Modified Gauss–Bonnet gravity with radiating fluids

Abstract

The main purpose of this paper is to discuss structure scalars in the context of f (G, T ) gravity, where G is the Gauss-Bonnet invariant and T is the trace of stress energy tensor. For this aim, we have considered the spherically symmetric spacetime and dissipative anisotropic fluid coupled with radiation and heat ejecting shearing matter distributions. We have found these scalar variables by orthogonally decomposing the Riemann curvature tensor in f (G, T ) gravity. Moreover, the evolution equations of shear and expansion are also developed with the help of these scalar functions. We have also analysed these scalars by taking G and T as constants for dust cloud. The physical behaviour of structure scalars for radiating matter distributions has been examined in the presence of modified gravity. It is shown that the evolutionary stages of relativistic stellar structures can be explored via modified scalar functions.

Regular black holes in f(G) gravity

“…3. We see that f G diverges for small values of G(r ), which corresponds to r → ∞ in (27). The gravity theory clearly is not general relativity, however, can always be recover to c 1 …”

“…For points close to the origin these functions tend to a constant and tend to zero in the infinity of the radial coordinate. From (75) together with (27) and (76), we can prove that the gravity theory is not general relativity. In Fig.…”

“…This type of behavior is already known in f (R), where we have the No-Go theorem. To construct the function f (G), we need calculate G(r ) from (14) and invert the function to get r = r (G) to replace in (27). Integrating (27) in G we get that…”

“…It clearly shows that the solution is regular. From (60) we can write r (G) and with (27) and (61) we construct the functions f (G) and f G (G), whose nonlinear behavior is shown in the Fig. 3.…”

“…Different of the curvature scalar, it's not possible to invert G(r ) to obtain an analytical form of r (G). So that, to show the nonlinear behave of the gravitational theory, we use (89) with (27) and f (G) in terms of the radial coordinate, that is given by …”