# Tagged Questions

Mathematical discipline which uses the techniques of calculus to study geometric problems. General relativity is written in this language.

62 views

### Spacetime manifold surgery: is this result still a valid etc. spacetime?

Given a valid classical GR spacetime manifold $M$ (i.e. 4D, Lorentzian, Hausdorff, paracompact, ?etc.), and $B\subset M$, a closed spatial subset (e.g. a closed ball at fixed $t$) to be excised, [...
24 views

### Book recommendations on geometrical methods for physicists (like Topology, Diff. Geometry) [duplicate]

I would like to obtain a book that has to do with geometrical methods/subjects for physicists. When I say geometrical methods/subjects I mean things like Topology, Differential Geometry, Lie ...
35 views

### probability of striking the circular ring by gas molecules

In kinetic theory we use probabilistic case to derive pressure, no. Of molecules having speed c to c+dc or in such cases.and to derive such equations we introduce a term called "SOLID ANGLE" I come ...
67 views

### If we live on the surface of Earth then why Earth images shows maps around it? [closed]

If you visits google map and go to earth we see the image as attached below. My question is if the earth is round like sphere ball and if we live on the surface of this ball (point me if i am ...
94 views

### Why do we need connections, if we have the Lie derivative?

When I learned about the covariant derivative, it was motivated as a way of defining a good differentiation operation on tensors. To do this, we had to define a connection on the manifold, which was a ...
111 views

### What do we exactly mean by a “topological object” in physics?

I have been working on topological defects like monopoles, etc. for some time. One think that I have not been able to understand is the physical meaning of the phrase "topological object". I have ...
78 views

97 views

### Extrinsic curvature components

I'm trying to understand how to derive the extrinsic curvature (in order to understand some calculation on fluid/gravity dynamics). But I hit a wall in my progress. I stuck at trying to verify the ...
229 views

### How do we measure Schwarzschild coordinates?

In special relativity, we make a big fuss about setting up inertial frames of reference, and then constructing coordinate systems using networks of clocks and rulers. This gives an unambiguous ...
75 views

### A question regarding $f(R)$ Lagrangians

Consider the class of Lagrangian known as $f(R)$ Lagrangians where the Lagrangian is some function $f(R)$, $$S=\int\sqrt{g}d^4x\ f(R)$$ assuming there are no (or ignoring)...
64 views

### Complex tetrad vs. Real metric

I asked this question almost a month ago on mathoverflow (http://mathoverflow.net/q/228138/) but received no response. I thought I could have better luck here: I have a question on the relationship ...
88 views

### Is it possible to integrate a function over a null hypersurface?

For $f$ a compactly supported function on a spacetime $(\mathcal{M},g)$, one may define its integral over $\mathcal{M}$ by $$f\longmapsto \int_\mathcal{M}\star f,$$ where $\star$ is the Hodge star of ...
89 views

### How do you know what kind of space(time) you have when solving the Einstein Field Equations?

I'm experimenting with the EFE, and I ''invented'' a metric; a diagonal non-zero metric, and I discovered that the Riemann tensors are equal to zero which implies the Einstein tensor $G_{mn}$ equals ...
55 views

### Physical meaning of the Morse functions? [closed]

What is the physical correspondence of the Morse functions in a physical system? Currently I am studying Mirror symmetry but I can not get a physical intuition out of it.
66 views

117 views

### Why only gauge transformations in electromagnetism?

first of all, I need to say that I'm a mathematician, so this question may sound a little stupid. Keeping this is mind, please, try to use coordinate-free notations. Along this question, I will use ...
634 views

### Stokes theorem in Lorentzian manifolds

I've fallen accross the following curious property (in p.10 of these lectures): in order to be able to apply Stokes theorem in Lorentzian manifolds, we must take normals to the boundary of the volume ...
98 views

### Geometric derivation of quantum mechanics from Lagrangian mechanics

I have used classical Lagrangian mechanics for quite a while, and what I like about it is that everything can be derived from a very small number of geometric principles. There are just three things ...