universe Article Gravitational Effects on Neutrino Decoherence in the Lense–Thirring Metric Giuseppe Gaetano Luciano 1,2, * ,† and Massimo Blasone 1,2, * ,†   Citation: Luciano, G.G.; Blasone, M. Gravitational Effects on Neutrino Decoherence in the Lense–Thirring Metric. Universe 2021, 7, 417. https:// doi.org/10.3390/universe7110417 Academic Editor: Tina Kahniashvili Received: 27 September 2021 Accepted: 29 October 2021 Published: 1 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Dipartimento di Fisica, Università di Salerno, 84084 Fisciano, SA, Italy 2 Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Gruppo Collegato di Salerno, 84084 Fisciano, SA, Italy * Correspondence: gluciano@sa.infn.it (G.G.L.); blasone@sa.infn.it (M.B.) † These authors contributed equally to this work. Abstract: We analyze the effects of gravity on neutrino wave packet decoherence. As a specific example, we consider the gravitational field of a spinning spherical body described by the Lense– Thirring metric. By working in the weak-field limit and employing Gaussian wave packets, we show that the characteristic coherence length of neutrino oscillation processes is nontrivially affected, with the corrections being dependent on the mass and angular velocity of the gravity source. Possible experimental implications are finally discussed. Keywords: neutrino oscillations; decoherence; gravity; Lense–Thirring metric; wave packets 1. Introduction Neutrinos are among the elementary particles in the Standard Model (SM) of funda- mental interactions. In spite of this, their essential nature has not yet been fully revealed, and has become even more puzzling after Pontecorvo’s pioneering idea of neutrino mass and mixing [1–3] and the subsequent discovery of flavor oscillations [4–7]. Further studies in Quantum Field Theory (QFT) have highlighted the shortcomings of the standard quan- tum mechanical (QM) predictions by pointing out the unitary inequivalence between the Fock spaces for definite flavor fields and definite mass fields [8–10]. Phenomenological implications of this inequivalence have been investigated in a variety of contexts, ranging from vacuum effects [11–15] to particle decays [16–19] and apparent violations of the weak equivalence principle [20]. Neutrino mixing and oscillations are typically analyzed in the plane wave approxi- mation. However, a more realistic treatment that accounts for neutrinos being localized particles should involve the use of wave packets (WPs), which introduce decoherence among the mass eigenstates. The first WP approach was developed in [21], showing the existence of a coherence length beyond which the interference between massive neu- trinos becomes negligible. This effect arises from the different group velocities of the different mass states, which leads WPs to spread over macroscopic sizes and separate during the propagation. Wave packet models of neutrino oscillations were later developed within the framework of QM [22–24] and QFT [25–28], both in vacuum and matter [29–31] (see [32] for a review). In particular, in dense environments, decoherence through WP separation was shown to depend on the model chosen for the adiabaticity violation of WP evolution [30,31]. All of the above investigations were performed in flat spacetime. The effects of gravity on neutrino decoherence were addressed in [33] by considering a static and spherically symmetric field described by the Schwarzschild metric. By adopting the density matrix for- malism [31] with Gaussian WPs and exploiting previous achievements of [34–36], neutrino decoherence was quantified by a coherence coordinate distance and a proper time. As a result, it was shown that these quantities are nontrivially modified with respect to the flat Universe 2021, 7, 417. https://doi.org/10.3390/universe7110417 https://www.mdpi.com/journal/universe