Research On Geodesic Problems In Extra Dimension Based On The Gravitational Wave Event Observations

Since Einstein’s theory of general relativity predicted the existence of gravitational waves（GW）,people have been working on the detection of GW.From the first GW event GW150914 on September 14,2015 to November 8,2021,the number of GW events detected by laser interferometer gravitational wave observatories around the world has reached as many as 90.It is of great help to us to study and explore the law of GW.In the Brane-world model,we think that the material world lives on a Brane and the Brane is embedded in a higher-dimensional Bulk,where electromagnetic interactions are confined to the Brane and gravity can penetrate the Brane to transmit in the Bulk.It is widely accepted that GW and electromagnetic waves（EMW）travel at the speed of light in our four-dimensional space-time.However,in the Brane-world model EMW propagate along the Brane and GW propagate in Bulk,which leads to the causal connections of GW propagation and EMW propagation are different,thus gave the famous"shortcut"effect in the Brane-world model.In the GW events GW170817 and GW150914,electromagnetic counterpart signals with delays of 1.74 seconds and 0.4 seconds were observed respectively.Based on the above situation,this dissertation considers the"shortcut"effect from a completely new perspective and attempts to limit the model with GW events.The following major innovations have been achieved:（1）We propose a novel method to study the"shortcut"effect in the extra dimension theory.Different from the Killing vector method reported in the previous literature,we obtain the action quantity of the test particle by constructing the Lagrangian of the system,and variational the action quantity to obtain the three momentums of the test particle,as well as the equation of motion of the test particle.（2）In this paper,we focus on non-zero Schwarzschild-like mass null geodesic,and find that geodesic in the R direction follows the law of hypergeometric function₂F₁（1/2,1,5/4,1/（1+γR⁴））,geodesic in the T direction follows the law of Appell hypergeometric function F₁（1/4,-1/4,1,5/4,1/（1+γR⁴）,（1+l²γμ）（1+γR⁴））.（3）Under the condition of Schwarzschild-like mass loss,we used the above Lagrangian method to study the three-dimensional flat space and obtain Caldwell-Langlois null geodesic.Similarly,we also study a three-dimensional non-zero curvature space and obtain Yu-Gu-Huang null geodesic.The framework of the paper is shown below:the first two chapters present the background knowledge and theoretical models of our research content,which are general relativity,GW and extra dimensional theory.Chapter 3 describes the observation process and results of relevant GW events.Chapters 4 contain some of the previous work in the references with our analysis and calculation of non-zero mass scale null geodesic.Chapter5 is research method that limits extra dimensional parameters based on astronomical observations.Chapter 6 is the conclusion.Next,we will use the GW event GW178017 and the electromagnetic counterpart short gamma-ray burst GRB170817A event to limit the parameter model.