RELATIVE TIME DELAY IN ACCELERATING ROTATING BLACKHOLE SPACETIME

The paper studies a potentially observable effect – relative time delay– on the background of the rotating accelerating black holes, called the C-metric. The C-metric proposed by Griffiths and Podolsky is an exact solution to Einstein's equations. The metric is characterized by mass, angular momentum and acceleration parameter, and is reduced to Kerr's solution when the acceleration parameter is zero. Relative time delay occurs if two light beams come from a variable source located behind a rotating gravitational lens. Passing on opposite sides of the lens, the rays arrive at the observer with a time difference. The time difference arises due to the frame dragging effect. Black holes described by the C-metric have the angular momentum which is necessary to occur the relative time delay. To calculate the relative delay of signals, the Dymnikova method was used. The xpression for the relative delay was expanded into a series to determine the influence of the acceleration parameter of the C-metric. It was found that the relative time delay in the leading order for the C-metric does not depend on the mass of black holes and the acceleration parameter, but depends only on the angular momentum. In the corrections, the relative time delay for the C-metric differs from the corrections to the delay in the Kerr solution by the influence of the free parameter of the C-metric. To estimate the influence of the acceleration parameter on the relative time delay, numerical delay values were obtained for a range of accelerations. Numerical values were calculated by substituting observed data from realistic pulsar–black hole configurations into the expression for the relative signal delay. The obtained numerical estimates show that the magnitude of the relative time delay in the first order is measurable with the capabilities of modern technology. Considering that all previously studied solutions of objects using relative delay had the influ- ence of mass, the numerical values of the delay in the C-metric are significantly different. Therefore, black holes described by the C-metric can be distinguished from previously studied black hole solutions using potential observations of relative time delay. However, the corrections containing the influence of the acceleration parameter are too small to take their influence into account.