On the total energy conservation of the Alcubierre spacetime

Abstract

In this article, we consider the Alcubierre spacetime, such a spacetime describes a “bubble” that propagates with arbitrary global velocity. This setting allows movement at a speed greater than that of light. There are some known problems with this metric, e.g., the source's negative energy and the violation of the source's energy conservation when the bubble accelerates. We address these two issues within the realm of the Teleparallel Equivalent of General Relativity (TEGR). The energy conservation problem can be solved when considering the energy of the gravitational field itself. The total energy of the spacetime, gravitational plus source, is conserved even in accelerated motion. We explicitly show the dependence of energy and gravitational energy flux on the frame of reference, one adapted to a static observer and the other to a free-falling one in the same coordinate system. Addressing the problem of energy negativity of the source, we find that a static observer measures positive energy of the source, while an Eulerian observer measures a negative one. Thus, we surmise that negative energy may be a reference problem.

On reference frames and coordinate transformations

“…The analogy between choosing a reference frame in General Relativity and selecting a basis for a quantum state in Dirac notation offers a compelling perspective on the interplay between spacetime geometry and quantum states. This parallelism, though not the focus of our current study, suggests a fertile ground for future research, particularly in understanding the quantum properties that might influence spacetime structures, such as those in the Alcubierre warp drive [7,10]. Such explorations could potentially bridge gaps in our understanding of quantum mechanics and general relativity, contributing to the broader quest for a unified theory in physics.…”

“…There are physical scenarios in which we have T 00 < 0, but T (0)0 > 0 for real physical observers. One example is the energy density T (0)0 of the hypothetical source responsible for the Alcubierre spacetime [10], which yields positive values for stationary observers and negative values for unphysical ones capable of traveling faster than light [7].…”

“…For instance, it allows us to study electromagnetic radiation emitted by an accelerated source in two different frames within the same coordinate system, as explored in reference [6]. Similarly, it facilitates the analysis of gravitational energy flux in the context of a propagating accelerated gravitational bubble of Alcubierre spacetime from both a co-moving and a static frame, all within the same coordinate system, as examined in reference [7].…”