Recent content by user1139

Still, how do they get ##\Sigma## from ##\Psi##? Did they just consider the asymptotic behaviour of ##\Psi## and define ##\Sigma## as such?

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...

Yes @MathematicalPhysicist I have perused Polichinski's book in particular and could not find a mention of the time-invariant Kaluza-Klein metric.

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.

@ergospherical could you list a reference or two on what you have written? I would like to read more about it.

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...

Does it then make sense to use a left-hand convention for defining the curl in a right-handed coordinate system?

But the second definition will incur an overall minus sign relative to the first definition after calculating the determinant.

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...

The matrix is singular and hence, cannot be inverted.

Do you know how to solve it? I ran out of ideas.

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.]