Olivier Minazzoli, Bertrand Chauvineau
We present a derivation of 2PN/RM metric field equations from the Einstein field equation in General Relativity. We use the exponential parametrization and the $c^{-3}$ isotropic spatial coordinates such as in IAU2000 recommendations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
This work derives the elements of classical Einstein Cartan theory (EC) from classical general relativity (GR) in two ways. (I) Derive discrete versions of torsion (translational holonomy) and the spin torsion field equation of EC from one Kerr solution in GR. (II) Derive the field equations of EC as the continuum limit of a distribution of many Kerr masses in classical GR. The convergence computations employ epsilon delta arguments, and are not as rigorous as convergence in Sobolev norm. Inequality constraints needed for convergence restrict the limits from continuing to an infinitesimal leng…
A differential bulk-surface relation of the lagrangian of General Relativity has been derived by Padmanabhan. This has relevance to gravitational information and degrees of freedom. An alternate derivation is given based on the differential form gauge theory formulation of gravity due to Gockeler and Schucker. Also an entropy functional of Padmanabhan and Paranjape can be rewritten as the Gockeler and Schucker lagrangian.
A Derivation of Three-Dimensional Inertial Transformations
推导的惯性系之间的转换由Mandarin和Sexl被推广到三维任意方向的速度。假定长度收缩和时间膨胀具有相对论性值，得到一组运动学上等价于狭义相对论的变换。“时钟假说”允许推导扩展到加速系统。一个理论的惯性变换保持绝对的一致性被证明是唯一一个逻辑上符合加速运动。讨论了这些变换的代数性质。关键词：狭义相对论、同步、单向光速、以太、时钟假说。
Starting from Plebanski's action for general relativity with cosmological constant, we show that by integrating out all the auxiliary fields Krasnov's action immediately emerges. We also perform the Hamiltonian analysis of the latter and show that the constraints are those of the Ashtekar formalism.
A Simple Derivation of the Einstein-Maxwell Field Equations from the 2nd Ordinary Exterior Differential of a Precursor to the Soldering Form
对于具有一般线性联络的n维可微流形，特别是在5维广义相对论中，给出了Einstein-Maxwell场方程由soldering形式前体的二阶常外微分的简单推导.
The objective of this second part of the work is to present heuristic derivations of the three classical tests of general relativity. These derivations are based on the Einstein equivalence principle and use Newtonian physics as a theoretical framework. The results obtained are close to Einstein's original predictions. Historical and anecdotal aspects of the subject are also discussed.
The Fully Covariant Energy Momentum Stress Tensor For Gravity and the Einstein Equation in General Relativity
我们给出了一个完全协变的能量动量应力张量的引力场，这是很容易的物理动机，并导致一个非常普遍的推导爱因斯坦方程的引力。除了对称性之外，我们不需要假设表面物质场的能量、动量、应力张量的任何性质。我们给出了一个物理动机，这种选择使用激光的压力。作为我们推导的结果，当时空是4维时，总源物质和场的能量动量应力张量必须是无发散的。此外，如果假设总的源物质场是无发散的，那么要么时空是4维的，要么时空具有常数标量曲率。
Lagrangian Brane Dynamics in General Relativity and Einstein-Gauss-Bonnet Gravity
本文给出了广义相对论和Einstein-Gauss-Bonnet引力中膜作用量和膜动力学的一种新的、简明的推导方法。我们提出了一个统一的处理，适用于类时表面层和类空过渡层，并包括考虑更困难的类光的情况。
Temperature of a spinning black hole via a simple derivation
本文通过经典广义相对论和热力学推导克尔黑洞温度，旨在教学用途，强调小黑洞蒸发及暗物质可能来源
Using Nottale's theory of scale relativity, we derive a generalized Schrödinger equation applying to dark matter halos. This equation involves a logarithmic nonlinearity associated with an effective temperature and a source of dissipation. Fundamentally, this wave equation arises from the nondifferentiability of the trajectories of the dark matter particles whose origin may be due to ordinary quantum mechanics, classical ergodic (or almost ergodic) chaos, or to the fractal nature of spacetime at the cosmic scale. The generalized Schrödinger equation involves a coefficient ${\cal D}$, possibly …
We prove that the field equations of general relativity and other metric theories can be derived from the conservation of energy-momentum without using the assumption of least action principle. We show a new procedure for perturbative derivation of symmetric pseudo-energy momentum for the gravity field.
