How a Conformally Flat (GR)4 Impacts Gauss‐Bonnet Gravity?. Issue 10 (20th August 2021) - De, Avik; Loo, Tee‐How; Solanki, Raja; Sahoo, P.K.
Abstract: First and foremost, we show that a 4‐dimensional conformally flat generalized Ricci recurrent spacetime ( G R ) 4 is an Einstein manifold. We examine such a spacetime as a solution of f ( R, G ) ‐gravity theory and it is shown that the additional terms from the modification of the gravitational sector can be expressed as a perfect fluid. Several energy conditions are investigated with f ( R, G ) = R + G and f ( R, G ) = R 2 + G l n G . For both the models, weak, null and dominant energy conditions are satisfied while strong energy condition is violated, which is a good agreement with the recent observational studies which reveals that the current universe is in accelerating phase. Abstract : First and foremost, it is shown that a 4‐dimensional conformally flat generalized Ricci recurrent spacetime ( G R ) 4 is an Einstein manifold. The authors examine such a spacetime as a solution of f ( R, G ) = R + G ‐gravity theory and it is shown that the additional terms from the modification of the gravitational sector can be expressed as a perfect fluid. Several energy conditions are investigated with f ( R, G ) = R + G and f ( R, G ) = R 2 + G l n G . For both the models, weak, null and dominant energy conditions are satisfied while strong energy condition is violated, which is a good agreement with the recent observational studies which reveals that the current universe is in accelerating phase.