Quantum Obesity and Steering Ellipsoids for Fermionic Fields in Garfinkle-Horowitz-Strominger Dilation Spacetime

This paper investigates the impact of Garfinkle-Horowitz-Strominger (GHS) spacetime dilation on three key measures of quantum correlations: quantum obesity (QO), quantum discord (QD), and the quantum steering ellipsoid (QSE) for two-qubit Gisin states. In this context, one qubit remains in an asymptotically flat region, while the other is positioned near the event horizon, where it experiences GHS dilation effects. The quantifiers QO, QD, and QSE capture quantum correlations beyond entanglement and can indicate the presence of entanglement. The analysis covers three scenarios: the first qubit remains stationary while the second qubit is either in GHS dilation spacetime or in anti-GHS dilation spacetime. Additionally, the interaction between the second qubit in both the GHS and anti-GHS regions is examined. Results show that in region I, where the second qubit is directly affected by GHS dilation, both QD and QO consistently decrease as the dilation parameter increases. However, in the anti-particle region, their values stabilize at finite dilation parameters, influenced by the Pauli exclusion principle and Fermi-Dirac statistics, before gradually increasing. The behavior of the QSE is also notable: it expands with increasing Dirac field frequencies and smaller dilation parameters in region I, while in the anti-particle region, higher dilation parameters lead to contraction. These findings provide deeper insights into how quantum correlations behave under different spacetime conditions, emphasizing the role of GHS dilation in shaping these correlations.