This thesis is a study of Lorentz invariance in two different contexts.

In the absence of gravitation and spacetime curvature, the isometry group of Minkowski spacetime is the inhomogeneous Lorentz group. Quantum Information Science is analyzed in the context of quantum field theory which is fully compatible with the principles of quantum mechanics and special relativity. We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin-1/2 particles, Einstein-Podolsky-Rosen-Bell entangled states and their behavior under the Lorentz group are analyzed in the context of quantum field theory. Group theoretical considerations suggest a convenient definition of the Bell states which is slightly different from the conventional assignment. The behavior of Bell states under arbitrary Lorentz transformations can then be described succinctly.

In curved spacetimes, Lorentz symmetry is manifested as the local gauge symmetry of the freedom to choose at each spacetime point the local Lorentz frame of the tangent space which is isomorphic to Minkowski spacetime. The invariance of the curved spacetime metric under local Lorentz transformations of the vierbein one-forms is made use of to construct black hole metrics which are regular at the horizon(s). An obstruction to the implementation of spatially flat Painlevé-Gullstrand(PG) slicings is demonstrated, and explicitly discussed for Reissner-Nordström and Schwarzschild-anti-deSitter spacetimes. Generalizations of PG slicings which are not spatially flat but which remain regular at the horizons are introduced. These metrics can be obtained from standard spherically symmetric metrics by physical Lorentz boosts. Generalized PG coordinates for stationary axisymmetric spacetimes are also explicitly constructed; and the results are applied to the Kerr-Newman family of rotating black hole solutions. Our generalizations are free of coordinate singularities at the horizon(s).

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