Momentum and velocity-dependent spacetime geometries: Traces of quantum gravity, fields in media and the gravitational field of kinetic gases

动量和速度相关的时空几何：量子引力的痕迹、介质中的场和运动气体的引力场

• 批准号: 420243324
• 负责人: Dr. Christian Pfeifer
• 金额: --
• 依托单位: Zentrum für angewandte Raumfahrttechnologie und Mikrogravitation (ZARM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/420243324?language=en
• 关键词: Momentum; velocity; dependent; spacetime; geometries

Despite all of its successes, general relativity cannot be the final answer to our understanding of gravity. On the observational side, its predictions are not consistent with the accelerated expansion of the universe and the rotation curves of galaxies. These led to the conclusion that the universe is filled with dark energy and dark matter, and only a small part is made out of the constituents of the standard model of particle physics. On the theoretical side, general relativity can still not be extended to a quantum theory of gravity in a self consistent way and moreover, it predicts singularities. Due to the absence of a fundamental theory of quantum gravity, I will employ momentum-dependent spacetime geometry as an effective model, which realises the following intuitive picture: Elementary particles, such as photons and neutrinos, probe the structure of spacetime, i.e. gravity, at scales inversely proportional to their energy. Thus, higher energetic particles interact more strongly with the quantum nature of gravity than lower energetic ones. A fundamental theory of quantum gravity should describe this effect in terms of the scattering matrices between the probe particles and gravitons. The aim is, on the one hand, to predict qualitatively and quantitatively observable effects, like energy-dependent (1) time of arrivals of photons, (2) black hole shadows, (3) gravitational lensing images as well as (4) products of particle collisions near black holes, and to identify them in data taken from telescopes like HESS, Veritas, MAGIC or the EHT. On the other hand, the mathematical relation between momentum-dependent spacetime geometry and curved non-commutative spacetimes will be investigated and extensions of the Einstein equations, which determine the momentum-dependent spacetime geometry, will be derived. An additional application of momentum-dependent spacetime geometry is the effective description of classical and quantum fields in media. A new approach to understand dark energy and dark matter is to consider physical systems in the universe which are usually modelled as fluids (the universe as a whole, ordinary and neutron stars, accretion discs) as kinetic gases. The advantage of this viewpoint is that the gravitational field of the gas can be described by a velocity-dependent Finsler spacetime geometry, which includes the contribution of the kinetic energy and the velocity distribution of the gas particles. Usually, in the Einstein-Vlasov equations, only the average over the velocity distribution of the gas particles is taken into account. This procedure enables us to construct a cosmological model which incorporates that the constituents of the cosmological fluid/gas have a velocity distribution, they move relatively to each and only propagate in the cosmological time direction on average. This may be the source of dark matter.

尽管取得了所有成功，但一般相对论并不是我们对重力理解的最终答案。在观察侧，其预测与宇宙的加速膨胀和星系的旋转曲线不一致。这些得出的结论是，宇宙充满了暗能量和深色物质，并且只有一小部分是由标准粒子物理模型的组成部分构成的。从理论方面来说，一般相对论仍然不能以自我一致的方式扩展到重力理论，并且可以预测奇点。由于缺乏量子重力的基本理论，我将使用动量依赖的时空几何形状作为有效模型，它实现了以下直觉的图像：诸如光子和中微子等基本粒子，探测时空的结构，即重力，即在与其能量成比例成分的尺度上。因此，较高的能量颗粒与重力的量子性质相比，比较低的能量性质更强烈。量子重力的基本理论应用探针颗粒和重力群之间的散射矩阵来描述这种效果。一方面，目的是在定性和定量上可观察到的效果，例如能量依赖性（1）光子到达的时间，（（2）黑洞阴影，（3）引力镜头图像以及（4）黑洞附近粒子碰撞的产物（4）在黑洞附近的粒子碰撞产物，以及从远程图中识别出诸如hess，Veritas，veritas，veritas，veritas，veritas，veritas，veritas，veritas，veritas，veritas，veritas，veritas，veritas or eht or eht or eht or e eht or eht of eht of the of the。另一方面，将研究将研究动量依赖的时空几何形状和弯曲的非交通空间之间的数学关系，并将得出爱因斯坦方程的扩展，这些方程将得出动量依赖性的时空几何形状。动量依赖性时空几何形状的附加应用是对介质中经典和量子场的有效描述。一种理解暗能量和深色物质的新方法是将通常以流体（整体，普通和中子星，增生盘）为动力的宇宙中的物理系统视为动力气体。这种观点的优点是，气体的重力场可以通过速度依赖性的鳍时空几何形状来描述，其中包括动能的贡献和气体颗粒的速度分布。通常，在爱因斯坦 - 维拉索夫方程中，仅考虑气体颗粒速度分布的平均值。该过程使我们能够构建一个宇宙学模型，该模型结合了宇宙流体/气体的成分具有速度分布，它们相对与每个速度相对移动，并且仅在宇宙学时间方向上传播。这可能是暗物质的来源。