Well yes, but actually hm ?
Energy
Curving spacetime isnt hard, a pencil can do it, warping it at small scales with strong curvature only requires a lot of energy. Whenever these papers talk about Earth masses, they are referring to mass energy, all $E = mc^2$. The paper you mentioned predicts a mass energy equivalent of $E_{tot} = Cv^2_{s}\frac{R^2}{w}$. With apparently works out to a couple of Earth masses for a Radius of 100 meters.
The issue is not getting this much mass, its getting an energy source capable of outputting this much energy on such a small scale. The Energy density here is absurd. We can do the math for this rather easily, a 100 meter sphere has a volume of $4188790 m^3$, one Earth mass is $5.9722\times 10^{24} kg$,
$E = mc^2$
$E = 5.9722\times 10^{24} kg \times 299792458 \frac{m}{s}^2$
$E = 1.7904\times 10^{41} J$
$E_{\rho} = \frac{E}{V}$
$E_{\rho} = \frac{ 1.7904\times 10^{41} J}{4188790 m^3}$
$E_{\rho} = 4.274\times 10^{34} \frac{J}{m^3}$
or in other terms, $4.274 \times 10^{25}$ tons of TNT per cubic meter. This is an absurd amount of Energy per cubic meter. The Energy contained in one cubic meter of this Energy source is an order of magnitude more than the Asteroid that killed the Dinosaurs released in total. That was a 20 kilometer wide rock.
Certainly not impossible, but absurdly dangerous. No known reaction can release this much energy. But there are many things which release more energy as a sum of many small reactions. The Sun obviously releases more than this, but the sun is not 100 meters across !
So, can your guys do it ? If you accept there is a way to make and contain whatever Energy source they are using than yeah. Should be doable in the context of a Sci Fi setting.
Personally, i would argue the less you say about the Energy source the better. You wont be able to create something that actually works, because the only thing i can think of is a Black Hole generator and that is a whole other can of worms. The only known method of extracting Energy from a Black hole is the Penrose process (leaving aside Hawking radiation), and with such an enormous energy expenditure you will burn through the angular momentum of any black hole really quickly. Keep in mind, small black holes cannot contain that much angular momentum. Earth has more Angular momentum than a black hole of its mass can even theoretically have. So if you dont plan to haul a Multi stellar mass black hole with you, even a black hole generator wont do the trick. Not to mention that you would need to somehow feed the black hole faster than your drive burns through energy, without emitting such intense Gamma Radiation half the galaxy is sterilized.
Short Tangent - Alcubierre is not FTL
I want to include this section so that you avoid this older than time mistake. Alcubierre, Wormholes and similar exact solutions to Einstein´s field equations are categorically not Faster-Than-Light. The definition of FTL is, according to the Wiki;
Faster-than-light (also FTL, superluminal or supercausal) travel and
communication are the conjectural propagation of matter or information
faster than the speed of light (c).
Otherwise known as, FTL is the process by which the velocity of a massive or massless particle exceeds c.
In General Relativity there are two definitions for Velocity. The local and coordinate velocity. The Local Velocity describes the velocity of massive and massless particles through spacetime, while the coordinate velocity is the "speed" of spacetime itself. Both relative to some observer obviously.
The local velocity is constraint by c. While the coordinate velocity is not. Furthermore, these two velocities are independent. Your local velocity can be $0 \frac{m}{s}$ while the coordinate velocity is $10c$. This is possible because the Coordinate Velocity is not subject to any relativistic effects. There is no maximum velocity the underlying spacetime can have.
Wormholes, Alcubierre and so on exploit this fact. They construct spacetimes in which the coordinate velocity is really high, while the local velocity is 0. Take Alcubierre, the spacetime inside the Warp Bubble is flat with no local velocity at all. Meanwhile the overall bubble can move at an arbitary multiple of c, without violating any principles of GR. Because GR only stipulates that the local velocity cannot be bigger than c. Hence why there is no time dilation inside the bubble as well.
Moreover, these metrics (Solutions) do not violate Causality. Which is a corner stone of actual FTL.
Imagine Bob shooting at Alice. The bullet travels at true FTL speeds, its local velocity is > c. From Alices frame of reference, the bullet arrives before the information that the gun was fired. So from her POV, the effect (Bullet hitting her) literally happens before the cause (Gun fired). This breaks Causality because Alice can mathematically prove that from her frame of reference Cause and Effect were reversed.
Imagine the same scenario, but this time Bob fires a Alcubierre bullet. The moment the gun is fired the bullet is enveloped by a Warp drive that travels at the same Coordinate Velocity as the local velocity in the previews example. So v > c. Why doesn't this violate Causality ? While the overall Warp bubble may have v > c, the bullet itself inside the bubble is not moving. Its local velocity is 0, meanwhile light still travels at c. So as the Warp bubble propagates, light containing the information about the event (Gun being fired) constantly leaves the bubble. The bubble travels faster than light so the light ends up damming up in front of the bubble. When the Bubble arrives at Alice, the first thing she sees is the extremely blue shifted light at the front of the Warp bubble, containing the causal information before the bullet hits. This happens no matter the frame of reference. The light may only arrive a fraction of a nanosecond before the bullet, but it always arrives first.
Alcubierre violate Causality in other ways, and only some of the time. This dosnt matter for this discussion, just be aware that these systems are Categorically not FTL.
