SAGNAC EFFECT IN THE ROTATING BLACK HOLE SPACE-TIME IN THE FOUR-DIMENSIONAL EINSTEIN-GAUSS-BONNET THEORY

Recently, Glavan and Lin proposed a new four-dimensional theory of Einstein-Gauss-Bonnet (EGB) gravity by rescaling the Gauss-Bonnet (GB) coupling constant ߙ→ ܦ(/ߙ− 4) and adopting the ܦ→ 4 constraint at the level of the equations of motion. The GB coupling constant contributes to the field equations and thus bypasses Lovelock's theorem. This theory preserves the number of degrees of freedom and avoids Ostrogradsky instability. Glavan and Lin obtained an exact solution for nonsingular static and spherically symmetric black holes in the four-dimensional EGB theory of gravity. Later, Kumar and Ghosh applied the Newman-Janis algorithm to the static solution and constructed a solution for a rotating black hole in the 4-dimensional EGB theory of gravity. Since the theory solves many observational problems in astrophysics and is promising for research, the influence of the GB coupling parameter on astrophysical effects is actively studied in the literature. However, this theory has not been tested previously using time effects. The work examines one of the most interesting time effects – the Sagnac effect. Thus, the goal of the work is to study the Sagnac effect in the space-time of a rotating black hole in the four-dimensional EGB theory and obtain a constraint on the GB coupling parameter using observational data of the Sagnac effect. In the most general case, the Sagnac effect is understood as the difference in the time it takes light beams moving in opposite directions to pass through a closed circle. The effect has many applications, is observable on Earth and is taken into account in satellite navigation systems (GPS, GLONASS) when synchronizing time signals.