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In general relativity, the nature of mass is non-local. However, an appropriate def-inition of mass at a quasi-local level could give a more detailed characterization ofthe gravitational field around massive bodies. Several attempts have been made tofind such a definition. One of the candidates is the Hawking mass. This thesispresents a method for calculating the spin coefficients used in the expression for theHawking mass, and gives a closed-form expression for the Hawking mass of ellipsoidal2-surfaces in Minkowski spacetime. Furthermore, the Hawking mass is shown to havethe correct limits, both in Minkowski and Schwarzschild, along particular foliationsof leaves approaching a metric 2-sphere. Numerical results for Schwarzschild are alsopresented.

<p>In general relativity, the nature of mass is non-local. However, an appropriate def-inition of mass at a quasi-local level could give a more detailed characterization ofthe gravitational field around massive bodies. Several attempts have been made tofind such a definition. One of the candidates is the Hawking mass. This thesispresents a method for calculating the spin coefficients used in the expression for theHawking mass, and gives a closed-form expression for the Hawking mass of ellipsoidal2-surfaces in Minkowski spacetime. Furthermore, the Hawking mass is shown to havethe correct limits, both in Minkowski and Schwarzschild, along particular foliationsof leaves approaching a metric 2-sphere. Numerical results for Schwarzschild are alsopresented.</p>

<p>In this thesis we calculate the Hawking mass numerically for surfaces in Kerr spacetime. The Hawking mass is a useful tool for proving the Penrose inequality and the result does not contradict the inequality. It also does not contradict the assumption that the Hawking mass should be monotonic for surfaces in Kerr spacetime. The Hawking mass is quasi-local and defined by the spin coefficents of Newman and Penrose, so first we give a discussion about quasi-local quantities and then a short description of the Newman-Penrose formalism.</p>

In this thesis we calculate the Hawking mass numerically for surfaces in Kerr spacetime. The Hawking mass is a useful tool for proving the Penrose inequality and the result does not contradict the inequality. It also does not contradict the assumption that the Hawking mass should be monotonic for surfaces in Kerr spacetime. The Hawking mass is quasi-local and defined by the spin coefficents of Newman and Penrose, so first we give a discussion about quasi-local quantities and then a short description of the Newman-Penrose formalism.