arXiv:2404.08026v1 Announce Type: new
Abstract: The investigation of non-vacuum cosmological backgrounds containing black holes is greatly enhanced by the Kiselev solution. This solution plays a crucial role in understanding the properties of the background and its relationship with the features of the black hole. Consequently, the gravitational memory effects at large distances from the black hole offer a valuable means of obtaining information about the surrounding field parameter N and parameters related to the hair of the hairy Kiselev Black hole. This paper investigates the gravitational memory effects in the context of the Kiselev solution through two distinct approaches. At first, the gravitational memory effect at null infinity is explored by utilizing the Bondi-Sachs formalism by introducing a gravitational wave (GW) pulse to the solution. The resulting Bondi mass is then analyzed to gain further insight. Therefore, the Kiselev solution is being examined to determine the variations in Bondi mass caused by the pulse of GWs. The study of changes in Bondi mass is motivated by the fact that it is dynamic and time-dependent, and it measures mass on an asymptotically null slice or the densities of energy on celestial spheres. In the second approach, the investigation of displacement and velocity memory effects is undertaken in relation to the deviation of two neighboring geodesics and the deviation of their derivative influenced by surrounding field parameter N and the hair of hairy Kiselev black hole. This analysis is conducted within the context of a gravitational wave pulse present in the background of a hairy Kiselev black hole surrounded by a field parameter N.
Gravitational Memory Effects in the Context of the Kiselev Solution
The Kiselev solution is a valuable tool in understanding non-vacuum cosmological backgrounds that contain black holes. By examining the properties of the background and its relationship with the black hole, we can gain insights into the surrounding field parameter N and parameters related to the hair of the hairy Kiselev Black hole.
Approach 1: Gravitational Memory Effect at Null Infinity
In the first approach, we explore the gravitational memory effect at null infinity using the Bondi-Sachs formalism. To introduce a gravitational wave pulse to the solution, we analyze the resulting Bondi mass. The variations in Bondi mass caused by the pulse of gravitational waves will provide us with valuable insights.
Approach 2: Displacement and Velocity Memory Effects
In the second approach, we investigate the displacement and velocity memory effects in relation to the deviation of two neighboring geodesics and the deviation of their derivative. This analysis takes into account the surrounding field parameter N and the hair of the hairy Kiselev black hole, as well as a gravitational wave pulse present in the background.
Roadmap for Future Research
Understanding the gravitational memory effects in the context of the Kiselev solution opens up several avenues for future research. Here are some potential challenges and opportunities that lie on the horizon:
- Further investigating the relationship between the surrounding field parameter N and the properties of the black hole
- Exploring the impact of different parameters related to the hair of the hairy Kiselev black hole on the gravitational memory effects
- Studying the dynamic and time-dependent nature of the Bondi mass and its implications on mass measurement and energy densities
- Examining the role of the gravitational wave pulse in influencing the displacement and velocity memory effects
By addressing these challenges and pursuing these opportunities, we can deepen our understanding of non-vacuum cosmological backgrounds containing black holes and gain valuable insights into the nature of the Kiselev solution.
Original Article: “Gravitational Memory Effects in the Context of the Kiselev Solution” by [Author Name]