Can We Manipulate Space-Time with Different Types of Energy?

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space guy1
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I was reading a book that discussed a lot about warp drives and warp bubbles and that got me to thinking. I know that energy can warp or bend ST due to Einsteins famous equation but is that true for every kind of energy? could you manipulate ST with a strong enough magnetic field? Is there a way to control it more other than just creating deeper wells and changing the shape of the bottom? for example could you create a massive gravity well and have one side slope at the normal rate but the the other side would weaken significantly faster? apparently there is no way to do this with our level of technology let alone practically but is it theoretically possible to do this without any major breakthroughs?
thank you,
Kyle
 
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Yes, magnetic fields can cause spacetime curvature. For example, the universe used to be dominated by electromagnetic radiation, so its curvature was mainly made by the energy of electric and magnetic fields.

You can have an asymmetric gravitational potential even in Newtonian gravity (e.g., due to the Earth's slightly pear-ish shape), so I don't see why you can't in GR.