A theory that describes how matter produces and responds to the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

learn more… | top users | synonyms (1)

1
vote
2answers
115 views

Inner products in relativity

In physics, the definition of a dot (inner) product is often between a vector (“contravariant vector”) and a covector (“covariant vector”). However, in mathematics, a dot product is always defined ...
1
vote
0answers
54 views

Do wormholes have a side to their path through space?

In theory do wormholes have a side to their path through space? What is there at a point in line with the entry and exit, would anything look different at that point in space? Could a space ant get ...
0
votes
0answers
66 views

How to move from Special to General Relativity

I have understood special relativity nicely, and right now I am trying to learn general relativity from D'Inverno's book. I an finding it rather difficult to understand the pre-requisite math (i.e. ...
3
votes
4answers
302 views

What is difference between Inertial mass and gravitational mass [duplicate]

I recently read that the mass we deal with in Equation $F=Ma$ is called inertial mass and the mass we deal with in $F=Mg$ is gravitational mass. Suppose I am taking a same ball in a free fall and in ...
0
votes
1answer
219 views

Why does the Alcubierre drive require negative energy?

The Alcubierre drive is an idea for a faster-than-light spaceship. It works by contracting space-time in front of the ship, and expanding it behind the ship. Physicists say that this requires the use ...
5
votes
1answer
275 views

What is the entropy of the universe today?

What's the entropy of the universe today? How does one go about calculating this? I've heard the statement that black holes account for the bulk of the entropy in the universe today, but don't know ...
2
votes
6answers
313 views

Curvature of Spacetime

I have been exploring for some time both the Special and General Relativity, hoping to glean at least a conceptual grasp of their basic tenets. In reading the book "Gravitation" by Misner, Thorne and ...
2
votes
1answer
156 views

If distant observers never see a black hole form in finite time how can the information paradox be a problem?

So, at least as reported in the media, the physics community is still struggling with the problem of resolving the impossibility of retrieving information from beyond the event horizon of a black hole ...
13
votes
1answer
409 views

In there such a thing as the Black Hole Information Paradox?

When I first heard about the black hole information paradox, I thought it had no content. At the time, papers about it had been written for numerous years and they keep on coming. Now that the press ...
5
votes
2answers
216 views

What is the meaning of the “expansion of space”?

When we say that "the space between galaxies is expanding," what do we really mean? For instance, if I think of space as being a Cartesian grid, then when space expands should I think of it as adding ...
2
votes
2answers
122 views

Affine connection notation

Can ${g}^{\mu\sigma}{\Gamma}^{\rho}_{\sigma\nu}$ be written as ${\Gamma}^{\mu\rho}_{\nu}$? If so how come this symbol never appears in any GR book?
0
votes
2answers
181 views

Has anyone checked whether the speed of light varies according to gravitation

My physics is fairly basic, but I hope someone can answer without being too rude. A transparent medium such as water or glass refracts light and also reduces its speed, so I was wondering whether ...
0
votes
0answers
18 views

Calculating dragging frame of satellite orbiting Earth [duplicate]

Say there is a satellite polar-orbiting the Earth at 600km. How much would the satellite be dragged additionally due to dragging force? Such that $$ \Omega = \dfrac{r_s \alpha r c}{\rho^2(r^2 + ...
1
vote
1answer
103 views

Can we calculate the frame dragging force of the Earth?

Although clearly this force would be significantly greater with a rotating black hole, is it still possible to calculate this drag for say a satellite orbiting the Earth?
12
votes
4answers
459 views

Is the concept of tensor rank useful in physics?

The term 'tensor rank' is sporadically used in the mathematical literature to denote the minimum number of simple terms (i.e. tensor products of vectors) needed to express the tensor. This is ...
1
vote
0answers
55 views

Contracting Indices in General relativity [duplicate]

I was reading a book about general relativity and I came across these two equations $$ \begin{align} \mathrm{g}^{\mu\nu}_{,\rho}+ \mathrm{g}^{\sigma\nu}{\Gamma}^{\mu}_{\sigma\rho}+ ...
2
votes
2answers
226 views

Bracket Notation on Tensor Indices

I know about the () symmetrisation and [] anti-symmetrisation brackets on tensor indices so long as they appear on their own, such as : $$V_{[\alpha \beta ]}=\frac{1}{2}\left ( V_{\alpha \beta ...
2
votes
0answers
82 views

Why is the mass of a Kerr black hole proportional to it's angular momentum?