In spite of alleged impossibility proofs, "simple derivations" of the Schwarzschild metric, based solely on Einstein's equivalence principle and Newton's free fall velocity formula, are presented.
Rotating metrics admitting non-perfect fluids in General Relativity
利用球对称度量中的Newman-Janis算法，给出了一类场方程的嵌入旋转解.这些解决方案允许非完美流体
A Systematic Derivation of the Riemannian Barrett-Crane Intertwiner
通过求解对应于四面体的量子Barrett-Crane约束（非简并条件除外），系统地导出了黎曼广义相对论中的Barrett-Crane纠缠子. Reisenberger指出Barrett-Crane缠绕机是唯一的解决方案。系统的推导可以被认为是唯一性的另一种证明。推导中的新元素是交叉简单性约束的严格强加。
Metric Relativity and the Dynamical Bridge: highlights of Riemannian geometry in physics
本文探讨了度量相对性与动态桥梁在描述经典与量子配置相互作用中的最新发展。
Differential Form Approach for Stationary Axisymmetric Maxwell Fields in General Relativity
将稳态轴对称电磁场转化为各向异性流体，导出了广义相对论中稳态轴对称电磁场的一个表达式。几个简化的形式主义进行，以分析不同的功能的领域，如推导电磁源的麦克斯韦场的形式，薄层，建设新的解决方案，和生成技术。
We investigate the consequences of the pseudo-complex General Relativity within a pseudo-complexified Roberston-Walker metric. A contribution to the energy-momentum tensor arises, which corresponds to a dark energy and may change with the radius of the universe, i.e., time. Only when the Hubble function $H$ does not change in time, the solution is consistent with a constant $Λ$.
Canonical Analysis of General Relativity Formulated with the New Metric f^{ab}=(-g)^αg^{ab}
本文研究以新度规 f^{ab}=(-g)^αg^{ab} 表述的广义相对论的典范形式，求得相应哈密顿量，并证明其约束结构与标准表述一致。
Does General Relativity Require a Metric
引力场和时空度规之间的联系是爱因斯坦发展广义相对论的一个基本要素，并使他发现了引力场/度规的场方程。我在这里要论证的是，度规实际上是这个理论的一个不必要的要素，可以完全抛弃。它在理论中的唯一功能是描述由理想时钟和棒进行的时空测量。然而，模型钟和测量棒的行为可以直接从广义相对论的场方程使用Einstein-Infeld-Hoffmann（EIH）近似程序导出。因此，人们不需要引入这些理想的钟和杆，因此不需要公制。
We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra ${\cal A}$. Such a derivation, introduced by Bresar in 1991, is given by a linear mapping $u: {\cal A} \rightarrow {\cal A}$ such that there exists a usual derivation $d$ of ${\cal A}$ satisfying the generalized Leibniz rule $u(a b) = u(a) b + a \, d(b)$ for all $a,b \in \cal A$. The generalized geometry "is tested" in the case of the algebra of smooth functions on a manifold. We then apply this machinery to study generalized general relativity. We define the Einstein-Hilbert action …
Derivation of the Tully-Fisher Law from General Relativity Theory: Doubts about the Existence of Halo Dark Matter
观测表明，盘状星系的恒星绕星系核心的圆周速度的四次方与光度L成正比。这就是所谓的塔利-费舍尔定律。由于L与星系的质量M成正比，因此圆速度的四次方与M成正比。然而，牛顿力学告诉我们，圆周速度的平方与M成正比。为了纠正这一巨大的差异，天文学家假设晕暗物质的存在。在本文中，我们表明，广义相对论理论产生一项的塔利-费舍尔形式。这使人们对星系晕暗物质的必要性和存在性产生了怀疑。
Energy-Momentum Problem of Bell-Szekeres Metric in General Relativity and Teleparallel Gravity
本文研究了两种理论中的能量-动量问题，广义相对论和平行引力。我们使用Einstein，Landau-Lifshitz，Bergmann-Thomson和Möller的公式计算了这两种理论中Bell-Szekeres度规的能量动量分布。结果表明，在广义相对论和遥平行理论中，这些规定给出了相同的能量动量密度分量。穆勒的处方在两个理论中都产生了恒定的能量。
A consistent variational derivation of the Majorana 4-spinor field equations coupled to Einstein's theory of gravitation is given. The equivalence of the first and the second order variational field equations is explicitly demonstrated. The Lagrange multiplier 2-forms we use turn out to be precisely the Belinfante-Rosenfeld 2-forms that are needed to symmetrize the canonical energy-momentum tensor of the Majorana spinor.
