Gravity is a conserved vector field. Any closed path through a gravitational potential leaves you with the same energy you started with. And if it doesn’t you’ve stolen energy that was creating the gravity in the first place leaving less for the next circle to take and are thus just transforming energy from one to another.
Does that apply when the space isn’t simply connected? It could be conservative at every neighborhood, but not conservative over all if you allow portals.
Gravity would propagate through the connected space. The potential would probably be very VERY weird shaped but i see no reason it wouldnt be conservative or otherwise consistent with GR (the math of which is far beyond me). Though keep in mind in GR space curvature IS gravity and can change over time, I doubt you could maintain a knife edge thin aperture, it would all smooth out.
What’s really fun though are gravetomagnetic effects.
These are to gravity what magnetism is to the electric field. Both the electric field and gravitational field are conservative. But changing or accelerating charges generate magnetic fields which are NOT conservative hence how an electron spinning around a coil in a field in a generator gains energy even though it returns to its starting point. However in doing so it accelerates up to velocity as well generating a counteracting field that cancels out some of the field accelerating it, the motion moving it, or both. Thus the nonconservative fields have a potential energy associated with them that can be extracted from them or used to couple two phenomena that are both coupled to them.
To get gravetomagnetic effects you need huuuuuge mass flows and accelerations. But you can similarly steal the energy that drives them. Think frame dragging and extraction of black hole rotation.
but i see no reason it wouldnt be conservative or otherwise consistent with GR
I’m assuming GR holds. Does it actually prove the field is conservative, or just irrotational? If it’s irrotational and simply connected, then it’s conservative, but if you stick a portal in it, it might not be.
I doubt you could maintain a knife edge thin aperture, it would all smooth out.
Portals don’t need a knife edge. For example: Flight Through a Wormhole. You do need negative energy density or it will collapse, but that on its own shouldn’t break conservation of energy.
Gravity is a conserved vector field. Any closed path through a gravitational potential leaves you with the same energy you started with. And if it doesn’t you’ve stolen energy that was creating the gravity in the first place leaving less for the next circle to take and are thus just transforming energy from one to another.
Does that apply when the space isn’t simply connected? It could be conservative at every neighborhood, but not conservative over all if you allow portals.
Gravity would propagate through the connected space. The potential would probably be very VERY weird shaped but i see no reason it wouldnt be conservative or otherwise consistent with GR (the math of which is far beyond me). Though keep in mind in GR space curvature IS gravity and can change over time, I doubt you could maintain a knife edge thin aperture, it would all smooth out.
What’s really fun though are gravetomagnetic effects.
These are to gravity what magnetism is to the electric field. Both the electric field and gravitational field are conservative. But changing or accelerating charges generate magnetic fields which are NOT conservative hence how an electron spinning around a coil in a field in a generator gains energy even though it returns to its starting point. However in doing so it accelerates up to velocity as well generating a counteracting field that cancels out some of the field accelerating it, the motion moving it, or both. Thus the nonconservative fields have a potential energy associated with them that can be extracted from them or used to couple two phenomena that are both coupled to them.
To get gravetomagnetic effects you need huuuuuge mass flows and accelerations. But you can similarly steal the energy that drives them. Think frame dragging and extraction of black hole rotation.
I’m assuming GR holds. Does it actually prove the field is conservative, or just irrotational? If it’s irrotational and simply connected, then it’s conservative, but if you stick a portal in it, it might not be.
Portals don’t need a knife edge. For example: Flight Through a Wormhole. You do need negative energy density or it will collapse, but that on its own shouldn’t break conservation of energy.