The general-relativity tag has no wiki summary.
2
votes
1answer
231 views
Euler characteristic of Cauchy surface in Lorentz manifold
Are there any known topological restrictions on what kinds of manifolds can form the Cauchy hypersurface of a Lorentzian manifold? I'm particularly interested about restrictions on Euler ...
1
vote
1answer
124 views
manifolds whose charts are maps to Minkowski space
I'm doing a project involving tilings of Minkowski space. For instance in 2d I have rectangular tiles determined by a spacelike line segment: the rectangle is the region caused by the line segment. ...
0
votes
0answers
77 views
Hitchin–Thorpe inequality for Lorentzian manifold
I've recently read the following:
For which $b$ it is possible that $S^n$ can have a Lorentz metric? Why?
An answer shows that a compact, oriented, simply connected manifold carries a Lorentz metric ...
2
votes
1answer
80 views
Dimension of the space of null geodesics
So that is my question. If I have a manifold with Lorentz metric, how do I know the dimension of the space of null geodesics. For example, in the general relativity the space of null geodesics is 5... ...
3
votes
1answer
68 views
Global conformal equivalence of two regions of Minkowski spacetime
I am wondering whether the region $H:=\{(t,x):x^2−t^2<1\}$ of $(1+1)$-dimensional Minkowski spacetime, equipped with the restriction $g_H$ of the standard Minkowski metric $g=−\mathrm{d} t\otimes ...
5
votes
0answers
241 views
Why does closed string theory have only one dilaton field instead of $22$?
Looking at $5D$ Kaluza-Klein theory, the Kaluza-Klein metric is given by
$$
g_{mn} = \left(
\begin{array}{cc}
g_{\mu\nu} & g_{\mu 5} \\
g_{5\nu} & g_{55} \\
\end{array}
\right)
$$
...
2
votes
0answers
95 views
Solving ODE with negative expansion power series
I'm moving this here, as suggested from physics.stackexchange. The original is here.
So, I need to solve a system of ODE, using negative power expansion. I will give all the necessary equations and ...
10
votes
4answers
399 views
Einstein field equations in perspectives from PDE and functional analysis
The Einstein field equations have been subject of research in theoretical physics, and differential geometry, apparently with methods from classical analysis and geometry. In particular, solutions in ...
10
votes
1answer
551 views
Does the gluing procedure in Robert Wald’s book *General Relativity* yield a Hausdorff spacetime?
Before I state my problem, let me provide some definitions pertaining to the Cauchy Problem in General Relativity.
Definition 1: A triplet $ (\Sigma,h,k) $ is called an initial data set if $ ...
-2
votes
1answer
153 views
Can Hartogs' extension theorem be used to prove there's no naked singularity?
Maybe for the first time my question doesn't deal with number theory. Tonight a friend of mine told me about Hartogs' extension theorem and said his work in analytic microlocal analysis was somehow ...
0
votes
0answers
57 views
Null vector fields given Bondi metric
I'm trying to understand how to compute the null future-directed vector fields if I have a given (Bondi) metric
$g=-e^{2\nu}du^{2}-2e^{\nu+\lambda}dudr+r^{2}d\Omega$
with $d\Omega$-standard metric ...
2
votes
1answer
132 views
naked singularity and null coordinates
I'm trying to understand the notion of a naked singularity on a more mathematical level (intuitively, it's a singularity "one can see and poke with a stick", but I'm having troubles on how to actually ...
0
votes
0answers
134 views
covarient derivative of electromagnetic field tensor
I'm trying to prove the energy momentum tensor in curved spacetime for Electromagnetic field is Divergence-less directly(Without using general lie derivative method which can prove any energy momentum ...
0
votes
0answers
200 views
Functional Analysis and Differential Manifold incompatibility
From the mathematical point of view, where is the idea of the incompatibility between functional analysis, at the basis of quantum mechanics, and differential geometry, at the basis of general ...
3
votes
1answer
186 views
Are all null curves of a Lorentzian metric extrema?
Suppose $g$ is a Lorentzian metric on $\mathbb{R}^4$, then consider the variational problem of finding extrema of
$$F(\gamma) = \int_a^b \| \dot{\gamma}(s) \|_g ds$$
The so-called "null curves" are ...
8
votes
1answer
424 views
The Speed of Gravitational Waves in General Relativity
Is it possible to mathematically prove that the speed of gravitational waves in general relativity equals the speed of light, without linearizing the Einstein Field Equations? The approach via the ...
4
votes
1answer
547 views
Geometric derivation of the Einstein’s field equation from the Hilbert action.
It is well-known that the equation for stationary solutions of the Einstein-Hilbert functional is given by the Einstein field equation (for a statement, see previous question). The standard derivation ...
7
votes
1answer
438 views
Coordinate-free derivation of the Einstein's field equation from the Hilbert action.
It is well-known that the equation for stationary solutions of the Einstein-Hilbert functional (without matter and cosmological constant, which is irrelevant here):
$$S = \int_M R \mu_g,$$
is given by ...
4
votes
1answer
220 views
Work on an Einstein-Hilbert type action but with the *absolute value* of scalar curvature?
This is only my second question on mathoverflow, so my apologies if this would be more appropriate at a physics site. My question concerns a modification to the Einstein-Hilbert action. The standard ...
7
votes
5answers
890 views
Is there a relation between 4-dimentional general relativity and exotic smooth structures on $\mathbb{R}^4$?
Let's say General Relativity is the study of the Einstein equation on smooth Lorentzian manifolds, i.e. pseudo-Riemanniann manifolds of signature $(n-1,1)$.
I've heard more than once people say that ...
7
votes
2answers
722 views
10
votes
1answer
561 views
Regge calculus: Questions of consistency resolved?
Hello,
Regge calculus is an approximation scheme for General Relativity, which has been introduced in early-sixties and has been adopted both in numerical relativity and numerical quantum relativity. ...
10
votes
4answers
906 views
Singular semi-Riemannian Geometry: usefulness and state of the art
My question has two parts, one concerning the state of the art of the subject, and the other the usefulness.
1. State of the art.
Can someone provide references reflecting the state of the art in ...
2
votes
2answers
2k views
Killing vectors and Ricci Tensor
Hi all,
We all know that the lie derivative of the metric tensor along a Killing Vector vanishes, by definition. I am trying to show that the Lie derivative of the Ricci tensor along a Killing vector ...
4
votes
1answer
657 views
Christodoulou's paper on naked singularities in inhomogeneous dust collapse
I have been studying of late about formation of naked singularities in certain collapse scenarios in Einstein's theory. It seems to me that the canonical paper to read about how such a formation is ...