The Area Metric Reality Constraint in Classical General Relativity
一个经典的基础上的现实条件下的自旋泡沫（Barrett-Crane模型）的想法。我提取经典的实广义相对论（所有签名）从复杂的广义相对论通过施加面积度量现实约束;面积度量是真实的当且仅当一个非退化的度量是真实的或虚的。首先，我回顾普列班斯基理论的复广义相对论开始从一个复杂的矢量作用。然后通过增加一个拉格朗日乘子来引入面积度量实在性条件，从而得到经典的实广义相对论。我研究两种类型的行动：复杂的和真实的。复作用量理论场方程的所有非平凡解都符合实广义相对论。具有实作用量的理论的场方程的一半非平凡解对应于实广义相对论。在Barrett-Crane理论的背景下，面积度量现实约束的离散化进行了讨论。在Barrett-Crane理论的上下文中，面积度量实性条件等价于与四个单形的三角形相关联的双向量的标量积是实的条件。通过引入面积度量实在条件，简要讨论了退化情形的Plebanski形式和Palatini形式.
The notion that the metric field in general relativity can be understood as a property of space-time rests on a feature of the theory sometimes called universal coupling -- the claim that rods and clocks "measure" the metric in a way that is independent of their constitution. It is pointed out that this feature is not strictly a consequence of the central dynamical tenets of the theory, and argued that the metric field would better be regarded as a (possibly emergent) field in space-time, rather than as the very fabric of space-time itself.
We perform a short comparison between the local and linear constitutive tensor $χ^{λνσκ}$ in four-dimensional electrodynamics (Sec.2), the elasticity tensor $c^{ijkl}$ in three-dimensional elasticity theory (Sec.3), and the DeWitt metric $G^{abcd}$ in general relativity, with ${a,b,\dots=1,2,3}$ (Sec.4). We find that the DeWitt metric has only six independent components.
Approximate Equations of Motion for Compact Spinning Bodies in General Relativity
本文用Einstein、Infeld、Hoffmann曲面积分法导出了陀螺仪在地球引力场中运动的近似方程。该方法不需要知道与陀螺仪相关的能量-动量-应力张量，并且仅使用其外部场来表征。所得的运动方程不同于以前的推导。
A brief introduction to Cadabra: a tool for tensor computations in General Relativity
Cadabra是一个强大的计算机程序，用于处理张量方程。它被设计用于高能物理，但其丰富的结构和易用性使其本身很好地适用于广义相对论所需的例行计算。在这里，我们将提出一系列简单的例子，显示如何Cadabra可以使用，包括验证列维-奇维塔连接是一个度量连接和诱导和环境曲率之间的高斯方程的推导。
Gravitational collapse of plasmas in General Relativity
本文利用广义相对论的3+1公式推导了等离子体物理与引力的协变关系，并讨论了洛伦兹力定律。然后，我们减少了系统的球对称的情况下，并表明，时空的所有区域可以表示在一个单一的坐标系，从而撤销需要的交界处的条件。我们进一步证明了坍缩区域外的区域自然地由非零坐标中的带电Vaidya时空描述。
We show how the Minkowskian space-time emerges from a topologically homogeneous causal network, presenting a simple analytical derivation of the Lorentz transformations, with metric as pure event-counting. The derivation holds generally for d=1 space dimension, however, it can be extended to d>1 for special causal networks.
General Relativity at an interface
在这项工作中，提出了一个简单的玩具模型，在空间和时间的体相之间的自由界面，来自广泛的热力学变量的Meinhold-Heerlein的平衡方程。在这种情况下，自由界面代表时空中的测地线，从而可以推导出引力场的爱因斯坦方程。平衡方程的效果进行检查，并推导出一个简单的表达式冷暗物质。最后讨论了该模型的理论意义。
An Elementary Derivation of the Five Dimensional Myers-Perry Metric
通过直接求解真空爱因斯坦场方程的初等方法，导出了五维Myers-Perry度规。这种方法是由Clotz首先提出的，它只涉及Ricci张量的四个分量，并且在度量矩阵取适当形式的情况下，只需要处理一些不含二阶导数项的方程。
We derive a new constraint algebra for a Hamiltonian formulation of the Teleparallel Equivalent of General Relativity treated as a theory of cotetrad fields on a spacetime. The algebra turns out to be closed.
