Curved spacetimes with local κ -Poincaré dispersion relation
Curved spacetimes with local κ -Poincaré dispersion relation
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具有局部 κ -庞加莱色散关系的弯曲时空
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
C. Pfeifer
中科院分区：
文献类型：
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作者：
Leonardo Barcaroli;Lukas K. Brunkhorst;Giulia Gubitosi;N. Loret;C. Pfeifer
我们使用之前开发的相空间上的哈密顿函数的色散关系识别来局部实现通用弯曲时空每个点动量空间中的 $ensuremath{kappa}$-Poincar'e 色散关系。我们使用这种通用构造来构建与球对称性和普朗克尺度变形兼容的最通用的哈密顿量，以便在局部框架中再现 $ensuremath{kappa}$-Poincar'e 色散关系。专门研究普朗克尺度变形的史瓦西几何，我们发现黑洞周围的光子球体变成了一个厚壳，因为不同能量的光子将在不同高度的圆形轨道上绕黑洞运行。我们还计算了静止时不同观察者之间光子的红移，发现只有当检测到光子的观察者具有不同的质量时，才会对通常的红移进行普朗克尺度校正。
We use our previously developed identification of dispersion relations with Hamilton functions on phase space to locally implement the $ensuremath{kappa}$-Poincar'e dispersion relation in the momentum spaces at each point of a generic curved spacetime. We use this general construction to build the most general Hamiltonian compatible with spherical symmetry and the Plank-scale-deformed one such that in the local frame it reproduces the $ensuremath{kappa}$-Poincar'e dispersion relation. Specializing to Planck-scale-deformed Schwarzschild geometry, we find that the photon sphere around a black hole becomes a thick shell since photons of different energy will orbit the black hole on circular orbits at different altitudes. We also compute the redshift of a photon between different observers at rest, finding that there is a Planck-scale correction to the usual redshift only if the observers detecting the photon have different masses.