A theory that describes how matter interacts dynamically with 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.

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257 views

Can a sufficiently large black hole be singularity-free?

This came to me after reading that a black-hole that has the mass of the observable universe will also have an event horizon that covers the observable universe. Since the definition of a black hole ...
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1answer
101 views

Geodesic equation

I have a technical question about the geodesic equation. Assume we have a frame $(E_{1},E_{2},E_{3},E_{4})$ (not necessarily a coordinate frame). Assume we have a parametrized curve $\gamma(s)\in M$ ...
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1answer
87 views

What is a nongeodesic orbit?

I have read that in the Schwarzschild spacetime for a nongeodesic circular orbit the radial acceleration becomes positive for $r<3r_S$. Intuitively, the acceleration should be negative, pulling the ...
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3answers
156 views

Is it valid to apply Einstein's Relativity to scenarios involving expansion of space?

IIs it valid to apply Einstein's Relativity to scenarios involving expansion of space? For a practical example of this: Is it legitimate to speak of distant red-shift galaxies as experiencing time ...
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1answer
119 views

Aether atmospheres

http://arxiv.org/abs/1004.1467 claims to have an alternative explanation of the interaction of light around massive objects. Many of the general-relativity-tests such as bending of light near a ...
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3answers
381 views

Given the Wikipedia notion of “arc length”, how is its manifestly real “signed variant” to be called and denoted?

I am dissatisfied with the presentation (not to say "definition") of "arc length", in its "Generalization to (pseudo-)Riemannian manifolds", as given in Wikipedia. (Who isn't?. But I'll sketch it here ...
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1answer
183 views

Why does the electric field escape a black hole? [duplicate]

An (unlikely) charged black hole can be described with the mass, angular momentum, charge and the thermal radiation. The reasoning behind the thermal radiation rests on the particle creation outside ...
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0answers
128 views

Questions about “geodesic path” and “arc length of a geodesic path” in the context of GTR and “Lorentzian manifolds”

I'd like to check my understanding of the notions "geodesic path" and "arc length of a geodesic path" in the context of GTR and "Lorentzian manifolds". Considering a set of "spacetime events", $\...
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1answer
355 views

Dirac operator in curved spacetime in 2 dimensions – hermitian?

I'm currently trying to learn about the Dirac equation in curved spacetime and have come across an odd remark in Nakahara's well-known textbook "Geometry, Topology and Physics" that I would like to ...
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0answers
226 views

Boyer–Lindquist coordinates

In the Kerr solution to the vacuum Einstein Equation written in Boyer–Lindquist coordinates. Because it is not spherical polar coordinates, $r$ ranges from 0 to infinity does not cover all the space, ...
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2answers
79 views

Bending of space vs. bending of a body - which is larger, and by what factor?

This is not homework, but is a problem I am asking myself. A long rod with known elastic material properties floats in flat space - suspended and kept in place by a number of massless ropes. Now we ...
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1answer
142 views

Different forms of the Einstein field equation

I am working my way through the wonderfully written introduction "General relativity for mathematicians" by Sachs & Wu. I am indeed a mathematics student and find this book to be well suited to ...
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1answer
81 views

Energy-Momentum Tensor with mixed indices

I know that $T_{\mu\nu}$ is the Energy-Momentum Tensor and $T=g^{\mu\nu}T_{\mu\nu}$, but does anyone know what $T^{\nu}_{\mu}$ is and how its calculated?
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2answers
240 views

Gravity as a particle-based force vs space-time warp

I'm interested to understand the interpretation of gravity as a result of exchange of force particles (ie gravitons) vs General Relativity-based warping of space-time. Related to this is while a ...
2
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1answer
538 views

Inverse Metric Tensor

First the setup: Let $\mathcal M$ be a $2$-dimensional manifold. Let $U_P$ be some open neighbourhood of a point $P \in \mathcal M$. Let $\mathcal F : U_P \rightarrow \mathbb R \times \mathbb R$ be ...
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1answer
152 views

Fastest way to find the curvature terms from a given metric [closed]

I want to find the spherically symmetric, static solutions to Einstein's equations $$ R_{\mu \nu} - \frac{1}{2}Rg_{\mu \nu} = 0 $$ in four dimensions using the metric $$ g_{\mu \nu}dx^{\mu}dx^{\nu} ...
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1answer
48 views

Calculation, radius of Saggriatus A* (SMBH) , Error in Wikipedia?

The parameter Schwarzschild Radius of Saggriatus A* is given in Wiki by 2.08×1015 (~0.2 ly) see in Parameters http://en.wikipedia.org/wiki/Schwarzschild_radius However, when I do the calculation ...
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2answers
97 views

If a theory gets two predictions right, how likely it is that the rest of the predictions are true too? [closed]

The question lucidly defines what I am trying to inquire, so there is no need to elucidate it any further. Another question would be, General/Special Relativity has gotten some predictions right as ...
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2answers
2k views

Why is spacetime not Riemannian?