Gravitation in the solar system and metric extensions of general relativity
尽管广义相对论与太阳系中的引力测试惊人地一致，但它在更大的尺度上受到了挑战。先驱者10/11号探测器在太阳系中进行的大规模测试未能证实预期的引力定律。我们在这里讨论广义相对论的扩展，它保留了它的几何性质，同时显示出调和先锋异常与其他重力测试的能力。进一步可检验的现象学后果也简要讨论。
General Relativity on Random Operators
我们提出了一个统一了广义相对论和量子力学数学结构的数学结构。它由紧支撑的复值函数${\mathcal A}$的非交换代数组成，卷积作为乘法，在广群$Γ$上，广群的基是时空$M$上的框架丛的总空间$E$。基于${\mathcal A}$的导子的微分几何适当地推广了时空的标准微分几何，并且代数${\mathcal A}$在希尔伯特空间的丛中表示时，定义了推广通常的量子力学的随机算子的冯诺依曼代数${\mathcal M}$。本文的主要结果是：存在一个空间${\mathcal M_0}$，它在${\mathcal M}$中稠密，与代数${\mathcal A}$同构.这种同构允许我们将所有微分几何结构，包括广义爱因斯坦方程，在${\mathcal A}$（及其衍生物）的帮助下转移到空间${\mathcal M_0}$。这样，我们得到了Hilbert空间丛上随机算子对广义相对论的推广。然而，这种推广不能扩展到整个${\mathcal M}$，这是主要的数学障碍，至少在这种方法中，完全统一引力理论与量子物理学。
The Field Nature of Time in General Relativity
本文致力于描述通过分解约束和构造等价的无约束系统得到的广义相对论的重参数化不变动力学。约束壳作用量揭示了广义相对论中几何时间的“场性质”。观测者的手表所测得的时间与场变量之一相吻合，但与重参数化非不变坐标演化参数不吻合。我们给出了这个问题的新的解决方法，如推导出广义相对论哈密顿方案中因果格林函数的路径积分表示。
This work refers to the new formula for the superpotential Uikl in conservation laws in general relativity satisfying the integral and differential conservation laws within the Schwarzschild metric. The new superpotential is composed of two terms. The first term is based on Mollers concept and its a function of the metric gik and its first derivative only. The second term is the antisymmetric tensor density of weight plus one and it consists of higher derivatives of the metric gik. Although the new superpotential consists of higher derivatives of the metric gik it might bring a new evaluation …
The origin of the spacetime metric: Bell's `Lorentzian pedagogy' and its significance in general relativity
本文的目的是评价J. S.贝尔在他的论文《如何教授狭义相对论》中，探讨了狭义相对论与爱因斯坦1905年至1952年思想的一致性。一些言论也在这方面外尔的哲学相对论和他1918年的规范理论。最后，有人认为，洛伦兹教学法-它强调运动学和动力学之间的重要联系-澄清杆和时钟在广义相对论的作用。
In this paper we show that it is possible to derive the Kerr solution in an alternative, intuitive way, based on physical reasoning and starting from an orthogonal metric ansatz having manifest ellipsoidal space-time symmetry (ellipsoidal symmetry). This is possible because both flat metric in oblate spheroidal (ellipsoidal) coordinates and Kerr metric in Boyer-Lindquist coordinates can be rewritten in such a form that the difference between the two is only in the time-time and radial-radial metric tensor components, just as is the case with Schwarzschild metric and flat metric in spherical co…
Cadabra is an open access program ideally suited to complex tensor commutations in General Relativity. Tensor expressions are written in LaTeX while an enhanced version of Python is used to control the computations. This tutorial assumes no prior knowledge of Cadabra. It consists of a series of examples covering a range of topics from basic syntax such as declarations, functions, program control, component computations, input and output through to complete computations including a derivation of two of the BSSN equations from the ADM equations. Numerous exercises are included along with complet…
Reference frames and rigid motions in relativity
一个参考系由参考空间、时间尺度和空间度量组成。这些对象在时空中诱导的几何结构的发展。一类空间度量的存在，是刚性的，有自由流动性，可以推导出作为一个轻微的变形的雷达度量，示出。
In this paper we study some features of the Reissner-Nordström metric both from an analytic and a visual point of view. We perform an accurate ray tracing and study of null geodesics in various situations. Among the issues we focus on are (i) the comparison with the Schwarzschild case, (ii) the naked singularity case, where, if the electric charge is not too large, some dark shell appears on images despite there is no horizon in the metric, and (iii) the wormhole crossing case, i.e., a visual exploration of the maximal analytic extension of the metric.
