Triply special relativity from six dimensions
S. Mignemi
我们表明，双狭义相对论的推广到一个弯曲的德西特背景，可以得到从一个六维时空上的位置和动量坐标的二次约束。
We show that the generalization of Doubly Special Relativity to a curved de Sitter background can be obtained starting from a six-dimensional spacetime on which quadratic constraints on position and momentum coordinates are imposed.
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Numerical relativity with characteristic evolution, using six angular patches
数值相对论的特征方法是演化引力系统的一个有用工具。在过去，这已经使用两个立体角坐标片来实现。在其他应用中，六块角坐标系已被证明是有效的。在这里，我们调查使用一个六补丁系统的特征数值相对论，通过比较现有的两个补丁实现（使用二阶有限差分贯穿）与一个新的六补丁实现（使用二阶或四阶有限差分的角度导数）。我们比较这些不同的代码通过监测爱因斯坦约束方程，数值独立的进化评估。我们发现，相比（二阶）两个补丁代码在同等分辨率，二阶六补丁代码的错误是小的约2倍，和四阶六补丁代码的错误是小的近50倍。
It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.
A Class of Collisions of Plane Impulsive Light--Like Signals in General Relativity
我们提出了一个系统的研究碰撞的均匀，平面-正面，脉冲光-类信号不相互作用后，头部碰撞。对于两个这样的信号的正面碰撞，涉及六个实参数，每个输入信号三个。我们发现这六个参数满足两个必要条件，使碰撞后的信号不相互作用。当这些必要条件成立时，我们就一般地解决了碰撞问题。碰撞后，两个信号在彼此信号前沿的外尔曲率奇点处彼此聚焦。我们的解族包含一些已知的碰撞解作为特例。
In this short review we present some recently obtained traversable wormhole models in the framework of general relativity (GR) in four and six dimensions that somehow widen our common ideas on wormhole existence and properties. These are, first, rotating cylindrical wormholes, asymptotically flat in the radial direction and existing without exotic matter. The topological censorship theorems are not violated due to lack of asymptotic flatness in all spatial directions. Second, these are cosmological wormholes constructed on the basis of the Lemaitre-Tolman-Bondi solution. They connect two copie…
General Relativity can be reformulated as a diffeomorphism invariant gauge theory of the Lorentz group, with Lagrangian of the type $f(F\wedge F)$, where $F$ is the curvature 2-form of the spin connection. A theory from this class with a generic $f$ is known to propagate eight degrees of freedom: a massless graviton, a massive graviton and a scalar. General Relativity in this formalism avoids extra degrees of freedom because the function $f$ is special and leads to the appearance of six extra primary constraints on the phase space variables. Our main new result is that there are other theories…
The Snyder-de Sitter model is an extension of the Snyder model to a de Sitter background. It is called triply special relativity (TSR) because it is based on three fundamental parameters: speed of light, Planck mass, and the cosmological constant. In this paper, we study the three dimensional DKP oscillator for spin zero and one in the framework of Snyder-de Sitter algebra in momentum space. By using the technique of vector spherical harmonics the energy spectrum and the corresponding eigenfunctions are obtained for both cases.
