M. Brown which is online at:
https://arxiv.org/abs/physics/0204044

Yes. I wrote it. It should answer your questions. If not then your comments would be invaluable to me.

[mad aetherist]

You did get lost. Its not possible to have a non-zero Riemann tensor for a uniform gravitational field. Its actually the definition of a uniform field.

Yes, I changed a γ by a δ of one of the Γ's. There are a lot of them. But now I checked everyone, and all components are really zero.

So, in the specific case of an uniform gravitational field, the spacetime is flat for any observer (being or not in free fall).

For conventional (non uniform) gravitational fields, the spacetime is curved for any observer.

The gravitational field of a vacuum domain wall has zero curvature everywhere off the wall itself. In this case the wall is repulsive. The field around a straight cosmic string is zero for both the curvature and there is no gravitational field around the string giving the space around it a conical solace but does not exert gravitational forces on things nearby.

I reckon that the gravitational field around an infinitely long straight wire (or a long straight string) is not zero --
 & the field varies as per 1/R (the field around a ball varies as per 1/RR). How could it be zero?

[mad aetherist]

Ok, I still don't understand why gravity exists though. Why do two masses attract?

Dont expect an answer from Einsteinians. I am told that according to Einstein's field equations (which i dont understand) two stationary masses do not attract. Alltho "stationary" i think has no meaning in SR & GR.

[Bill S]

  I reckon that the gravitational field around an infinitely long straight wire (or a long straight string) is not zero –

One trouble with thoughts about anything “infinitely long” is that, whatever the maths/theory might establish, you will never be able to provide physical “proof”.

Tipler had some interesting ideas along these lines, even postulating time travel using an infinitely long cylinder. 
Come to think of it; he had some flamboyant ideas about omega-point theory, that Teilhard de Chardin might never have intended.

[mad aetherist]

  I reckon that the gravitational field around an infinitely long straight wire (or a long straight string) is not zero –

One trouble with thoughts about anything “infinitely long” is that, whatever the maths/theory might establish, you will never be able to provide physical “proof”.

Yes & no. U can get a useful result by simply bringing the test particle up very close, eg if the wire/string is only 1000 m long (instead of infinite m) u can place the test particle 1 mm away (& get a 0.999999 result).

[mad aetherist]

  I reckon that the gravitational field around an infinitely long straight wire (or a long straight string) is not zero –

One trouble with thoughts about anything “infinitely long” is that, whatever the maths/theory might establish, you will never be able to provide physical “proof”.

That a linear mass (wire/rod) has gravity dropping off as an inverse of radius (instead of inverse squared) derives directly from Newton's equations, and M-A gives a valid finite way to test this.  It doesn't require infinite length.

I dont think i have heard of 1/R deriving from Newton. My own idea is simply based on aether flowing in to the wire-string to replace aether annihilated in the wire-string, such inflow streamlines being 2 dimensional (giving 1/R) instead of the 3D inflow streamlines for a ball (giving 1/RR).

A flat sheet has gravity that doesn't drop off at all.  If Earth was flat and large enough, gravity would be 1 g all the way up.

Here i say no, the gravity would be 0.00 g for a distance, then as u got further away the g would gradually rise, & when u were far enuff away (& could see the whole Earth below) the g would be nearnuff its full value, say 1.00 g.

This is based on g near an infinite plate being  0.00 g at all distances. This is due to the fact that the inflow streamlines must all be parallel, ie there will be no acceleration of aether flowing in to the plate, & if no acceleration of aether then no gravity (& no mass)(depending on how u define mass). All of  this is Aether 101.

If u accept that then u must accept that g near a spiral galaxy aint g. There are Nobel prizes waiting for this stuff, but Einsteinians are happy to die ignorant.

Just realized. Einsteinians must surely say that spacetime is flat near an infinite plate, in which case 0.00 g at all distances is pure Einsteinian 101 also.

