Junction conditions for generalized hybrid metric-Palatini gravity with applications

Abstract

The generalized hybrid metric-Palatini gravity is a theory of gravitation that has an action composed of a Lagrangian $f(R,\mathcal{R})$, where $f$ is a function of the metric Ricci scalar $R$ and a new Ricci scalar $\mathcal{R}$ formed from a Palatini connection, plus a matter Lagrangian. This theory can be rewritten by trading the new geometric degrees of freedom of $f(R,\mathcal{R})$ into two scalar fields, $\phi$ and $\psi$, yielding an equivalent scalar-tensor theory. Given a spacetime theory, the next step is to find solutions. To construct solutions it is often necessary to know the junction conditions between two regions at a separation hypersurface $\Sigma$, with each region being an independent solution. The junction conditions for the generalized hybrid metric-Palatini gravity are found here, in the geometric and in the scalar-tensor representations, and in addition, for each representation, the junction conditions for a matching with a thin-shell and for a smooth matching at $\Sigma$ are worked out. These junction conditions are applied to three configurations, a star, a quasistar with a black hole, and a wormhole. The star has a Minkowski interior, a thin shell at the interface with all the energy conditions being satisfied, and a Schwarzschild exterior with mass $M$, and for this theory the matching can only be performed at the shell radius given by $r_{\Sigma }=\frac{9M}{4}$, the Buchdahl radius in general relativity. The quasistar with a black hole has an interior Schwarzschild black hole surrounded by a thick shell that matches smoothly to a mass $M$ Schwarzschild exterior at the light ring, and with the energy conditions being satisfied everywhere. The wormhole has an interior that contains the throat, a thin shell at the interface, and a Schwarzschild-AdS exterior with mass $M$ and negative cosmological constant $\Lambda$, with the null energy condition being obeyed.

arXiv comment26 pages, 3 figures

References in corpus (33)

• Generalised Israel Junction Conditions for a Gauss-Bonnet Brane World
• Study on anisotropic strange stars in $f(R,T)$ gravity: An embedding approach under simplest linear functional of matter-geometry coupling
• Junction Conditions in f(R) Theories of Gravity
• Junction conditions for F(R)-gravity and their consequences
• Thin-shell wormholes in d-dimensional general relativity: Solutions, properties, and stability
• Generalized hybrid metric-Palatini gravity
• Wormholes in generalized hybrid metric-Palatini gravity obeying the matter null energy condition everywhere
• Cosmological solutions in generalized hybrid metric-Palatini gravity
• Junction conditions and thin-shells in perfect-fluid $f\left(R,T\right)$ gravity
• Junction conditions in Palatini $f(R)$ gravity
• Composite vacuum Brans-Dicke wormholes
• Singular Hypersurfaces in Scalar-Tensor Theories of Gravity
• Double gravitational layer traversable wormholes in hybrid metric-Palatini gravity
• Cosmological phase space of generalized hybrid metric-Palatini theories of gravity
• Thin-shell wormholes with a double layer in quadratic F(R) gravity
• Spherically symmetric black holes and wormholes in hybrid metric-Palatini gravity
• Scalar modes in extended hybrid metric-Palatini gravity: weak field phenomenology
• Existence and stability of relativistic fluid spheres supported by thin shells
• Thick brane structures in generalized hybrid metric-Palatini gravity
• Gravitational double layers
• On the junction conditions in $f(R)$-gravity with torsion
• Revisiting the Darmois and Lichnerowicz junction conditions
• Static compact objects in Einstein-Cartan theory
• Junction conditions in scalar-tensor theories
• Sudden singularities in generalized hybrid metric-Palatini cosmologies
• Weak-field regime of the generalized hybrid metric-Palatini gravity
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• Cosmic strings in generalized hybrid metric-Palatini gravity
• Double layer from least action principle
• Thin shells in F(R) gravity with non-constant scalar curvature
• Plethora of relativistic charged spheres: The full spectrum of Guilfoyle's static, electrically charged spherical solutions
• Self-collision of a portal wormhole
• Vacuum thin shells in Einstein-Gauss-Bonnet brane-world cosmology

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• Traversable wormholes with double layer thin shells in quadratic gravity
• Junction conditions in gravity theories with extra scalar degrees of freedom
• Dynamical reconstruction of the $\Lambda$CDM model in hybrid metric-Palatini gravity
• On the visibility of singularities in general relativity and modified gravity theories
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• Junction conditions in bi-scalar Poincaré Gauge gravity
• Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism
• Gravitational wave propagation in generalized hybrid metric-Palatini gravity
• Dark energy from a geometrical gauge scalar-tensor theory of gravity
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