Thank you haushofer i will download the book and have a look on it.haushofer said:See e.g.Carlip's book on 2+1 quantum gravity. In three dimensions, the Riemann tensor is completely determined by the Ricci tensor and the metric. Hence the vacuum einstein eqns state the Riemann tensor vanishes. Hence no gravitational waves.
I will download it to, i also find the book of Steven Carlip interesting too!haushofer said:Zwiebach's book onstring theory has a nice exposition of the counting of degrees of freedom in phase space. This amount is proportional to (D-3). So no graviton propagation for D=3.
Ther is also a book for John David Brown. It is interesting too.haushofer said:Zwiebach's book onstring theory has a nice exposition of the counting of degrees of freedom in phase space. This amount is proportional to (D-3). So no graviton propagation for D=3.
The degree of freedom in relation to gravity in 3D refers to the number of independent directions in which an object can move under the influence of gravity. In 3D space, there are three degrees of freedom for an object affected by gravity: up and down, left and right, and forward and backward.
The degree of freedom for a specific object is calculated by looking at the number of constraints or limitations that are present. For example, a ball suspended in the air by a string has two degrees of freedom because it can only move up and down, while a free-falling object has all three degrees of freedom.
The degree of freedom affects an object's motion in 3D space by determining the number of possible directions in which the object can move. An object with more degrees of freedom has more options for movement and can, therefore, have more complex and varied motion.
Yes, the concept of degree of freedom applies to all objects affected by gravity in 3D. This includes both natural objects, such as planets and satellites, and man-made objects, such as vehicles and structures.
The degree of freedom is a vital concept in the study of mechanics and engineering, as it is used to analyze and predict the behavior and motion of objects. Understanding the degree of freedom of a system is essential in designing structures and machines that can withstand the forces of gravity and other external influences.