[CPT ArkAngel]

I just want to add a comment on the original discussion with Pete (PMB). Pete is entirely right according to GR. The problem is the same we have with the singularity. In GR, there is no limit to space and time, no limit to energy density and so on. If we put limits, then tidal forces appear. If there is no limit, there is no point of talking of curvature, simply because it would be totally relative and fields are defined as continuous which implies infinitely small units of space-time. You can then define a uniform field at a specific point without any problem. The acceleration g is constant at specific points in space-time but it is not constant along the trajectory of a mass falling toward the Earth. The problem is what are the limits? What are the implications?

[mad aetherist]

Difference between an infinite plane, which, having no thickness, has no mass, and an infinite plate, which has mass and therefore a gravitational field since it is an infinite array of infinitesimal masses, each of which has a field, and gravitation is additive. Indeed it is exactly this additivity that makes it special.

I missed this posting. Yes a plane has no mass. I wonder why the plane came up in the discussion, must be re some technical aspect of looking up Einstein's quoit with a microscope.

Yes gravity is additive (in which case it is also subtractive).
But i might not say infinitesimal masses. I reckon that there are only two types of mass, free-photons (eg light), & confined-photons (elementary particles). And a third type of mass if u like, which is electromagnetic fields (these being made up of photinos (my name) which are a part of every photon, & emanate out to infinity from every photon (if indeed photinos have mass)(i havnt made up my mind)(so i include them here just in case)(i think that Einstein said that they did have mass).
Einstein said that gravitational fields have mass. I dont agree (so i dont include it).
Einstein said that energy had a mass equivalence in some circumstances, but i dont think that that meant that mass increased with speed (so i dont include relativistic mass).

[CPT ArkAngel]

Even though gravity is invisible apart from its effect on relative motion of bodies, gravitational energy is real. Gravitational waves prove beyond any reasonable doubt that GR is right on that specific topic. All energy produces a gravitational potential, gravity itself included. Many experiments proved the gravity-inertia equivalence, none proved the contrary. When you throw an object, you transfer some of your mass-energy to the object and the object increases its relativistic mass-energy by the same amount. Gravity included, relative to any inertial frame (or non accelerating observer).

[mad aetherist]

Even though gravity is invisible apart from its effect on relative motion of bodies, gravitational energy is real. Gravitational waves prove beyond any reasonable doubt that GR is right on that specific topic. All energy produces a gravitational potential, gravity itself included. Many experiments proved the gravity-inertia equivalence, none proved the contrary. When you throw an object, you transfer some of your mass-energy to the object and the object increases its relativistic mass-energy by the same amount. Gravity included, relative to any inertial frame (or non accelerating observer).

Nah i dont believe any of that.  GWs that travel at c dont exist. Ligo's GWs are fake (or an error)(praps a harmonic of the calibration signal). What we have are gravity pulses, that travel at over 20 billion c (Van Flandern). Plus we have gravity turbulence, which travels at 500 kmps south to north throo Earth (Cahill).

Yes gravity energy is of course real, but that doesnt mean that it has mass or wt (it doesnt have mass or wt).

Yes all energy produces a gravity potential (ie due to having a gravity field), except that gravity energy (ie a gravity field) does not produce a gravity field. That would be silly, a field producing a field which produces a field which produces a field which produces a field which produces a field which produces a field etc etc.

Yes gravitational mass equals inertial mass, because gravitational mass is inertial mass, because of the way we measure gravitational mass, we measure it by measuring its inertial mass, & then they trumpet about how they have proven them to be equal to umpteen decimals, when all they have proven is that inertia equals inertia (give that man a Nobel).

Yes, when u throw an object u increase its energy, but  no u dont increase its mass. Its ok for an object to have an energy relative to a frame or something. But its not ok for an object to have a mass relative to a frame or something -- Einsteinians have been saying that sort of thing & getting away with it for so long that they dont even think about it any more.  Mass is absolute, it has one value, however i am ok with the notion that apparent mass depends on the frame of reference, ie that it depends on gamma (affecting apparent time, & affecting apparent length), that is a possibility (i will say for sure after i think it throo one day).

[yor_on]

affine connections

Maybe this will give a intuitive idea of what it is
https://www.physicsforums.com/threads/affine-connection.216136/