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Register a new userHorizon thermodynamics in $f(R)$ theory
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We investigate whether the new horizon first law proposed recently still work in $f(R)$ theory. We identify the entropy and the energy of black hole as quantities proportional to the corresponding value of integration, supported by the fact that the new horizon first law holds true as a consequence of equations of motion in $f(R)$ theories. The formulas for the entropy and energy of black hole found here are in agreement with the results obtained in literatures. For applications, some nontrivial black hole solutions in $f(R)$ theories have been considered, the entropies and the energies of black holes in these models are firstly computed, which may be useful for future researches.
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We investigate whether the new horizon first law still holds in $f(R,R^{mu u}R_{mu u})$ theory. For this complicated theory, we first determine the entropy of black hole via Wald method, then we derive the energy by using the new horizon first law, the degenerate Legendre transformation, and the gravitational field equations. For application, we consider the quadratic-curvature gravity and firstly calculate the entropy and the energy for a static spherically symmetric black hole, which reduces to the results obtained in literatures for a Schwarzschild-(A)dS black hole.
The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in $f(R)$ gravity and Horndeski theory, both containing scalar modes. These theories predict that in addition to the familiar $+$ and $times$ polarizations, there are transverse breathing and longitudinal polarizations excited by the massive scalar mode and the new polarization is a single mixed state. It would be very difficult to detect the longitudinal polarization by interferometers, while pulsar timing array may be the better tool to detect the longitudinal polarization.
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.
The article presents modeling of inflationary scenarios for the first time in the $f(R,T)$ theory of gravity. We assume the $f(R,T)$ functional from to be $R + eta T$, where $R$ denotes the Ricci scalar, $T$ the trace of the energy-momentum tensor and $eta$ the model parameter (constant). We first investigated an inflationary scenario where the inflation is driven purely due to geometric effects outside of GR. We found the inflation observables to be independent of the number of e-foldings in this setup. The computed value of the spectral index is consistent with latest Planck 2018 dataset while the scalar to tensor ratio is a bit higher. We then proceeded to analyze the behavior of an inflation driven by $f(R,T)$ gravity coupled with a real scalar field. By taking the slow-roll approximation, we generated interesting scenarios where a Klein Gordon potential leads to observationally consistent inflation observables. Our results makes it clear-cut that in addition to the Ricci scalar and scalar fields, the trace of energy momentum tensor also play a major role in driving inflationary scenarios.
We investigate the qualitative evolution of (D+1)-dimensional cosmological models in f(R) gravity for the general case of the function f(R). The analysis is specified for various examples, including the (D+1)-dimensional generalization of the Starobinsky model, models with polynomial and exponential functions. The cosmological dynamics are compared in the Einstein and Jordan representations of the corresponding scalar-tensor theory. The features of the cosmological evolution are discussed for Einstein frame potentials taking negative values in certain regions of the field space.
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