I am trying to understand how one derives the dilaton monopole interaction. In "Black holes and membranes in higher-dimensional theories with dilaton fields", Gibbons and Maeda mentioned that one could obtain the dilaton monopole interaction as such:
where the action is given by
However, I...
From this post-gradient energy in classical field theory, one identifies the term ##E\equiv\frac{1}{2}\left(\partial_x\phi\right)^2## as the gradient energy which can be interpreted as elastic potential energy.
Can one then say that $$F\equiv -\frac{\partial...
Homework Statement:: Please see below.
Relevant Equations:: Please see below.
I am trying to find a reference to a textbook or a paper that details the following time-invariance Kaluza-Klein metric:
\begin{equation}...
@ergospherical I see. However, I’m trying to understand specifically your argument. Hence, I’m hoping there’s a reference that details the arguments you laid out.
Homework Statement:: See below.
Relevant Equations:: See below.
I am trying to calculate the event horizon and ergosphere of the Kerr metric. However, I could not seem to find a proper derivation or formula to calculate the event horizon and ergosphere. Could someone point me to the...
The curl is defined using Cartersian coordinates as
\begin{equation}
\nabla\times A =
\begin{vmatrix}
\hat{x} & \hat{y} & \hat{z} \\
\frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\
A_x & A_y & A_z
\end{vmatrix}.
\end{equation}
However, what are the...
Working with Cartesian coordinates, I will be able to equate the respective components on the LHS and RHS. The problem comes when I want to find ##A_x##, ##A_y## and ##A_z## since the equations are now coupled.
Consider the following
\begin{equation}
\nabla\phi=\nabla\times \vec{A}.
\end{equation}
Is it possible to find ##\vec{A}## from the above equation and if so, how does one go about doing so?
[Moderator's note: moved from a homework forum.]