2018/02/28 by Prado Martín–Moruno, Prado Martin-Moruno, Matt Visser
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic number #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Eigenvalues and eigenvectors #Einstein #Entropy (arrow of time) #Hawking #Interpretation (philosophy) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Simple (philosophy) #Theoretical physics #Type (biology) #gr-qc #hep-th
paper · pdf · doi:10.1088/1361-6382/aac147
published as Classical and Quantum Gravity 35 (2018) 125003 · V1: 18 pages; V2: reformatted, now 14 pages; some clarifications added; no significant physics changes. This version accepted for publication in Classical and Quantum Gravity
openalex publication_date 2018/04/30 · arxiv created 2018/05/11 · arxiv updated 2018/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract The Hawking–Ellis (Segre–Plebański) classification of possible stress–energy tensors is an essential tool in analyzing the implications of the Einstein field equations in a more-or-less model-independent manner. In the current article the basic idea is to simplify the Hawking–Ellis type I, II, III, and IV classification by isolating the ‘essential core’ of the type II, type III, and type IV stress–energy tensors; this being done by subtracting (special cases of) type I to simplify the (Lorentz invariant) eigenvalue structure as much as possible without disturbing the eigenvector structure. We will denote these ‘simplified cores’ type II 0 , type III 0 , and type IV 0 . These ‘simplified cores’ have very nice and simple algebraic properties. Furthermore, types I and II 0 have very simple classical interpretations, while type IV 0 is known to arise semi-classically (in renormalized expectation values of standard stress–energy tensors). In contrast type III 0 stands out in that it has neither a simple classical interpretation, nor even a simple semi-classical interpretation. We will also consider the robustness of this classification considering the stability of the different Hawking–Ellis types under perturbations. We argue that types II and III are definitively unstable, whereas types I and IV are stable.