We will also solve Einstein's equations to deduce the axisymmetric geometry around rotating stars and explore the rotational frame-dragging (or Lense-Thirring) effect. The above solutions will be applied to the special case of rotating and non-rotating black holes. The intriguing similarities between the laws of black hole mechanics and thermodynamics will be presented.
In linearized gravity, the gravitational wave solution in this theory will be derived. The Hulse and Taylor binary pulsar system, which proved the existence of gravitational waves will be studied. Moreover, the newly discovered double pulsar system J0737-3039A, which turns out to be a fantastic test bed of General Relativity, will be discussed.
When applied to the case of isotropic and homogeneous spacetime geometries, the Einstein field equations give us the cosmological solutions for different types of geometries and energy components (such as radiation, matter, and the dark energy). We will study these solutions and find the spacetime geometry and the mix of the energy components that best fit the current observations. Certain lines of attack on the dark energy problem will be explored.
For questions and suggestions, please email me!
Sukanta Bose, sukanta at wsu dot edu