The canonical tensor model (CTM) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the ADM formalism of general relativity, and is studied as a discretized model for quantum gravity. In this paper, we analyze the classical equation of motion (EOM) of CTM in a formal continuum limit through a derivative expansion of the tensor up to the forth order, and show that it is the same as the EOM of a coupled system of gravity and a scalar field derived from the Hamilton-Jacobi equation wi…
Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations
我们认为非手性，充分洛伦兹集团为基础的普列班斯基制定的广义相对论在其版本中，利用拉格朗日乘子字段Φ与“内部”指数。这个版本的理论的哈密顿分析原来是简单的比以前考虑在文献中的版本与披进行时空指数。然后，我们扩展到更一般的一类理论，其行动包含标量不变量从φ构建的哈密顿分析。这些理论最近在引力与其他力统一的背景下被考虑。我们表明，这些更一般的理论有六个额外的传播自由度相比，广义相对论，一些尚未得到赞赏的文献治疗他们没有太大的不同GR。
The nonlinear behavior of higher dimensional black hole spacetimes is of interest in several contexts, ranging from an understanding of cosmic censorship to black hole production in high-energy collisions. However, nonlinear numerical evolutions of higher dimensional black hole spacetimes are tremendously complex, involving different diagnostic tools and "dimensional reduction methods". In this work we compare two different successful codes to evolve Einstein's equations in higher dimensions, and show that the results of such different procedures agree to numerical precision, when applied to t…
Six ways to quantize (2+1)-dimensional gravity
我们还不知道如何在3+1维中解释引力，但在更低的维度中，我们面临着相反的问题：许多最初为（3+1）维引力开发的方法可以在2+1维中成功实现，但由此产生的量子理论并不都是等价的。在这次演讲中，我讨论了六种这样的方法-减少相空间ADM量子化，陈-西蒙斯/连接表示，协变正则量子化，循环表示，惠勒-德维特方程，晶格方法-对于空间拓扑结构是环面的时空的简单情况。对由此产生的量子理论进行比较，可以为理解任何维数下量子引力的概念问题提供一些有用的见解。(Talk 1993年5月在安大略省滑铁卢举行的关于广义相对论和相对论天体物理学的第五届加拿大会议上发表）
We give a possible splitting method to a Hamiltonian for the description of charged particles moving around the Reissner-Nordstrom-(anti)-de Sitter black hole with an external magnetic field. This Hamiltonian can be separated into six analytical solvable pieces, whose solutions are explicit functions of proper time. In this case, second- and fourth-order explicit symplectic integrators are easily available. They exhibit excellent long-term behavior in maintaining the boundness of Hamiltonian errors regardless of ordered or chaotic orbits if appropriate step-sizes are chosen. Under some circums…
We first derive the Hamiltonian for Lovelock gravity and find that it takes the same form as in general relativity when written in terms of the Misner-Sharp mass function. We then minimally couple the action to matter fields to find Hamilton's equations of motion. These are gauge fixed to be in the Painlevé-Gullstrand co-ordinates and are well suited to numerical studies of black hole formation. We then use these equations of motion for the massless scalar field to study the formation of general relativistic black holes in four to eight dimensions and Einstein-Gauss-Bonnet black holes in five …
Beyond general relativity: gravitational waves in non-minimally coupled theories
研究物质与曲率张量非最小耦合对引力波的影响，通过模型无关参数化探索，扩展参数化纳入早期宇宙效应，应用于三个模型以同时研究暗物质和广义相对论之外的物理。
In this work we show that Einstein gravity in four dimensions can be consistently obtained from the compactification of a generic higher curvature Lovelock theory in dimension $D=4+p$, being $p\geq1$. The compactification is performed on a direct product space $\mathcal{M}_D=\mathcal{M}_4\times\mathcal{K}^p$, where $\mathcal{K}^p$ is a Euclidean internal manifold of constant curvature. The process is carried out in such a way that no fine tuning between the coupling constants is needed. The compactification requires to dress the internal manifold with the flux of suitable $p$-forms whose field…
We first consider the Klein-Gordon equation in the 6-dimensional space $M_{2,4}$ with signature $+ - - - - +$ and show how it reduces to the Stueckelberg equation in the 4-dimensional spacetime $M_{1,3}$. A field that satisfies the Stueckelberg equation depends not only on the four spacetime coordinates $x^μ$, but also on an extra parameter $τ$, the so called evolution time. In our setup, $τ$ comes from the extra two dimensions. We point out that the space $M_{2,4}$ can be identified with a subspace of the 16-dimensional Clifford space, a manifold whose tangent space at any point is the Cliffo…
Effective field theories describing gravity coupled to matter are investigated, allowing for operators of arbitrary mass dimension. Terms violating local Lorentz and diffeomorphism invariance while preserving internal gauge symmetries are included. The theoretical framework for violations of local Lorentz and diffeomorphism invariance and associated conceptual issues are discussed, including transformations in curved and approximately flat spacetimes, the treatment of various types of backgrounds, the implications of symmetry breaking, and the no-go constraints for explicit violation in Rieman…
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