Casimir energy of a thin shell in the JNW spacetime

Abstract We study the Casimir energy of a massless scalar field confined to a thin, static shell composed by two concentric spherical material boundaries. We imagine the shell surrounding the source of a Janis–Newman–Winicour (JNW) spacetime. We compute the Casimir energy starting from the evaluation of the Komar mass of the whole JNW-shell system, as measured by a distant observer. We show that both the confining boundaries and the influence of the background JNW geometry affect the value of the Casimir energy. In particular, we analyze the limiting case in which the radius of the shell approaches the singularity location, considering different values of the parameter γ governing the JNW metric. We study how, depending on that parameter, the absolute value of the Casimir energy (and energy density) changes, according to the measurements performed by a distant observer and a local observer, as the shell gets closer to the minimum allowed radius. We also explore the weak-field limit, in which the shell radius is much greater than the minimum allowed radius b . We find that, although for large values of the parameter γ the JNW metric approaches the ( γ = 1) Schwarzschild metric in the considered weak-field limit, the Casimir energy of the shell shows a different response, depending on the very nature (Schwarzschild-like, γ = 1 or wormhole-like, γ → ∞ ) of the JNW source.