Recent content by Martin Scholtz

Thanks, I didn't know this.

This cannot be true since it is not a differential equation for the metric. #Ric=0# are vacuum Einstein's equations and thus 2nd derivatives must appear. I don't have the book you cite, can you give us some context?

On general manifold, vectors live in different mathematical spaces. Imagine a sphere and consider any vector tangent to the sphere. What is well defined is the starting point of the vector, but the end point (the end of the arrow) lies outside the sphere and hence does not belong to the...

Sorry, I wasn't very focused when I wrote the first post. So let's go from the beginning. We agree that the Lie derivative of tensor field ##T## in the direction of vector field V at point P is $$L_V T = \lim_{t\to 0} \frac{1}{t}( \Phi_t^* T(\Phi_t(P)) - T(P)),$$ right? ##\Phi_t## is the flow...

I am not sure what exactly you worry about but I'll try to answer. Yes, you have to evaluate both terms in the definition of the Lie derivative at the same point. If $$P$$ is that point and $$\Phi_t$$ is the flow of the vector field $$V=V^\mu \partial_\mu$$, let the point Q be the point lying...

Yes, of course, you are right. I don't use this terminology so I remembered it wrong. Thanks for the correction.

As far as I know (remember), rapidity is just the ratio $$\beta = \dfrac{v}{c}$$ i.e the velocity expressed in the units of speed of light on vacuum. For example$$\beta=0.5$$ is the half of the speed of light, like 0.5Mach is the half of the speed of the sound in the air. If you write...

I will answer in detail but do you need to clarify the boosts first in general, or just in the example of the Misner space? Boosts are analogous to rotations but ty they represent transformations between two inertial frames, rather than two frames rotated with respect to each other with zero...

OK, I think we can agree, it makes no sense to repeat everything again. After all, whether we call it a force or just interaction or even differently is just a matter of terminology. My logic was to explain the classical notion of force and that even in GR and its geometrical formulation...

Thank you for the reaction. I don't necessarilly have to add a qualifier :) I did it in order to emphasize that classicaly force is something causing acceleration. Even in GR gravity has this property. I elaborated on this a bit in the post 11 which was a reaction on similar criticism in the...

Thank you for your comment. I probably understand what you want to say and you are right. But first, I wrote that it is a force in classical sense and I explained in detail what is meant by that. We talk about two different accelerations. You are talking about an observer who is already moving...

I am not sure how your question is related to gravitons (see your Summary). Gravity is the force in a classical sense. By force we mean the acceleration, i.e. the change of velocity. Suppose you hold a book in your hand 2 meters above the ground. It doesn't change the position with respect to...

I was kindly warned in the post by Kent David about a potential confusion of my answer. Please, see his post and my reaction.

Hello, thank you for the warning, yes, my explanation is potentially confusing. Nevertheless, we know from the beginning that intervals in inertial frames have isotropic diagonal for, cf. eqs. 1. and 2. at the beginning of my explanation. The purpose of symmetries etc. is to relate the general...

Thank you, I'm glad if my answer clarified anything. Maybe Schutz wanted to motivate the assumption but he should tell it more explicitly. Good luck with further study of gravity!