Analytically approximation solution to $$R^{2}$$ gravity

Abstract

In this paper, we obtain analytical approximate black hole solutions in the framework of f(R) gravity and the absence of a cosmological constant. In this area, we apply the equations of motion of the theory to a spherically symmetric spacetime with one unknown function and derive black hole solutions without any constraints on the Ricci scalar. To do so, first, we obtain the near horizon and asymptotic solutions and then use both of them to obtain a complete solution by utilizing a continued-fraction expansion. Finally, we investigate the stability of the solutions by employing the thermodynamics and quasi-normal modes.

Holographic anisotropic background in 5D Einstien–Gauss–Bonnet gravity

“…The case c = 0, μ = 0 In this case the differential equation (12), becomes 13 Plots of c 2 s (red lines) and C V (blue lines) in terms of z h for ν = 1 (dashed lines), 4.5 (solid lines)…”

“…Higher-order gravitational models have recently received attention [10][11][12][13][14], in part because string theory predicts that at low energies Einstein's equations are subject to first-order corrections [15]. In AdS/CFT context, higher-order gravities have been used as tools to characterize numerous properties of strongly coupled conformal field theories [16][17][18].…”

“…The anisotropic black hole solutions in the gauge/gravity correspondence and applications to the QGP have been investigated in [6]- [22]. Higher-order gravitational models have recently received attention [23]- [25], because of string theory predicts that at low energies Einstein's equations are subject to first-order corrections due to the interactions of the strings with the additional dimensions. The natural correction of Lovelock gravity to the Einstein-Hilbert gravity appears in five and higher dimensions and is given by a precise combination of quadratic curvature terms yields the second-order field equations known as the Gauss-Bonnet term [26], [27], [28].…”