I'm a third year mathematics undergrad, and have just started the module General Relativity and spacetime geometry, I also have a keen interest in black holes. However I would like to know why and ...
2
votes
3answers
445 views

Does a moving object curve space-time as its velocity increases?

We always hear how gravity bends space-time; why shouldn't velocity? Consider a spaceship traveling through space at a reasonable fraction of the speed of light. If this spaceship, according to ...
9
votes
1answer
316 views

Contracting Indices

Does anyone know how to get from (1) to (2) in the system $$ \begin{align} \mathrm{g}^{\mu\nu}_{,\rho}+ \mathrm{g}^{\sigma\nu}{{\Gamma}}^{\mu}_{\sigma\rho}+ ...
0
votes
0answers
39 views

Quantum Mechanics and General Relativity in Macroscopic Level [duplicate]

Hi I read a book yesterday.The book was Brian Greene's The Elegant Universe. I learned that uncertainty principle affects space-time very microscopic levels and this affection makes conflict in ...
1
vote
1answer
94 views

Null lines and degenerate plane

Can anyone explain me what null lines are and degenerate plane? I don't know anything about it, I don't have physics background and I am a mathematics student and please tell me if there is any good ...
1
vote
0answers
137 views

Understanding spherically symmetric metric

In these lecture notes the static isotropic metric is treated as follows (p. 71): Take a spherically symmetric, bounded, static distribution of matter, then we will have a spherically symmetric ...
1
vote
1answer
61 views

Unable to resolve 2 equivalent geodesic equations

A free particle moves along geodesics, one form being \begin{split} \ddot x^\mu &= -\Gamma^{\mu}_{\sigma \rho} \dot x^\sigma \dot x^\rho \\ &= -\frac{1}{2}g^{\mu \nu}(\partial_\sigma g_{\rho ...
4
votes
1answer
83 views

Invariants of Connection Form

I am somewhat going out "on a limb" here, since I am much more grounded in the physics side of things than I am in mathematics. Nonetheless, I am wondering if someone is able to comment on the ...
2
votes
0answers
108 views

equation of motion for the scalar field via variational principle in general relativity

I would like to find the equation of motion for the scalar field $\phi$ by varying the following action in General Relativity. Special Relativity: $$ S = -\tfrac{1}{2}\int d^4\xi\, \eta^{ab} ...
3
votes
2answers
183 views

Vanishing of Weyl Tensor Contraction

Within the context of Einstein space-times, we know that the contraction of the Weyl tensor across a set of indices always vanishes, like so : $$C{^{\alpha }}_{\mu \alpha \nu }=0$$ From a purely ...
1
vote
2answers
200 views

Gravitational field has no curl? What about gas discs around stars, black holes, etc.?

So everybody says the gravitational field has no curl, and is not comparable to a liquid swirling around a drain. Observationally, of course, there are many examples of vector fields (which I think ...
0
votes
0answers
61 views

About divergence of a vector field and geodesic sphere

I have a question. I want to know the difference between the sphere and the geodesic sphere. Another question: given a vector field, $Y$, on a manifold $M$ defined by: $Y(p)=p$ for every point $p \in ...
0
votes
0answers
81 views

Light cones and reference frames

I'd like to know what does it mean exactly to find a reference frame in which two events occur at the same time or in the same space coordinates. As I picture it if we have two events A and B in a (x, ...
4
votes
2answers
258 views

Geodesics equations via variational principle

I would like to recover the (timelike) geodesics equations via the variational principle of the following action: $$ \mathcal{S}[x] = -m \int d\tau = -m \int \sqrt{-g_{\mu\nu}\,dx^{\mu}\,dx^{\nu}} $$ ...
1
vote
1answer
74 views

Linear Metric Perturbation and Brans-Dicke Theory

Recently, I have been researching about modified gravity theories and one of the theories has been the theory of the graviton. If one starts with the metric tensor $g_{\mu\nu}$ and then performs the ...
16
votes
3answers
584 views

Does black hole formation contradict the Pauli exclusion principle?

