Spherical doubly warped spacetimes for radiating stars and cosmology

Abstract

Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a spherically symmetric metric, the Ricci and electric tensors become rank-2, built with a velocity vector field and its acceleration. Their structure dictates the general form of the energy-momentum tensor in the Einstein equations in DW spherical metrics. The anisotropic pressure and the heat current of an imperfect fluid descend from the gradient of the acceleration and the electric part of the Weyl tensor. For radiating stellar collapse with heat flow, the junction conditions of the doubly warped metric with the Vaidya metric are reviewed, with the boundary condition for the radial pressure. The conditions for isotropy simply accomodate various models in the literature. The anisotropy of the Ricci tensor in the special case of spherical GRW space-times (geodesic velocity), gives Friedmann equations deviating from standard FRW cosmology by terms due to the electric tensor. We introduce "perfect 2-scalars" to discuss f(R) gravity with anisotropic fluid source in a doubly warped spacetime, and show that the new geometric terms in the field equations do not change the tensor structure of the fluid energy-momentum tensor.

arXiv comment27 pages, submitted to GERG

References in corpus (35)

• Spherically symmetric dissipative anisotropic fluids: A general study
• Hydrostatic equilibrium and stellar structure in f(R)-gravity
• The Mass-Radius relation for Neutron Stars in $f(R)$ gravity
• A simple characterization of generalized Robertson-Walker spacetimes
• Generalized Robertson-Walker space times, a survey
• Extended Gravity Description for the GW190814 Supermassive Neutron Star
• Inhomogeneous cosmological models: exact solutions and their applications
• Junction conditions for F(R)-gravity and their consequences
• Collapsing spherical stars in f(R) gravity
• Cosmological perfect-fluids in f(R) gravity
• A covariant approach for perturbations of rotationally symmetric spacetimes
• Higher-dimensional evolving wormholes satisfying the null energy condition
• On the Weyl and Ricci tensors of Generalized Robertson-Walker space-times
• Spherical collapse with heat flow and without horizon
• Collapsing Spheres Satisfying An "Euclidean Condition"
• Twisted Lorentzian manifolds, a characterization with torse-forming time-like unit vectors
• Anisotropic Fluid Cosmology: an Alternative to Dark Matter?
• Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies
• Spherical collapse of a heat conducting fluid in higher dimensions without horizon
• Temporal evolution of a radiating star via Lie symmetries
• Dynamical wormholes in Lovelock gravity
• Conformally Flat Collapsing Stars in f (R) gravity
• Spherical Universes with Anisotropic Pressure
• A classification of spherically symmetric spacetimes
• Gravitationally collapsing stars in $f(R)$ gravity
• Gravitational collapse in f(R) gravity for a spherically symmetric spacetime admitting a homothetic Killing vector
• Cosmological solutions of the Einstein equation with heat flow
• Geometric Perfect Fluids from Extended Gravity
• Collapse in $f(R)$ gravity and the method of $R$ matching
• Gravitational collapse of compact stars in $f(R)=\xi R^4$ gravity
• On the uniqueness of a shear-vorticity-acceleration-free velocity field in space-times
• A simple characterization of doubly twisted spacetimes
• Doubly Torqued Vectors and a classification of Doubly Twisted and Kundt spacetimes
• Geometry of almost-product Lorentzian manifolds and relativistic observer
• Novel Stellar Astrophysics from Extended Gravity

Cited by in corpus (6)

• A note on Harada's Conformal Killing gravity
• Codazzi tensors and their space-times, and Cotton gravity
• Conformal Killing gravity in static spherically-symmetric spacetimes
• The covariant approach to static spacetimes in Einstein and extended gravity theories
• Probing dark fluids and modified gravity with gravitational lensing
• Thermodynamic formulation of Cotton gravity in the Codazzi parametrization