Brown's formulation of dynamical perfect fluids in Minkowski space-time is extended to ADM tetrad gravity in globally hyperbolic, asymptotically Minkowskian space-times. For the dust we get the Hamiltonian description in closed form in the York canonical basis, where we can separate the inertial gauge variables of the gravitational field in the non-Euclidean 3-spaces of global non-inertial frames from the physical tidal ones. After writing the Hamilton equations of the dust, we identify the sector of irrotational motions and the gauge fixings forcing the dust 3-spaces to coincide with the 3-spaces of the non-inertial frame. The role of the inertial gauge variable York time (the remnant of the clock synchronization gauge freedom) is emphasized. Finally the Hamiltonian Post-Minkowskian linearization is studied. The future application of this formalism will be the study of cosmological back-reaction (as an alternative to dark energy) in the York canonical basis.
Hamiltonian Expression of Curvature Tensors in the York Canonical Basis: II) The Weyl Tensor, Weyl Scalars, the Weyl Eigenvalues and the Problem of the Observables of the Gravitational Field
The Einstein-Maxwell-Particle System in the York Canonical Basis of ADM Tetrad Gravity: III) The Post-Minkowskian N-Body Problem, its Post-Newtonian Limit in Non-Harmonic 3-Orthogonal Gauges and Dark Matter as an Inertial Effect
The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field
A note on classification of proper teleparallel conformal symmetries of spherically symmetric static space-times in the teleparallel theory of gravitation using diagonal tetrads
Hamiltonian linearization of the rest-frame instant form of tetrad gravity in a completely fixed 3-orthogonal gauge: a radiation gauge for background-independent gravitational waves in a post-Minkowskian Einstein spacetime
在研究了在空间无穷远处全局双曲、渐近平坦的时空上正则四元引力的规范变换的哈密顿群之后，我们发现柯西超曲面$Σ_τ$通过规范变换与之相连，而柯西超曲面$Σ_τ$与$R^3, we find the dependence of the cotriads on $ <$_τ $ and of their momenta on the six parameters associated with rotations and space diffeomorphisms. The choice of 3-coordinates on $ <$_τ $ is equivalent to the parametrization of the cotriads with the last three degrees of freedom individuating the 3-geometries. The Shanmugadhasan canonical transformation, corresponding to the choice of 3-orthogonal coordinates on $ <$_τ $ and adapted to 13 of the 14 first class constraints, and the interpretation of the gauge t…
Initial value problem in General Relativity is often solved numerically; with only a few exceptions one of which is the "model" solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between $[0, 0.592)$. …
The Nontriviality of Trivial General Covariance: How Electrons Restrict 'Time' Coordinates, Spinors (Almost) Fit into Tensor Calculus, and 7/16 of a Tetrad Is Surplus Structure
On more general Gibbons-Hawking-York boundary terms for f(R) gravity
University of Insubria（因苏布里亚大学）；INFN section Milan（意大利国家核物理研究所米兰分部）；Como Lake Centre for AstroPhysics (CLAP)（科莫湖天体物理中心）；Vatican Observatory（梵蒂冈天文台）；INAF/OAS Bologna（意大利国家天体物理研究所博洛尼亚天文台）；INFN, Sezione di Bologna（意大利国家核物理研究所博洛尼分部）；INFN, Laboratori Nazionali di Frascati（意大利国家核物理研究所弗拉斯卡蒂实验室）
Hamiltonian ADM Gravity in Non-Harmonic Gauges with Well Defined Non-Euclidean 3-Spaces: How Much Darkness can be Explained as a Relativistic Inertial Effect?
Absolute Objects and Counterexamples: Jones-Geroch Dust, Torretti Constant Curvature, Tetrad-Spinor, and Scalar Density
James L.安德森分析了爱因斯坦引力理论的新颖之处，因为它缺乏“绝对对象”。迈克尔·弗里德曼的相关工作受到罗杰·琼斯和罗伯特·格罗赫的批评，因为他们难以置信地承认爱因斯坦理论中宇宙模型中尘埃的类时4速场是绝对的。使用罗森-索金拉格朗日乘数技巧，我完成安娜梅登斯的论点，这个问题并没有解决，禁止变化的绝对对象的行动原则。回顾安德森的“无关”变量的proscription，我推广到本地无关的变量，不工作，在某些模型的某些地方。这一举动证明了弗里德曼的直觉，并消除了琼斯-格罗赫反例：一些有灰尘的引力模型的某些区域是无尘的，因此自然缺乏类时4速度，因此与（1，0，0，0）的复纯等价被破坏了。Torretti的例子涉及常曲率空间被证明有一个绝对对象安德森的分析，即，共形空间度量密度。以前被忽视的威胁，一个绝对的对象从正交四元耦合旋量重力似乎可以解决消除不相关的领域。然而，根据安德森的定义，GTR本身有一个绝对的对象（正如罗伯特·格罗赫最近观察到的那样）：变量到共形度规密度和标量密度的变化表明后者是绝对的。
The Einstein-Maxwell-Particle System: II) The Weak Field Approximation in the Non-Harmonic 3-Orthogonal Gauges and Hamiltonian Post-Minkowskian Gravity: the N-Body Problem and Gravitational Waves with Asymptotic Background
The Hamiltonian formulation of the gravitational sector of the Standard-Model Extension (SME) with nondynamical fields $u$ and $s^{μν}$ is studied. We provide the relevant Hamiltonians that describe the constrained phase space and the dynamics of the induced metric on the ADM hypersurface. The generalization of the Gibbons-Hawking-York boundary term has been crucial to preventing second time-derivatives of the metric tensor in the Hamiltonians. By extracting the dynamics and constraints from the Einstein equations we have proved the equivalence between the Lagrangian and Hamiltonian formulatio…
SL(2N,C) Yang-Mills Theories: Direct Internal Forces and Emerging Gravity
Institute of Theoretical Physics, Ilia State University（伊利娅国立大学理论物理研究所）；Andronikashvili Institute of Physics, Tbilisi State University（第比利斯国立大学安德罗尼卡什维利物理研究所）
