On the total energy conservation of the Alcubierre spacetime

TL;DR

This paper investigates the energy conservation of the Alcubierre spacetime within Teleparallel Gravity, demonstrating total energy conservation including gravitational energy and addressing negative energy issues through frame dependence analysis.

Contribution

It shows that total energy, including gravitational energy, is conserved in Alcubierre spacetime when using TEGR, and clarifies the frame dependence of energy measurements.

Findings

Total energy conservation is achieved in TEGR for Alcubierre spacetime.

Energy negativity depends on the observer's frame of reference.

Gravitational energy flux varies with the observer's motion.

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.