Conformal Gravity and the Alcubierre Warp Drive Metric

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1. Recomputed in conformal gravity rather than general relativity, the Alcubierre warp drive metric does not require exotic matter. With the smoother Hartle shaping function the energy density comes out completely non-negative everywhere, so the weak energy condition is satisfied and no negative energy density is needed to establish the bubble — the authors call this their main result.Abstract; Section 3, bottom right panel of Figure 1 and the paragraph naming it the main result

2. The profile of the bubble decides the outcome. With Alcubierre’s original shaping function the conformal-gravity energy density is part positive and part negative and still violates the weak energy condition; only when the shaping function is replaced by the Hartle form does the density become non-negative. Fourth-order derivatives of the shaping function enter the conformal stress-energy tensor, and their interplay is hard to predict before the computation is done.Section 3, comparison of the two bottom panels of Figure 1; Equations 12 and 13

3. The mechanism itself is unchanged from Alcubierre’s: volume elements expand behind the ship and contract in front of it, the ship sits at rest in a locally flat region inside the bubble with no time dilation and no felt acceleration, and effective superluminal motion remains a viable outcome of the metric.Section 1, Introduction; Section 3, Equation 14 and the expansion panels of Figure 1

4. The non-negative energy density persists over a wide range of speeds. For the Hartle profile with its integer parameter set to two, the shape of the energy density is essentially unchanged up to one and a half times the speed of light and stays non-negative to about two and a half times the speed of light, where downward lobes go negative. The authors decline to read any physics into this apparent limit, judging it an artefact of the particular profile that a better choice may lift.Section 3, Figure 2 and the discussion of the apparent speed limit

5. Of the other two classical energy conditions, the strong condition is always satisfied — the trace of the conformal stress-energy tensor is identically zero for all these solutions, so the strong condition reduces to the weak one — while the dominant condition is violated in the central portion of the bubble. The authors judge that violation unimportant, since the dominant condition is tied to perfect-fluid matter and is not required of all classical forms of matter.Section 4, Other Energy Conditions; Figure 5

6. The energy bill is set by a constant nobody has measured well. Integrating the local energy density over the proper volume for a 100-metre bubble travelling at exactly the speed of light gives a total of 1.86 × 10¹⁰ times the conformal coupling constant, in ergs; with the only published value of that constant the total is about 6 × 10⁹² erg, equivalent to 6.81 × 10⁷¹ grams or 3.42 × 10³⁸ solar masses. But that is the macroscopic value: the microscopic one may be smaller by a factor of order the number of occupied baryonic states in a galaxy, about 10⁶⁸, or the number of baryons in the universe, about 10⁸⁰, so the estimate could fall by many orders of magnitude. Pinning down the coupling constant is the measurement that settles the cost.Section 4, Equations 16 to 18 and the paragraph on the coupling constant

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How to cite it

Gabriele U. Varieschi, Zily Burstein (2013) Conformal Gravity and the Alcubierre Warp Drive Metric doi:10.1155/2013/482734

Where it sits in the curriculum

• The metric, warp drives and wormholes