Peculiar anisotropic stationary spherically symmetric solution of Einstein equations

Abstract

Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a non-vanishing spacelike components of the stress-energy-momentum tensor. In spite of its strange nature, this solution provides with non-trivial descriptions of gravitational effects. We show that the main aspects found in the \emph{dark matter phenomena} can be satisfactorily described by this geometry. We comment on the relevance it could have to consider non-vanishing spacelike components of the stress-energy-momentum tensor ascribed to dark matter.

6 pages, 5 figures. To appear in Modern Physics Letters A

References in corpus (14)

• Exact solution to the averaging problem in cosmology
• The universe seen at different scales
• Multiscale cosmology and structure-emerging Dark Energy: A plausibility analysis
• Inhomogeneity effects in Cosmology
• Toward physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects
• Cosmological equivalence principle and the weak-field limit
• The Spatial Averaging Limit of Covariant Macroscopic Gravity - Scalar Corrections to the Cosmological Equations
• Averaging in Spherically Symmetric Cosmology
• Cosmic Inhomogeneities and the Average Cosmological Dynamics
• Measuring the dark matter equation of state
• Gravitational lens optical scalars in terms of energy-momentum distributions
• A Complete Cosmological Solution to the Averaged Einstein Field Equations as found in Macroscopic Gravity
• Regular hyperbolicity, dominant energy condition and causality for Lagrangian theory of maps
• Spherically Symmetric Solutions in Macroscopic Gravity

Cited by in corpus (9)

• Higher order corrections to deflection angle of massive particles and light rays in plasma media for stationary spacetimes using the Gauss-Bonnet theorem
• Gravitational lensing in dispersive media and deflection angle of charged massive particles in terms of curvature scalars and energy-momentum tensor
• Expressions for optical scalars and deflection angle at second order in terms of curvature scalars
• Generalized Gibbons-Werner method for stationary spacetimes
• Gravitational lens optical scalars in terms of energy-momentum distributions in the cosmological framework
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations
• Self-Gravitating Relativistic Models of Fermions with Anisotropy and Cutoff Energy in their Distribution Function