In this paper we study some features of the Kerr metric both from an analytic and a visual point of view by performing accurate raytracing in various situations. We focus on features that are unique to the maximal analytic extension of the Kerr metric as compared to that of the Schwarzschild or even the Reissner-Nordström one. A large number of new, yet underexplored phenomena appear, especially regarding the structure of bounded null geodesics and the aspect of the negative gravity regions whose visual characteristics are shown both from outside and inside it.
Relative velocity in special relativity and quantum field theory
本文通过显式洛伦兹不变量推导了相对速度，揭示了交叉截面定义中的任意性。
The gravitational time delay of light, also called the Shapiro time delay, is one of the four classical tests of Einstein's theory of general relativity. This article derives the Newtonian version of the Shapiro time delay from Einstein's principle of equivalence and the Newtonian description of gravity, in a manner that is accessible to undergraduate students and advanced high-school students. The derivation can be used as a pedagogical tool, similar to the way that simplified derivations of the gravitational deflection of light are used in teaching about general relativity without making use…
Universality of affine formulation in General Relativity theory
广义相对论的仿射变分原理，由我们中的一位（J.K.）于1978年提出，是一个很好的补救措施的非普遍性质的标准，度量制定，所产生的物质拉格朗日依赖于度量导数。仿射版本的理论治愈的标准缺点的度量版本，其中的领导（二阶）项的场方程取决于物质场和其因果结构违反光锥结构的度量。选择仿射联络（而不是度规联络）作为引力组态，大大简化了理论的正则结构，并且更适合于按照Ashtekar和Lewandowski的思路对其进行量子化（见http：//www.arxiv.org/gr-qc/0404018）。我们展示了如何仿射制定提供了一个简单的方法来处理边界积分在广义相对论理论。
Classical Oscilators in General Relativity
结果表明，在广义相对论中，某些静态度规能够模拟振荡运动。它们的形式取决于两个任意的实参数，这两个实参数决定了特定的振荡模式。结论是，这些指标可以用于新的几何模型的封闭，甚至开放的袋子。pac：04.02.- q和04.02.Jb
We use the Møller and Landau-Lifshitz energy-momentum definitions in General Relativity (GR) to evaluate the energy-momentum distribution of the phantom black hole space-time. The phantom black hole model was applied to the supermassive black hole at the Galactic Centre. We obtain that in both pseudotensorial prescriptions the energy distribution depends on the mass $M$ of the black hole, the phantom constant $p$ and the radial coordinate $r$. Further, all the calculated momenta are found to be zero. The limiting cases $r\rightarrow 0$, $r\rightarrow \infty $ and $r\rightarrow -\infty $ have a…
The tetrad method is used for an introduction of local Lorentz frames and a detailed analysis of local Lorentz transformations. A formulation of equations of motion in local Lorentz frames is based on the Pomeransky-Khriplovich gravitoelectromagnetic fields. These fields are calculated in the most important special cases and their local Lorentz transformations are determined. The local Lorentz transformations and the Pomeransky-Khriplovich gravitoelectromagnetic fields are applied for a rigorous derivation of a general equation for the Thomas effect in Riemannian spacetimes and for a considera…
We explain the necessity of application of semi-metric in general relativity. A detailed discussion on the energy-momentum conservation in the general relativity is presented using the mathematical tool of semi-metric. By means of the general covariant spacetime translation transformation, the most general covariant conservation law of energy-momentum is obtained, which is valid for any coordinates and overcomes the flaws of the expressions of Einstain, Landau and Moller.
