Institute of Physics: Fulling-Rindler VEVs Differ Exponentially for Small Acceleration

The difference between vacuum energy expectations for accelerated observers and those at rest is exponentially small, but not always. Researchers from the Institute of Physics, Yerevan State University and Institute of Mechanics RA report that for small accelerations, the difference between Fulling-Rindler and Minkowski vacuum expectation values (VEVs) is exponentially small. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions, and the phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions. A massless field with zero phases in the periodicity conditions is an exception to this trend. Near the Rindler horizon, off-diagonal components of the energy-momentum tensor vanish, appearing only with non-zero values in compactified dimensions.

The subtle distinction between what constitutes “empty space” for accelerating observers and those at rest reveals an interplay between geometry and quantum fields. Researchers from the Institute of Physics, Yerevan State University and Institute of Mechanics RA have investigated how the compactification of some spatial dimensions in Rindler spacetime affects the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a charged scalar field prepared in the Fulling-Rindler vacuum state. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions. The phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions. For small accelerations, the difference between the VEVs in the Fulling-Rindler and Minkowski vacua is exponentially small. A massless field with zero phases in the periodicity conditions is an exception.

Quantization Steps for Curved Spacetime Fields

The established procedure for quantizing fields in curved spacetime relies on a three-step process: selecting a complete set of classical solutions, expanding the field operator, and constructing the Fock space starting from a vacuum state. However, the definition of this vacuum is demonstrably observer-dependent, dictated by the chosen mode functions; differing choices yield inequivalent vacuum states and, consequently, varying predictions for observable quantities. Researchers from the Institute of Physics, Yerevan State University and Institute of Mechanics RA have recently explored how compactifying spatial dimensions within Rindler spacetime impacts vacuum expectation values (VEVs) of charged scalar fields, utilizing toral compactification with quasi-periodicity conditions. Their analysis reveals that for a general number of spatial dimensions, components of the VEVs separate into those corresponding to the Minkowski vacuum, mirroring the behavior in Rindler spacetime with trivial topology.

A massless field with zero phases in the periodicity conditions is an exception to this behavior. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions, and the phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions.

Researchers at the Institute of Physics, Yerevan State University and Institute of Mechanics RA are examining the interplay between Rindler spacetime, the geometry experienced by uniformly accelerating observers, and the subtle quantum effects near black hole horizons. Their work, submitted July 5, 2026, extends beyond theoretical curiosity, offering potential insights into the fundamental nature of vacuum energy and its behavior in extreme gravitational environments. The team’s approach involves considering a toral compactification, interpreting phases in periodicity conditions as representing magnetic flux enclosed within those dimensions, to model aspects of black hole physics. A key focus lies in understanding how the vacuum expectation values (VEVs) of quantum fields are altered by this compactification and acceleration. For small accelerations, the difference between the VEVs in the Fulling-Rindler and Minkowski vacua is exponentially small. A massless field with zero phases in the periodicity conditions is an exception.

The subtle interplay between acceleration and quantum vacuum fluctuations has revealed a sensitivity to spatial topology, with implications for understanding black hole horizons and even the early universe. Researchers at the Institute of Physics, Yerevan State University and Institute of Mechanics RA have demonstrated that compactifying some spatial dimensions, essentially rolling them up into tiny circles, significantly alters vacuum energy calculations in Rindler spacetime, which approximates the region near accelerating observers or black hole event horizons. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions. The phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions. However, this familiar picture changes when non-zero phases are introduced in the periodicity conditions, leading to off-diagonal components in the vacuum energy-momentum tensor within the compact subspace. For small accelerations, the difference between the VEVs in the Fulling-Rindler and Minkowski vacua is exponentially small. A massless field with zero phases in the periodicity conditions is an exception.

The expectation that vacuum energy is solely dictated by acceleration is not supported by recent work examining spatial dimensions beyond the standard three. This approach allows for a detailed examination of how topology influences quantum vacuum fluctuations. Specifically, a massless field with zero phases exhibits a markedly different behavior.

Recent work by A. A. Saharian, G. V. Mirzoyan, and V. S. Torosyan, from the Institute of Physics, Yerevan State University, and the Institute of Mechanics RA, reveals how compactifying spatial dimensions in Rindler spacetime affects vacuum expectation values (VEVs) of charged scalar fields. For small accelerations, the difference between the VEVs in the Fulling-Rindler and Minkowski vacua is exponentially small. A massless field with zero phases in the periodicity conditions is an exception.

The established framework for understanding vacuum fluctuations in curved spacetime continues to yield nuanced results, particularly when considering compactified dimensions and accelerated observers. Recent investigations by A. A. Saharian, G. V. Mirzoyan, and V. S. Torosyan at the Institute of Physics, Yerevan State University and Institute of Mechanics RA have focused on the interplay between Rindler spacetime, a model for accelerated frames and near-horizon black hole geometries, and the introduction of topological effects via toral compactification of spatial dimensions. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions. The phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions. For a general number of spatial dimensions, the components of the VEVs are explicitly separated, corresponding to the expectation values in the Minkowski vacuum. A key finding is that for non-zero phases, the vacuum energy-momentum tensor develops off-diagonal components specifically within the compact subspace. Importantly, these off-diagonal components vanish on the Rindler horizon, while exhibiting non-zero values within the compactified dimensions, indicating a localized topological effect.

Researchers from the Institute of Physics, Yerevan State University and Institute of Mechanics RA are focusing on the Fulling-Rindler vacuum, the quantum state experienced by uniformly accelerated observers, and how its properties change when spatial dimensions are “rolled up” into tori, effectively creating a universe with a non-trivial topology. Their work, submitted on July 5, 2026, details how these compact dimensions can exhibit Aharonov-Bohm-like effects, where magnetic fluxes alter vacuum energy. For small accelerations, the difference between the VEVs in the Fulling-Rindler and Minkowski vacua is exponentially small. A massless field with zero phases in the periodicity conditions is an exception, in which case the difference decays according to a power law as a function of acceleration. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions, and the phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions.

Recent investigations into vacuum energy fluctuations near black holes explore how the topology of spacetime around cylindrical and topological black holes impacts these quantum effects. Researchers affiliated with the Institute of Physics, Yerevan State University, and the Institute of Mechanics RA have extended their analysis of vacuum expectation values (VEVs) to consider how the compactification of spatial dimensions in Rindler spacetime affects these quantum effects. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions. The phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions. For small accelerations, the difference between the VEVs in the Fulling-Rindler and Minkowski vacua is exponentially small. A massless field with zero phases in the periodicity conditions is an exception.