Noether Symmetries of Spacetimes and Conservation Laws

In this book the Noether symmetries of the Lagrangians of the Spacetimes are given. The conservation law corresponding to each Noether symmetry is also given in tabulated form. The Spherically symmetric, Cylindrically symmetric and Plane symmetric static spacetimes are classified according to Noether symmetries. The Lagrangians of the general Spherically symmetric, Cylindrically symmetric and Plane symmetric static spacetimes are used in the Noether symmetry equation and obtained system of 19 determining partial differential equations in each case. The solution of the obtained 19 determining partial differential equations system gives us the required classification. Using the Noether theorem, the corresponding conservation laws are also listed in each case. Complete lists of the classification of Spherically symmetric static, Cylindrically symmetric static and Plane symmetric static spacetimes are given. The approximate Noether symmetries and the corresponding approximate conservation laws are also given in separate chapter, which give us the energy content of the gravitational wave imparted by the wave from the source.