Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism

Abstract

We use the distribution formalism to derive the complete set of junction conditions for general Local Rotationally Symmetric (LRS) spacetimes in the $1+1+2$ covariant formalism. We start by developing a parametric framework encompassing timelike, spacelike, or null hypersurfaces. We then introduce the distribution formalism in the $1+1+2$ framework and obtain the necessary conditions to preserve the regularity of the $1+1+2$ equations at the separation hypersurface. Using these results, we can deduce some general prescriptions on the junction of LRS spacetimes and the properties of the shell in the non-smooth cases. As examples of the application of the junction conditions, we use this formalism to perform the matching necessary to obtain well-known solutions, e.g., the Martinez thin-shell, the Schwarzschild constant-density fluid star, and the Oppenheimer-Snyder collapse.

23 pages. Several additions with respect to previous version

References in corpus (18)

• Junction Conditions in f(R) Theories of Gravity
• McVittie's Legacy: Black Holes in an Expanding Universe
• The use of Generalised Functions and Distributions in General Relativity
• A covariant approach for perturbations of rotationally symmetric spacetimes
• Junction conditions and thin-shells in perfect-fluid $f\left(R,T\right)$ gravity
• Junction conditions in Palatini $f(R)$ gravity
• Observational properties of relativistic fluid spheres with thin accretion disks
• Non-exotic traversable wormhole solutions in linear $f\left(R,T\right)$ gravity
• Junction conditions in extended Teleparallel gravities
• Double gravitational layer traversable wormholes in hybrid metric-Palatini gravity
• A Geometrical Approach to Strong Gravitational Lensing in f(R) Gravity
• Existence and stability of relativistic fluid spheres supported by thin shells
• Junction conditions for generalized hybrid metric-Palatini gravity with applications
• Observational properties of hot-spots orbiting relativistic fluid spheres
• Junction conditions of Palatini $f\left(\mathcal{R},T\right)$ gravity
• Two-fluid stellar objects in General Relativity: the covariant formulation
• Junction conditions in gravity theories with extra scalar degrees of freedom
• 1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations

Cited by in corpus (1)

• Locally Rotationally Symmetric Spacetimes in Einstein-Cartan Theory and Their Classification