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Register a new userInterior dynamics of neutral and charged black holes in f(R) gravity
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In this paper, we explore the interior dynamics of neutral and charged black holes in $f(R)$ gravity. We transform $f(R)$ gravity from the Jordan frame into the Einstein frame and simulate scalar collapses in flat, Schwarzschild, and Reissner-Nordstrom geometries. In simulating scalar collapses in Schwarzschild and Reissner-Nordstrom geometries, Kruskal and Kruskal-like coordinates are used, respectively, with the presence of $f$ and a physical scalar field being taken into account. The dynamics in the vicinities of the central singularity of a Schwarzschild black hole and of the inner horizon of a Reissner-Nordstrom black hole is examined. Approximate analytic solutions for different types of collapses are partially obtained. The scalar degree of freedom $phi$, transformed from $f$, plays a similar role as a physical scalar field in general relativity. Regarding the physical scalar field in $f(R)$ case, when $dphi/dt$ is negative (positive), the physical scalar field is suppressed (magnified) by $phi$, where $t$ is the coordinate time. For dark energy $f(R)$ gravity, inside black holes, gravity can easily push $f$ to $1$. Consequently, the Ricci scalar $R$ becomes singular, and the numerical simulation breaks down. This singularity problem can be avoided by adding an $R^2$ term to the original $f(R)$ function, in which case an infinite Ricci scalar is pushed to regions where $f$ is also infinite. On the other hand, in collapse for this combined model, a black hole, including a central singularity, can be formed. Moreover, under certain initial conditions, $f$ and $R$ can be pushed to infinity as the central singularity is approached. Therefore, the classical singularity problem, which is present in general relativity, remains in collapse for this combined model.
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With the successes of $f(R)$ theory as a neutral modification of Einsteins general relativity (GR), we continue our study in this field and attempt to find general natural and charged black hole (BH) solutions. In the previous papers cite{Nashed:2020mnp,Nashed:2020tbp}, we applied the field equation of the $f(R)$ gravity to a spherically symmetric space-time $ds^2=-U(r)dt^2+frac{dr^2}{V(r)}+r^2 left( dtheta^2+sin^2theta dphi^2 right)$ with unequal metric potentials $U(r)$ and $V(r)$ and with/without electric charge. Then we have obtained equations which include all the possible static solutions with spherical symmetry. To ensure the closed form of system of the resulting differential equations in order to obtain specific solutions, we assumed the derivative of the $f(R)$ with respect to the scalar curvature $R$ to have a form $F_1(r)=frac{df(R(r))}{dR(r)} propto frac{c}{r^n}$ but in case $n>2$, the resulting black hole solutions with/without charge do not generate asymptotically GR BH solutions in the limit $crightarrow 0$ which means that the only case that can generate GR BHs is $n=2$. In this paper, we assume another form, i.e., $F_1(r)= 1-frac{F_0-left(n-3right)}{r^n}$ with a constant $F_0$ and show that we can generate asymptotically GR BH solutions for $n>2$ but we show that the $n=2$ case is not allowed. This form of $F_1(r)$ could be the most acceptable physical form that we can generate from it physical metric potentials that can have a well-known asymptotic form and we obtain the metric of the Einstein general relativity in the limit of $F_0to n-3$. We show that the form of the electric charge depends on $n$ and that $n eq 2$. Our study shows that the power $n$ is sensitive and why we should exclude the case $n=2$ for the choice of $F_1(r)$ presented in this study.
We obtain a class of regular black hole solutions in four-dimensional $f(R)$ gravity, $R$ being the curvature scalar, coupled to a nonlinear electromagnetic source. The metric formalism is used and static spherically symmetric spacetimes are assumed. The resulting $f(R)$ and nonlinear electrodynamics functions are characterized by a one-parameter family of solutions which are generalizations of known regular black holes in general relativity coupled to nonlinear electrodynamics. The related regular black holes of general relativity are recovered when the free parameter vanishes, in which case one has $f(R)propto R$. We analyze the regularity of the solutions and also show that there are particular solutions that violate only the strong energy condition
We investigate static and rotating charged spherically symmetric solutions in the framework of $f({cal R})$ gravity, allowing additionally the electromagnetic sector to depart from linearity. Applying a convenient, dual description for the electromagnetic Lagrangian, and using as an example the square-root $f({cal R})$ correction, we solve analytically the involved field equations. The obtained solutions belong to two branches, one that contains the Kerr-Newman solution of general relativity as a particular limit and one that arises purely from the gravitational modification. The novel black hole solution has a true central singularity which is hidden behind a horizon, however for particular parameter regions it becomes a naked one. Furthermore, we investigate the thermodynamical properties of the solutions, such as the temperature, energy, entropy, heat capacity and Gibbs free energy. We extract the entropy and quasilocal energy positivity conditions, we show that negative-temperature, ultracold, black holes are possible, and we show that the obtained solutions are thermodynamically stable for suitable model parameter regions.
We studied the spherical accretion of matter by charged black holes on $f(T)$ Gravity. Considering the accretion model of a isentropic perfect fluid we obtain the general form of the Hamiltonian and the dynamic system for the fluid. We have analysed the movements of an isothermal fluid model with $p=omega e$ and where $p$ is the pressure and $e$ the total energy density. The analysis of the cases shows the possibility of spherical accretion of fluid by black holes, revealing new phenomena as cyclical movement inside the event horizon.
In this work, we study the possibility of generalizing solutions of regular black holes with an electric charge, constructed in general relativity, for the $f(G)$ theory, where $G$ is the Gauss-Bonnet invariant. This type of solution arises due to the coupling between gravitational theory and nonlinear electrodynamics. We construct the formalism in terms of a mass function and it results in different gravitational and electromagnetic theories for which mass function. The electric field of these solutions are always regular and the strong energy condition is violated in some region inside the event horizon. For some solutions, we get an analytical form for the $f(G)$ function. Imposing the limit of some constant going to zero in the $f(G)$ function we recovered the linear case, making the general relativity a particular case.
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