2025/10/14 by Stefano Vignolo, Giuseppe De Maria, Sante Carloni +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Covariant transformation #Dirac (video compression format) #Dirac algebra #Dirac equation #Dirac spinor #Field (mathematics) #Field equation #Noncommutative and Quantum Gravity Theories #Tetrad #gr-qc #hep-th #math-ph #math.MP #msc:83C99
paper · pdf · doi:10.1088/1361-6382/ae134b
28 pages, 12 figures
openalex publication_date 2025/10/14 · openalex created_date 2025/10/15 · openalex updated_date 2026/06/13 · arxiv created 2026/08/05 · arxiv updated 2026/08/06
Abstract We use the polar decomposition to describe the Dirac field in terms of an effective spinorial fluid. After reformulating all covariant equations in ‘spinorial’ signature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>+</mml:mo> <mml:mo>−</mml:mo> <mml:mo>−</mml:mo> <mml:mo>−</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , we develop a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> covariant approach for the Dirac field that does not require the use of tetrad fields or Clifford matrices. By identifying the velocity and spin fields as the generators of time-like and space-like congruences, we examine the compatibility of a self-gravitating Dirac field with locally rotationally symmetric space-times of types I, II, and III. We provide illustrative examples to demonstrate the effectiveness of our construction.