On the geometry of Lorentz spaces as a limit space
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In this paper, we prove that there is no branch point in the Lorentz space (M, d) which is the limit space of a sequence {(Mα, dα)} of compact globally hyperbolic interpolating spacetimes with C± -properties and curvature bounded below. Using this, we also obtain that every max- imal timelike geodesic in the limit space (M, d) can be expressed as the limit curve of a sequence of maximal timelike geodesics in {(Mα, dα)}. Finally, we show that the limit space (M, d) satisfies a timelike trian- gle comparison property which is analogous to the case of Alexandrov curvature bounds in length spaces.
Abstract
In this paper, we prove that there is no branch point in the Lorentz space (M, d) which is the limit space of a sequence {(Mα, dα)} of compact globally hyperbolic interpolating spacetimes with C± -properties and curvature bounded below. Using this, we also obtain that every max- imal timelike geodesic in the limit space (M, d) can be expressed as the limit curve of a sequence of maximal timelike geodesics in {(Mα, dα)}. Finally, we show that the limit space (M, d) satisfies a timelike trian- gle comparison property which is analogous to the case of Alexandrov curvature bounds in length spaces.
참고문헌 (9)
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