Raychaudhuri equation in spacetimes with torsion

Abstract

Given a spacetime with nonvanishing torsion, we discuss the equation for the evolution of the separation vector between infinitesimally close curves in a congruence. We show that the presence of a torsion field leads, in general, to tangent and orthogonal effects on the congruence; in particular, the presence of a completely generic torsion field contributes to a relative acceleration between test particles. We derive, for the first time in the literature, the Raychaudhuri equation for a congruence of timelike and null curves in a spacetime with the most generic torsion field.

arXiv comment8 pages

References in corpus (20)

• Evidence for oscillation of atmospheric neutrinos
• Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
• Thermodynamics of Spacetime: The Einstein Equation of State
• Lorentz-Violating Extension of the Standard Model
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• f(T) teleparallel gravity and cosmology
• Non-equilibrium Thermodynamics of Spacetime
• Dynamic wormholes, anti-trapped surfaces, and energy conditions
• Metric-affine f(R) theories of gravity
• The Raychaudhuri equations: a brief review
• Non-equilibrium Thermodynamics of Spacetime: the Role of Gravitational Dissipation
• Constraining Torsion with Gravity Probe B
• The dynamics of metric-affine gravity
• The role of nonmetricity in metric-affine theories of gravity
• The dynamics of generalized Palatini Theories of Gravity
• Propagation equations for deformable test bodies with microstructure in extended theories of gravity
• How does light move in a generic metric-affine background?
• Effect of Spin-Torsion Interaction on Raychaudhuri Equation
• Mathematical Structures of Space-Time
• Zero-size objects in Riemann-Cartan spacetime

Cited by in corpus (27)

• The Raychaudhuri equation in spacetimes with torsion and non-metricity
• Spacetime thermodynamics in the presence of torsion
• Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories
• Einstein manifolds with torsion and nonmetricity
• Static compact objects in Einstein-Cartan theory
• Sachs' free data in real connection variables
• Cosmic Acceleration with Torsion and Non-metricity in Friedmann-like Universes
• Symmetry breaking and lattice kirigami: finite temperature effects
• Raychaudhuri and optical equations for null geodesic congruences with torsion
• Super-entropic black hole with Immirzi hair
• Raychaudhuri equations and gravitational collapse in Einstein-Cartan theory
• Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory
• Fermion dynamics in torsion theories
• Revisiting wormhole energy conditions in Riemann-Cartan spacetimes and under Weyl transformations
• Singularity theorems and the inclusion of torsion in affine theories of gravity
• Spacetime Thermodynamics with Contorsion
• Kinematics and dynamics of null hypersurfaces in the Einstein-Cartan spacetime and related thermodynamic interpretation
• Projective and amplified symmetries in metric-affine theories
• Toward Singularity Theorems with Torsion
• Kinematics in Metric-Affine Geometry
• Symmetries and conserved quantities with arbitrary torsion: A generalization of Killing's theorem
• Focusing conditions for extended teleparallel gravity theories
• Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry
• Tidal heating in a Riemann-Cartan spacetime
• Light propagation and optical scalars in torsion theories of gravity
• Gauge-covariant Raychaudhuri dynamics for spin-nondegenerate Lorentz-violating congruences
• Possible fluid interpretation and tidal force equation on a generic null hypersurface in Einstein-Cartan theory