# Tagged Questions

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

5k views

### Are black holes perfect spheroids?

What I know about black holes (correct me if I'm wrong) is that they are the most compact objects in the universe that have been discovered. Due to all that gravity, wouldn't black holes be a perfect ...
24 views

65 views

91 views

### Learning about 4 topics in physics [closed]

This isn't really a question on any of those numerous underlying concepts behind the various sub-disciplines of physics, but hear me out: I'm still in Higher Secondary, but I'd really love to know ...
38 views

### Confusion with conclusion to positive mass theorem

I am trying to understand the positive mass theorem as it is presented in the survey paper by Corvino and Pollack http://arxiv.org/abs/1102.5050 I am fundamentally confused by the structure of their ...
36 views

40 views

### Construction of vector bundles of relativistic fields by Mackey's method of induced representation

I recently stumbled on Sternberg's book on group theory and physics. The ideas expressed in the book are really great, but the detailed reasoning is very hard to follow, I find. I am kind of stuck ...
47 views

### What is the difference between intrinsic and extrinsic curvature? [migrated]

In general relativity, energy bends spacetime. However, this doesn't mean that a fifth dimension for spacetime to "bend into" exists." That is, spacetime isn't embedded in a higher dimensional space, ...
42 views

113 views

### Proving constant curvature

I'm currently on section 5.1 in Wald's book. He is trying to prove that the cosmological principle implies that space has constant curvature. Given a spacelike hypersurface $\Sigma_t$ for some fixed ...
67 views

### Covariant derivative [closed]

Hi, Could you explain to me why the subtraction of vector at some point and parallel transported vector is covariant derivative vector. How is it possible
$$g = dt^2 - a^2(t) (dx^2+dy^2+dz^2) = dt^2-a^2(t)(dr^2+r^2d\Omega^2)$$ So this is my metric. What is the symmetry group of it? I think that my Killing vectors are 3 translation vectors: $$K_i = \... 0answers 42 views ### Multidimensional Area and Volume In 3D the volume is xyz, the product of three coordinates. But in N dimension ,how to define area and volume? 1answer 96 views ### What is the additional gravitational term from general relativity given by? Carroll gives the potential energy in general relativity by$$ V(r)=\frac{1}{2}\epsilon-\epsilon\frac{G\,M}{r}+\frac{L^{2}}{2r^{2}}-\frac{G M L^{2}}{r^{3}} $$My first question is does V(r) have ... 1answer 71 views ### Problem 1 Chapter 11 Wald I'm currently trying to solve problem 1, Chapter 11 of Wald, General Relativity. The request is to derive from the condition$$ \tilde\nabla_a \tilde\nabla_b \Omega=0\text{ at }\mathscr I^+, $$where ... 1answer 52 views ### A Calculation in Padmanabhan's Book I have seen this in Padmanabhan's book. How can I verify this:$$d\Sigma_{mn}=\frac{1}{2!}\epsilon_{mnab}\frac{\partial(x^a,x^b)}{\partial(\theta,\varphi)}d\theta d\varphi=\epsilon_{mn\theta\varphi}r^...
I'm trying to solve the Killing tensor equation $\nabla_{(a}K_{bc)} = 0$ in Minkowski space. I'd like to generalise the method we use to find Killing tensors in Minkowski space. We can take \$\...