We consider conceptual issues of deep learning (DL) for metric detectors using test particle geodesics in curved spacetimes. Advantages of DL metric detectors are emphasized from a view point of general coordinate transformations. Two given metrics (two spacetimes) are defined to be conneted by a DL isometry if their geodesic image data cannot be discriminated by any DL metric detector at any time. The fundamental question of when the DL isometry appears is extensively explored. If the two spacetimes connected by the DL isometry are in superposition of quantum gravity theory, the post-measurem…
We present a novel derivation of special relativity based on the information physics of events comprising a causal set. We postulate that events are fundamental, and that some events have the potential to receive information about other events, but not vice versa. This leads to the concept of a partially-ordered set of events, which is called a causal set. Quantification proceeds by selecting two chains of coordinated events, each of which represents an observer, and assigning a valuation to each chain. Events can be projected onto each chain by identifying the earliest event on the chain that…
We present an implementation of a ray tracing code in the Schwarzschild metric. We aim at building a numerical code with a correct implementation of both special (aberration, amplification, Doppler) and general (deflection of light, lensing, gravitational redshift) relativistic effects so as to simulate what an observer with arbitrary velocity would see near, or possibly within, the black hole. We also pay some specific attention to perform a satisfactory rendering of stars. Using this code, we then show several unexplored features of the maximal analytical extension of the metric. In particul…
We discuss a recently presented boosted Kerr black hole solution which had already been used by other authors. This boosted metric is based on wrong assumptions regarding asymptotic inertial observers and moreover the performed boost is not a proper Lorentz transformation. This note aims to clarify some of the issues when boosting black holes and the necessary care in order to interpret them. As it is wrongly claimed that the presented boosted Kerr metric is of Bondi-Sachs type, we recall out some of the necessary requirements and difficulties, when the casting the Kerr metric into a metric wi…
Metric Renormalization in General Relativity
在广义相对论的平均问题涉及到的困难，定义有意义的平均张量，我们认为这个问题的各个方面。我们首先解决宇宙学的反作用，因为平均爱因斯坦张量是不相同的平均度量的爱因斯坦张量。有人认为，逆反应可能解释了暗能量。我们在布歇特形式中用数值方法证明了（准）线性扰动的修正量仅为10^-5量级，并且充当了暗物质。然后，我们专注于构建平均度量，并提出了一个一般的协变平均过程，分解成Vielbeins度量和平行运输他们与相对论性Wegner-Wilson算子到一个单一的点，然后可以平均。Vielbein是在拉格朗日形式主义中选择的。在两个和三个空间维度的具体示例中展示了该过程的功能。这涉及到偏微分方程的数值解的模拟工具包Gascoigne的援助。
On the derivation of the spacetime metric from linear electrodynamics
在无度规电动力学的框架下，我们从激发2-形式$H = ({\cal D}, {\cal H})$和场强2-形式$F = ({E,B})$之间的{ \em线性}时空关系出发。这种线性关系受到所谓的闭合关系的约束。我们解决这个系统的代数和扩展以前的分析，如也包括奇异的解决方案。利用最近导出的描述电磁波在一般{ \em linear}介质中传播的四阶{ \em Fresnel}方程，我们发现对于所有解，四阶曲面都退化为光锥。由此我们推导出相应的度量直至保形因子。
Towards a general solution of the Hamiltonian constraints of General Relativity
目前的工作有双重目的。一方面，我们提请注意存在于Ashtekar形式主义和其他引力规范理论方法，特别是庞加莱规范理论之间的关系。另一方面，我们研究了两种解决方案的限制广义相对论，包括两个相互独立的部分，即一般的三个度量依赖的贡献的外在曲率$K_{ab}$的Cotton-York张量，除了它进一步的度量独立的贡献，我们分析特别是在存在的各向同性的三个度量。
General relativity is reconsidered by starting from the unquestionable interpretation of special relativity, which (Klein 1910) is the theory of the invariants of the metric under the Poincaré group of collineations. This invariance property is physical and different from coordinate properties. Coordinates are physically empty (Kretschmann 1917) if not specified by physics, and one shall look for physics again through the invariance group of the metric. To find the invariance group for the metric, the Lie "Mitschleppen" is ideal for this task both in special and in general relativity. For a ge…
We outline unimodular conformal and projective relativity (UCPR), an extension of unimodular relativity in which the conformal and projective structures play central roles. Under $SL(4,\mathbb{R})$ symmetry group, the pseudo-Riemannian metric naturally decomposes into a four-volume element and a conformal metric; and the affine connection decomposes into a one-form and a trace-free projective connection. In UCPR, these four space-time structures are treated as independent fields that have clear physical interpretations. A Palatini-type variational principle for the usual general relativity Lag…
We analyze the issue of ``particle motion'' in general relativity in a systematic and rigorous way by considering a one-parameter family of metrics corresponding to having a body (or black hole) that is ``scaled down'' to zero size and mass in an appropriate manner. We prove that the limiting worldline of such a one-parameter family must be a geodesic of the background metric and obtain the leading order perturbative corrections, which include gravitational self-force, spin force, and geodesic deviation effects. The status the MiSaTaQuWa equation is explained as a candidate ``self-consistent p…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。