The Singularity Problem for Space-Times with Torsion

The problem of a rigorous theory of singularities in space-times with torsion is addressed. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors have done, because their definition of geodesics only involves the Christoffel connection, though studying theories with torsion. We propose a preliminary definition of singularities which is based on timelike or null geodesic incompleteness, even though for theories with torsion the paths of particles are not geodesics. The study of the geodesic equation for cosmological models with torsion shows that the definition has a physical relevance. It can also be motivated, as done in the literature, remarking that the causal structure of a space-time with torsion does not get changed with respect to general relativity. We then prove how to extend Hawking's singularity theorem without causality assumptions to the space-time of the ECSK theory. This is achieved studying the generalized Raychaudhuri equation in the ECSK theory, the conditions for the existence of conjugate points and properties of maximal timelike geodesics. Hawking's theorem can be generalized, provided the torsion tensor obeys some conditions. Thus our result can also be interpreted as a no-singularity theorem if these additional conditions are not satisfied. In other words, it turns out that the occurrence of singularities in closed cosmological models based on the ECSK theory is less generic than in general relativity. Our work is to be compared with previous papers in the literature. There are some relevant differences, because we rely on a different definition of geodesics, we keep the field equations of the ECSK theory in their original form rather than casting them in a form similar to general relativity with a modified energy momentum tensor,Comment: 17 pages, plain-tex, published in Nuovo Cimento B, volume 105, pages 75-90, year 199

Dynamic spectrum of ectopic lymphoid B cell activation and hypermutation in the RA synovium characterized by NR4A nuclear receptor expression

Ectopic lymphoid structures (ELS) can develop in rheumatoid arthritis (RA) synovial tissue, but the precise pathways of B cell activation and selection are not well understood. Here, we identify a synovial B cell population characterized by co-expression of a family of orphan nuclear receptors (NR4A1-3), which is highly enriched in RA synovial tissue. A transcriptomic profile of NR4A synovial B cells significantly overlaps with germinal center light zone B cells and an accrual of somatic hypermutation that correlates with loss of naive B cell state. NR4A B cells co-express lymphotoxins α and β and IL-6, supporting functions in ELS promotion. Expanded and shared clones between synovial NR4A B cells and plasma cells and the rapid upregulation with BCR stimulation point to in situ differentiation. Together, we identify a dynamic progression of B cell activation in RA synovial ELS, with NR4A transcription factors having an important role in local adaptive immune responses

Single cell analysis of RA synovial B cells reveals a dynamic spectrum of ectopic lymphoid B cell activation and hypermutation characterized by NR4A nuclear receptor expression

ABSTRACT Ectopic lymphoid structures (ELS) can develop in rheumatoid arthritis (RA) synovial tissue, but the precise pathways of B cell activation and selection are not well understood. Here, we identified a unique B cell population in the synovium characterized by co-expression of a family of orphan nuclear receptors, NR4A1 (also known as NUR77), NR4A2 (NURR1) and NR4A3 (NOR1), that is highly enriched at both early and late stages of RA. NR4A B cells are rare in healthy peripheral blood, RA blood, and SLE kidney, but share markers with blood transcriptomic signatures that peak during RA disease flare. Using combined single cell transcriptomics and B cell receptor (BCR) sequencing, we demonstrate that NR4A synovial B cells have an activated transcriptomic profile that significantly overlaps with germinal center (GC) light zone (LZ) B cells and an accrual of somatic hypermutation that correlates with loss of naïve B cell status. NR4A B cells uniquely co-express lymphotoxin β and IL6, supporting important functions in ELS promotion and pro-inflammatory cytokine production. Further, the presence of shared clones in this activated B cell state and NR4A expressing synovial plasma cells (PC) and the rapid up-regulation with BCR stimulation points to in situ differentiation. Taken together, we identified a dynamic progression of B cell activation in RA synovial ELS, with NR4A transcription factors having an important role in antigen activation and local adaptive immune responses. One sentence summary B cells in the rheumatoid arthritis synovium undergo a spectrum of in situ activation, with the NR4A family of transcription factors having an important role in antigen stimulation, local adaptive immunity, and pathological B cell responses