Recent content by Barnak

So, no comments on this fascinating subject ?

I'm looking for the distribution of all wavelengths (or frequencies) of light that a stationary observer would receive at his location (at ##r = 0## and time ##t_0##), from all light sources emitting a single wavelength ##\lambda_{\text{e}}## (or angular frequency ##\omega_{\text{e}}##). The...

All the nice pictures of nebulae that we usually see everywhere are of false "exagerated" colors, or true colors from a long exposition. A nebula seen with the naked eye through a good telescope is usually a gray blob with maybe some weak/dark colour tint. But what would see an hypothetical...

Nobody knows anything about electromagnetic radiation here ? For reference, the energy radiated away from the quadrupole contribution is \frac{dE}{dt} = -\: \frac{1}{180} \, \frac{1}{4 \pi \varepsilon_0 c^5} \; \dddot{Q}_{ij} \; \dddot{Q}_{ij}. This is a standard well-known result.

I'm looking for the general formula for Angular Momentum radiated away from quadrupolar electromagnetic radiation. I searched the usual books (Jackson, Landau-Lifchitz, ...) and just found the usual dipolar contributions. Using dimensional analysis and energy radiated away, I found this...

Well, I badly expressed myself (sorry, English isn't my primary language). I mean an "absolute" or coordinates independent object, like a surface in 3D space. Or a region D in space. To me, it is almost clear (? not sure yet) that the integration domain D is a coordinates independent thing...

But then how should we indicate the domain below the integral sign ? As an invariant geometric object (D' \equiv D), or as a coordinates relative set (D' \ne D) ? Of course, the integration limits are changing with the coordinates change (obvious !), but those limits aren't the same as...

So you're saying that D isn't invariant : it's a representation of the values taken by a given set of variables (coordinates) ? I still have doubts on this. For example, when we define a surface integral like this : I = \int_{\mathcal{S}} {\bf A} \cdot d{\bf S}, the symbol \mathcal{S}...

I'm having an interpretation problem with the notation used in physics, under the integration sign. What is the proper interpretation of the domain of integration symbol, on the integration sign ? To be more precise, consider a function F(x) of one or several variables. Its integral on a...

I made a mistake in the last expression. The correct tensor is this one, which is pretty heavy : \mathcal{G}^{\mu \nu \lambda \kappa \rho \sigma} = 2 \, g^{\mu \nu} (\, M^{\lambda \rho \sigma \kappa} + M^{\lambda \sigma \rho \kappa}) + g^{\mu \rho} (\, M^{\nu \lambda \sigma \kappa} + M^{\nu...

I think I've found a solution to my "problem". In the simpler case of the Maxwell field, the lagrangian is this : \mathscr{L}_{\rm Maxwell} = -\, \frac{1}{4} \, F^{\mu \nu} F_{\mu \nu} \equiv \frac{1}{2} (\, g^{\mu \kappa} g^{\nu \lambda} - g^{\mu \nu} g^{\lambda \kappa})(\, \partial_{\mu} \...

I've found a sample of Padmanabhan's book, from this place : http://www.filestube.com/g/gravitation+foundations+and+frontiers On page 243, he gives an expression for the gravitation lagrangian that is indeed exactly like mine, with the symbol M instead of my H, and with a global sign...

Hmmm, that sounds very interesting. Could you say more about this ? Can you write down exactly his version ?

I'm trying to express the classical gravitation Einstein-Hilbert lagrangian into some nice way, and I'm having a problem. It is well known that the Einstein-Hilbert action is the following (I don't write the constant in front of the integral, to simplify things) : S_{EH} = \int R \, \sqrt{-g}...

I need to build a tensor from the product of the metric components, like this (using three factors, not less, not more) : H^{\mu \nu \lambda \kappa \rho \sigma} = g^{\mu \nu} \, g^{\lambda \kappa} \, g^{\rho \sigma} + g^{\mu \lambda} \, g^{\nu \kappa} \, g^{\rho \sigma} + ..., however, that...