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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写广义相对论General relativity方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写广义相对论General relativity代写方面经验极为丰富，各种代写广义相对论General relativity相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|广义相对论代写General relativity代考|Gravity and the Locally Inertial Frame

Liberal use is made of the thought experiments proposed by Einstein, illustrated in Figs. $3.1$ and 3.2, to crystallize his ideas concerning GR. When gravity is included, it acts everywhere. At first it isn’t clear that an inertial frame can be found. Standing in an elevator, gravity is experienced by the floor pushing up on our feet. There is no upward acceleration as gravity counters this force. If the elevator started accelerating upward, a stronger upward push would be experienced. However, an elevator observer couldn’t tell whether the effect was due to a stronger gravitational force, or a force due to a machine capable of lifting the elevator.

If the elevator cable broke and the elevator observer released some objects from rest, a camera fixed to the elevator would show all objects remaining at rest with respect to each other. It wouldn’t matter whether some objects were more or less massive or if they were made of different materials. Also the elevator observer would no longer feel an upward force from the floor. A camera fixed to the earth would show all objects falling with the same acceleration. This is because inertial mass and gravitational mass are the same. For example, from Newton’s law of gravity,
$$F=M_{I} a=M_{G} M / d^{2}, \quad a=M / d^{2} .$$

## 物理代写|广义相对论代写General relativity代考|Local Flatness Theorem

The existence of a locally inertial frame means that curved space has a flat space tangent at any point. Above, it was noted that at any point $P$ in spacetime, one can find a rectangular coordinate system $x^{\bar{\mu}}$, such that at $P$ the metric is the metric of SR. Then, its first partial derivative vanishes, but not necessarily its second partial. That is, the metric near $P$ is approximately that of $\mathrm{SR}$, the differences being second order in the coordinates.

The proof begins by noting that there is some relation between an arbitrary coordinate system and the locally inertial system, $x^{\mu}=x^{\mu}\left(x^{\bar{\nu}}\right)$, and all orders of the partial derivatives, $x^{\mu}, \bar{\nu}, \ldots$, exist. The latter and the metric are expanded in a Taylor series, shown below to second order. The expansion is about $P$, for coordinates close to $P$,
$x^{\mu}, \bar{\alpha}=x^{\mu},\left.\bar{\alpha}\right|{P}+x^{\mu}, \bar{\alpha},\left.\bar{\chi}\right|{P} \Delta^{\bar{\chi}}+x^{\mu}, \bar{\alpha}, \bar{\chi}, \bar{\xi} \mid P \Delta^{\bar{\chi}} \Delta^{\bar{\xi}} / 2$,
$x^{\mu}, \bar{\alpha} x^{\nu}, \bar{\beta} g_{\mu \nu}=g_{\bar{\alpha} \bar{\beta}}$
$=\left.g_{\bar{\alpha} \bar{\beta}}\right|{P}+\left.g{\bar{\alpha} \bar{\beta}, \bar{\chi}}\right|{P} \Delta^{\bar{\chi}}+g{\bar{\alpha} \bar{\beta}}, \bar{\chi}, \bar{\xi} \mid{ }{P} \Delta^{\bar{\chi}} \Delta^{\bar{\xi}} / 2$, $\Delta^{\bar{x}}=x^{\bar{x}}-\left.x^{\bar{x}}\right|{P}$, thus, $\left.\Delta^{\bar{x}}\right|_{P}=0$.

# 广义相对论代考

## 物理代写|广义相对论代写General relativity代考|Gravity and the Locally Inertial Frame

$$F=M_{I} a=M_{G} M / d^{2}, \quad a=M / d^{2} .$$

## 物理代写|广义相对论代写General relativity代考|Local Flatness Theorem

$x^{\mu}, \bar{\alpha}=x^{\mu}, \bar{\alpha}\left|P+x^{\mu}, \bar{\alpha}, \bar{\chi}\right| P \Delta \bar{\chi}+x^{\mu}, \bar{\alpha}, \bar{\chi}, \bar{\xi} \mid P \Delta \bar{\chi} \Delta \bar{\xi} / 2$ $x^{\mu}, \bar{\alpha} x^{\nu}, \bar{\beta} g_{\mu \nu}=g_{\bar{\alpha} \bar{\beta}}$
$x^{\mu}, \bar{\alpha} x^{\nu}, \bar{\beta} g_{\mu \nu}=g_{\bar{\alpha} \bar{\beta}}$
$=g_{\bar{\alpha} \bar{\beta}}|P+g \bar{\alpha} \bar{\beta}, \bar{\chi}| P \Delta^{\bar{x}}+g \bar{\alpha} \bar{\beta}, \bar{\chi}, \bar{\xi}\left|P \Delta^{\bar{x}} \Delta^{\bar{\xi}} / 2, \Delta^{\bar{x}}=x^{\bar{x}}-x^{\bar{x}}\right| P ，$ 因此， $\left.\Delta^{\bar{x}}\right|_{P}=0$.

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
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