Non-trivial black hole solutions in $f(R)$ gravitational theory

Abstract

Recent observation shows that general relativity (GR) is not valid in the strong regime. $f(R)$ gravity where $R$ is the Ricci scalar, is regarded to be one of good candidates able to cure the anomalies appeared in the conventional general relativity. In this realm, we apply the equation of motions of $f(R)$ gravity to a spherically symmetric spacetime with two unknown functions and derive original black hole (BH) solutions without any constrains on the Ricci scalar as well as on the form of $f(R)$ gravity. Those solutions depend on a convolution function and are deviating from the Schwarzschild solution of the Einstein GR. These solutions are characterized by the gravitational mass of the system and the convolution function that in the asymptotic form gives extra terms that are responsible to make such BHs different from GR. Also, we show that these extra terms make the singularities of the invariants much weaker than those of the GR BH. We analyze such BHs using the trend of thermodynamics and show their consistency with the well known quantities in thermodynamics like the Hawking radiation, entropy and quasi-local energy. We also show that our BH solutions satisfy the first law of thermodynamics. Moreover, we study the stability analysis using the odd-type mode and shows that all the derived BHs are stable and have radial speed equal to one. Finally, using the geodesic deviations we derive the stability conditions of these BHs.

21 pages, 21 figures, will appear in Phys. Rev. D. arXiv admin note: text overlap with arXiv:2010.04701

References in corpus (30)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• The type Ia supernova SNLS-03D3bb from a super-Chandrasekhar-mass white dwarf star
• Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Extreme neutron stars from Extended Theories of Gravity
• Higher dimensional charged $f(R)$ black holes
• Thermodynamics of apparent horizon and modified Friedman equations
• The underluminous Type Ia Supernova 2005bl and the class of objects similar to SN 1991bg
• Charged spherically symmetric black holes in $f(R)$ gravity and their stability analysis
• Structure of neutron stars in R-squared gravity
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• $f(R)$ Gravity Inflation with String-Corrected Axion Dark Matter
• Rapidly rotating neutron stars in $R$-squared gravity
• Thermodynamics of higher dimensional topological charged AdS black branes in dilaton gravity
• Static Solutions for 4th order gravity
• Phase transition of quantum corrected Schwarzschild black hole
• Rapidly rotating neutron stars with a massive scalar field - structure and universal relations
• Robust approach to f(R) gravity
• On the Energy Issue for a Class of Modified Higher Order Gravity Black Hole Solutions
• Spherically symmetric black holes with electric and magnetic charge in extended gravity: Physical properties, causal structure, and stability analysis in Einstein's and Jordan's frames
• Stability analysis for cosmological models in $f(R)$ gravity using dynamical system analysis
• $k$-essence $f(R)$ Gravity Inflation
• Effects of Spatial Curvature on the $f(R)$ Gravity Phase Space: no Inflationary Attractor?
• Gravitational Collapse in General Relativity and in $R^2$-gravity: A Comparative Study
• Modified gravity models and the central cusp of dark matter halos in galaxies
• Asymptotically flat vacuum solution in modified theory of Einstein's gravity

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• Charged analog of anisotropic dark energy star in Rastall gravity
• Observational constraints on cosmological parameters in the Bianchi type III Universe with f(R,T) gravity theory
• Generalized Hidden Conformal Symmetry in Quadratic $f(T)$ Gravity
• Exact Black Hole Solutions with a Conformally Coupled Scalar Field and Dynamic Ricci Curvature in $f(R)$ Gravity Theories
• Exact Analytical Taub-NUT like Solution in f(T) Gravity
• Thin-shell wormholes in N-dimensional F(R) gravity
• Universality in static spherically symmetric solutions of f(R) gravity
• The Equivalence and/or the Effacing principle in $f\left(R\right)$ theories of gravity
• Phase space analysis of Bianchi III Universe with $f(R,T)$ gravity theory
• Thermodynamics, Phase Transitions, and Geodesic Structure of F(R)-Phantom Banados-Teitelboim-Zanelli (BTZ) Black Holes