A star's collapse can be halted by the degeneracy pressure of electrons or neutrons due to the Pauli exclusion principle. In extreme relativistic conditions, a star will continue to collapse ...
4
votes
1answer
106 views

Sign of $dr$ in Schwarzschild geodesics

There is an equation that relates energy $E$, angular momentum $L$ and other constants and variables to find $\left(\frac{dr}{d\tau}\right)^2$ in a plane. ...
2
votes
1answer
66 views

Riemann normal chart and special relativity

When you pick Riemann normal coordinates at a point, then the Christoffel symbols vanish and the metric is flat, but the Riemann curvature tensor does not necessarily vanish. Since Einstein said that ...
4
votes
1answer
215 views

Non-coinciding event horizon and apparent horizon

Proposition: the event horizon and the apparent horizon of a black hole always coincide. As a reminder: the event horizon is defined as the boundary of the closure of the causal past of future ...
1
vote
1answer
198 views

Questions about MTW's “thousand” tests of the Einstein principle

In Misner, Thorne, Wheeler (henceforth written as "MTW"), "Gravitation", Box 16.4, there's an experimental setup construction (or method) presented by which "Each geodesic clock is constructed and ...
9
votes
3answers
200 views

Thermal equilibrium in general relativity

The Newtonian condition for thermal equilibrium for a static system is $T = \mathrm{const}$. In this homework I'm asked to show that it's curved space generalization is $T(-g_{00})^{\frac{1}{2}} = ...
1
vote
0answers
79 views

Ricci scalar higher dimensions

I was wondering if there is a straightforward way to compute the Ricci curvature of a metric that has the form (à la Kaluza-Klein): $g_{MM}\equiv\begin{pmatrix}g_{\mu\nu}&g_{\mu ...
5
votes
2answers
145 views

Can a revolving body self-gravitate?

If a body is revolving around a point at radius R with tangential velocity V, does General Relativity predict that at some tangential speed, the body will revolve around the point without any external ...
5
votes
1answer
144 views

Are conformal, Killing and homothetic vector fields the same in pseudo-riemannian manifolds?

I work in the Lorentzian manifolds, more generally in pseudo Riemannian manifolds and applications to general relativity. I know the definitions of conformal, Killing and homothetic vector fields in ...
0
votes
0answers
30 views

concept of density in gravitational lensing

I may just be being very dense (no pun intended) but i'm reading up on gravitational lensing and it seems to require a notion of density (e.g. see here) I'm working on a question involving light ...
1
vote
1answer
121 views

Do we still need Newtonian G in General Relativity?

I believe we can use Newtonian Physics to make incredibly good predictions about the movement of celestial bodies as long as they are not too fast/massive and there are only two of them (well, we can ...
3
votes
1answer
131 views

Would time dilation be too great for the early universe to expand?

I read that one second after the big bang the universe was composed of photons electrons and neutrinos. Wouldn't the density of energy/matter have caused such extreme time dilation that the universe ...
3
votes
0answers
74 views

Homeomorphism between the space of all Ashtekar connections and spacetime?

Excerpt from an essay of mine: Let $\Psi(\varsigma)$ be the wavefunction in the loop representation, where $\varsigma:[0,1]\to\mathcal{M}$, where $\mathcal{M}$ is spacetime. Then, let ...
4
votes
0answers
219 views

Superspace as the Hilbert Space for Quantum Gravity

Let $\mathcal{A}$ be the Ashtekar connection. Since $^{(3)}g_{AB}=i\frac{\delta}{\delta\mathcal{A}^{AB}}$ (see R. Penrose, 2004: Road to Reality. Vintage Books, 1136 pp.), the Ashtekar connection, in ...
4
votes
0answers
79 views

Timelike Loop Spaces as Projective Null Twistor Spaces

Let $\mathcal{M}$ be a spacetime, and let $\Omega\mathcal{M}$ denote the loop space of the spacetime. My idea is that the set of all closed timelike curves of $\mathcal{M}$ forms the projective null ...
0
votes
1answer
65 views

One particle near two Schwarzschild black holes

I have a particle near two Schwarzschild black holes. Let the black holes remain at rest so that only the particle is moving for the observer. We are in a plane. I calculate the distance travelled by ...
1
vote
1answer
149 views

Why in some cases $0\alpha$ component of stress-energy tensor don't form 4-vector?

In electrodynamics there is Poynting vector and energy density, which refer to $0\alpha $ components of stress-energy tensor, don't create 4-vector. Analogous situation with mass density and mass ...
0
votes
1answer
60 views

How 4-vector nature of the value is connected with it's conservation law?

In electrodynamics Poynting vector and energy flux of field don't create 4-vector. Also they aren't conserved independently from substance (conservation law includes summand connected with current ...