Nonstatic Reissner-Nordström metric in the perturbative $f(R)$ theory: Embedding in the background of the FLRW cosmology, uniqueness of solutions, the TOV equation

Abstract

This article introduces a nonstatic Reissner-Nordström metric, a metric that does not emit electromagnetic waves but can emit gravitational waves. We first use the GR theory to study a charged spherically symmetric gravitational source (CSSGS), the obtained results are further improved in comparison with the previous studies. In particular, this article considers that the field is not necessarily static. The metric tensors $g_{\mu \nu }$ are considered both outside and inside the gravitational source (the results show that in the first case $g_{\mu \nu }$ are time independent, in the latter case they are time dependent). The gravitational acceleration and the event horizon of a charged black hole are investigated. The results prove that the gravitational field is always attractive. We then use the perturbative $f(R)$ theory to consider CSSGS. The obtained results not only correct the solution of Einstein's equation in magnitude (this will describe astronomical and cosmological quantities more accurately than Einstein's equation), but also reveal new effects. Outside the gravitational source, the metric tensors can depend on time, this makes it possible for a spherically symmetric gravitational source to emit gravitational waves (Einstein's equation cannot give this effect). However, a spherically symmetric field still does not emit electromagnetic waves. Next we present a new method for embedding the spherically symmetric metrics of a star (or a black hole) in the background of the FLRW cosmological. Finally, we discuss the uniqueness of the solutions of the f(R) theory. The perturbative TOV equation is also found.

References in corpus (35)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Extended Theories of Gravity
• Monitoring stellar orbits around the Massive Black Hole in the Galactic Center
• Can modified gravity explain accelerated cosmic expansion?
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Solar System tests DO rule out 1/R gravity
• McVittie's Legacy: Black Holes in an Expanding Universe
• Static Spherically Symmetric Solutions in F(R) Gravity
• Charged spherically symmetric black holes in $f(R)$ gravity and their stability analysis
• Spherically symmetric spacetimes in f(R) gravity theories
• More on McVittie's Legacy: A Schwarzschild - de Sitter black and white hole embedded in an asymptotically $\Lambda$CDM cosmology
• The effect of a massive object on an expanding universe
• Robust approach to f(R) gravity
• A general solution in the Newtonian limit of f(R)- gravity
• Reissner-Nordström Metric in the Friedman-Robertson-Walker Universe
• How the expansion of the universe determines the causal structure of McVittie spacetimes
• Dust Static Spherically Symmetric Solution in $f(R)$ Gravity
• Some static spherically symmetric interior solutions of $f(R)$ gravity
• Spherical Symmetric Solution in f(R) Model Around Charged Black Hole
• The Post-Newtonian Limit of f(R)-gravity in the Harmonic Gauge
• Compact Star in General $F(R)$ Gravity: Inevitable Degeneracy Problem and Non-Integer Power Correction
• Spherically Symmetric Solutions in F(R) Gravity and Gravitational Repulsion
• Beyond Schwarzschild-de Sitter spacetimes: II. An exact non-Schwarzschild metric in pure $R^2$ gravity and new anomalous properties of $R^2$ spacetimes
• Specific neutral and charged black holes in $f(R)$ gravitational theory
• Rotating black hole in $f(R)$ theory
• Beyond Schwarzschild-de Sitter spacetimes: I. A new exhaustive class of metrics inspired by Buchdahl for pure $R^2$ gravity in a compact form
• Infinitely degenerate exact Ricci-flat solutions in f(R) gravity
• Perturbative solutions of the $f(R)$-theory of gravity in a central gravitational field and some applications
• Perturbative approach to $f(R)$-gravitation in FLRW cosmology
• Charge, geometry, and effective mass
• Testing the $f(R)$-theory of gravity
• Gravitational radiation of a spherically symmetric source in $f(R)$-gravitation
• Black Hole solutions in a cosmological spacetime background

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