论文标题
几何形状的现象学后果
Phenomenological consequences of a geometry in the cotangent bundle
论文作者
论文摘要
可以通过最大对称的动量空间在几何框架内理解变形的相对论运动学。但是，在考虑这种方法时，通常一种在平坦的时空和弯曲的动量空间中起作用。在本文中，我们将讨论一个可能的概括，以考虑曲线和一些可能的可观察效应。我们将首先解释如何在cotangent束中构造度量，以便在动量空间中具有弯曲的时空，并具有非平凡的几何形状以及与以变形Casimir为特征的相位空间中的作用的关系。然后，我们将在该提案中研究两个不同的时空几何形状。在Friedmann-Robertson-Walker宇宙中，由于指标在Cotangent Bundle中指标的动量依赖性，我们将看到大地测量学（红移，光度距离和地球膨胀）的修改。另外，我们将看到，当所考虑的时空是一个施瓦茨柴尔德黑洞时，一个人仍然具有不同能量的颗粒的共同范围，与洛伦兹的违规情况不同。然而，计算为剥离无效测量学的表面重力取决于能量。
A deformed relativistic kinematics can be understood within a geometrical framework through a maximally symmetric momentum space. However, when considering this kind of approach, usually one works in a flat spacetime and in a curved momentum space. In this paper, we will discuss a possible generalization to take into account both curvatures and some possible observable effects. We will first explain how to construct a metric in the cotangent bundle in order to have a curved spacetime with a nontrivial geometry in momentum space and the relationship with an action in phase space characterized by a deformed Casimir. Then, we will study within this proposal two different space-time geometries. In the Friedmann-Robertson-Walker universe, we will see the modifications in the geodesics (redshift, luminosity distance and geodesic expansion) due to a momentum dependence of the metric in the cotangent bundle. Also, we will see that when the spacetime considered is a Schwarzschild black hole, one still has a common horizon for particles with different energies, differently from a Lorentz invariance violation case. However, the surface gravity computed as the peeling off of null geodesics is energy dependent.
