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1answer
73 views

What are the units of dark energy?

Popular literature seems to equate dark energy with the cosmological constant of the Einstein field equations. We know however that the dimensions of any constituent of the field equations is ${\rm ...
1
vote
0answers
61 views

Geometrized units in Wald

I am trying to follow a derivation in this paper from Wald Specifically, at the end of the paper, just under Eq. 4.7 there is given the equation $$ Q/m \leq 2 B_0 m$$ where $Q$ is the system ...
4
votes
2answers
98 views

How to put $c$ back into relativistic equations?

Many books set the speed of light $c=1$ for convenience. For example, Weinberg in his textbook "Gravitation and Cosmology" (though $G$ is still left as a constant): $$\begin{align} \mathrm{d}\tau^2 &...
2
votes
1answer
262 views

What's the matter with Planck mass $M_P$ in Einstein-Hilbert action?

The Einstein-Hilbert (EH) action is often written as $$S_{EH}=\frac{c^4}{16\pi G}\int d^4x \sqrt{-g}R\tag{1}$$ and often as $$S_{EH}=\int d^4x \sqrt{-g}M_P^2 R\tag{2}.$$ Comparing (1) and (2), one ...
2
votes
5answers
170 views

Do the units of $G/c^4$ make intuitive sense?

In classical Newtonian mechanics, gravity is explained by: $$F=G \frac {Mm} {r^2}$$ Where $F$ is the force due to gravitation, $M$ and $m$ are the masses of the two bodies in question, $r$ is the ...
1
vote
1answer
245 views

Converting Hubble constant to GR Units

I'm working my way through Thomas Moore's General Relativity Workbook and having a problem with Exercise 24.4.1 (p. 288), which asks you to verify Hubble constant values (with errors) for a variety of ...
2
votes
1answer
331 views

Units of Einstein-Hilbert Action

Action is a quantity with units energy $\times$ time $=[kg \frac{m^2}{s}]$. The Einstein-Hilbert action is \begin{equation} S_{EH}=\frac{c^4}{16\pi G}\int \sqrt{-g}R d^4x \end{equation} Looking only ...
0
votes
2answers
68 views

Penrose Theorem: Comparing 2 different physical quantities?

Wikipedia says- Penrose's theorem is more restricted and only holds when matter obeys a stronger energy condition, called the dominant energy condition, in which the "energy is larger than the ...
0
votes
3answers
144 views

Strange unit $kg/m$ - How to interpret?

We have a publication. Page 4 in this publication. Cite: Note that the numerical value of $µ/c^{2}$, from Eq. (3) and the numbers given above, is about $10^{−19}$ kg/m, emphasizing the extremely ...
3
votes
3answers
1k views

How can geometrized units have more than one constant equal to 1?

I can understand how you could manipulate units to make a certain constant equal to $1$, like $c$ or $G$, et cetera. But how can you make it so two constants (in this case $c$ and $G$) are equal to $1$...
2
votes
1answer
269 views

Units of Velocity Components and Metric Tensor Components

I was watching a GR lecture on youtube, and the speaker explains that the units of the components of velocity are $[v^{\alpha}]=\frac{1}{T}$, the metric tensor has units $[g_{\alpha\beta}]=L^2$, and ...
4
votes
2answers
509 views

$c^4$ in Einstein field equations

I have read many derivations of Einstein field equations (done one myself), but none of them explain why the constant term should have a $c^4$ in the denominator. the $8{\pi}G$ term can be obtained ...
5
votes
5answers
1k views

What is the significance of Planck force?

I have been curious to find what could be the significance of Planck force? It is calculated by the formula $c^4/G = 1.21031359\times 10^{44} \, \mathrm{N}$, where $c$ is the speed of light and $G$ is ...
9
votes
3answers
498 views

Einstein tensor in Friedmann equations : where is the missing $c^2$?

I would like to demonstrate the several forms of the Friedmann equations WITH the $c^2$ factors. Everything is fine ... apart that I have a missing $c^2$ factor somewhere. In all the following $\rho$ ...
1
vote
3answers
188 views

How could the unit of a constant be unit of tension $N^{-1}$?

From my pervious Question:What are the units of the quantities in the Einstein field equation? i noticed that the unit of this constant $\frac {G}{c^4}$ is the unit of tenstion $$\frac {m^3}{kg.s^2}\...
13
votes
3answers
7k views

What are the units of the quantities in the Einstein field equation?

The Einstein field equations (EFE) may be written in the form: $$R_{\mu\nu}-\frac {1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=\frac {8\pi G}{c^4}T_{\mu\nu}$$ where the units of the gravitational constant $G$ ...
2
votes
2answers
2k views

Finding the correct units for the energy-momentum tensor?

I'm trying to understand the energy-momentum tensor $T^{\mu\nu}$ but I'm confused about the units. My textbook says the components of $T^{\mu\nu}$ are $\mathrm{Jm^{-3}}$. Four-momentum is is given by$$...