I apologize if this is a naïve question. I'm a mathematician with, essentially, no upper-level physics knowledge. From the little I've read, it seems that spacetime is Lorentzian. Unfortunately, the ...
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1answer
70 views

Simple question about the electromagnetic tensor written as a 2-form

I noticed that the 2 form (Electromagnetic tensor) is written as: $$F= F^{ab}e^a \wedge e^b$$ while we know that $$F= F_{\mu\nu}dx^\mu \wedge dx^\nu$$ Is there something wrong with the indices ...
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0answers
98 views

Topology of a black hole

How many dimensions are theorized for a black hole, in view of the fact that black holes are not observed directly.
4
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1answer
64 views

For gravitational wave from twin stars, how was the tidal effect counted?

As the primary indirect evidence, the work on calculating the rotational slow down earned the 1993 Nobel prize. However, I cannot find any where mention how the work deal with the tidal effect. Are ...
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1answer
303 views

Is dark energy around a black hole locally curved?

The repartition of dark energy in the vacuum is homogeneous all over the universe. The diagram below represents space with a black hole in the middle. The square is divided in small unit squares. If ...
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1answer
99 views

What are the differences between special and general relativity? [duplicate]

What are the differences between special relativity and general relativity? I am looking for a naive, non-mathematical explanation.
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2answers
114 views

Pumping charged particles (of same charge) into a blackhole

Would would happen if you started pumping charged particles of same charge into a black hole? Let's assume that you have an infinite number of those charged particles. What will happen to the event ...
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1answer
1k views

Why does the Ricci tensor vanishes in Schwarzschild metric? [duplicate]

If the Schwarzschild metric is suppose to describe the behaviour of a spherical object in flat space, so the Schwarzschild is different from the flat metric because it describes curved space so why ...
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1answer
18 views

Replacing the flat part of ads metric with another flat metric.

In the poincare co-ordinate representation metric of the ads space has a flat part that corresponds to the minkowski metric. Can one show that this flat part can be replaced by other metric that ...
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0answers
165 views

If gravitational field has negative energy density, how does gravitational radiation carry positive energy?

The following question uses the analogy between EM (electromagnetism) and GM (gravitomagnetism). In order to force two like electric charges nearby, some work has to be done. This implies that the ...
4
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1answer
185 views

Is it, and if so, why, impossible to build perpetual motion machines (PMMs) in GR?

I am wondering about this. I have heard that in General Relativity (GR), the energy in a space-time may not be well-defined. If that is the case, then it would seem "conservation of energy" would not ...
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1answer
84 views

Wondering about Energy [duplicate]

Me and Energy I'm trying to move along with my study of non-advanced physics but not grasping what energy really is, is driving me nuts. Whenever i see anything about energy ( Kinetic, Potential,...
5
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2answers
400 views

Evidence for electrodynamics in curved spacetime

Field theories in curved spacetime is usually formulated by integrating their Lagrangian over the curved spacetime. For example, for electrodynamics, we have the action $$ S = \int d^4x \left( -\frac{...
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2answers
360 views

Is there an accepted axiomatic approach to general relativity?

I am reading Steven Weinberg's book Gravitation and Cosmology. He makes a big deal out of the equivalence principle and showed a bunch of deductions you can make based on it. This surprised me since ...
4
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1answer
195 views

Eddington-Finkelstein coordinates: Why $\ln(r-2m)$ instead of $\ln|r-2m|$?

If one considers the Schwarzschild metric $$ \text d s^2 = -V(r)\text d t^2 + \frac{1}{V(r)}\text d r^2 + r^2 \text d \Omega^2\;,\qquad V(r) = 1-\frac{2m}{r}\;, $$ and introduces the Eddington-...
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0answers
69 views

Would an Alcubierre drive actually allow FTL travel? [duplicate]

If I do not phrase this question right, please forgive me in advance because I am a layman on the subject of physics, but a software engineer, nonetheless. I do understand many technical subjects. ...
1
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1answer
319 views

Inertial and Non-inertial frames of reference

I'm really beginner in physics and I recently started to study the concept of frames of reference, inertial and non-inertial ones. In the end, I thought I had understood it: frames of reference ...
0
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1answer
97 views

Confusion about Weinberg's discussion of equivalence principle. Help understanding formula

I am reading Steven Weinberg's book Gravitation and Cosmology. On pages 67-68, he begins his discussion of the Principle of Equivalence of Gravitation and Indertia by saying the following: The ...
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2answers
92 views

Hermitian Metric and Geodesics

Why isn't general relativity developed with a Hermitian metric and a theory of complex valued paths and geodesics? The concept of arc length and geodesic suffers under a pseudo-Riemannian metric. My ...
2
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2answers
323 views

Recommendation on books with problems for general relativity?

I am reading Sean Carroll's book on GR and have read the first two chapters, which are on manifolds and differential geometry. However, there are only 12 problems for both chapters. In fact, there ...
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1answer
55 views

Invariance of the low energy effective string action

It is well known that the action of General Relativity $$S = \frac{1}{16\pi G}\int R\;\sqrt{-g} d^D X$$ is invariant under "diffeomorphisms". The low energy effective action for bosonic strings is $...
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0answers
241 views

Is Energy attracted to Energy?

Newton taught us that bodies with mass attract each other according to the universal law of gravitation (mass-mass attraction) and Einstein taught us that mass and energy are equivalent though his ...
2
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1answer
151 views

Doubt regarding stress-energy tensor definition

I'm having some trouble understanding the following definition of the stress energy tensor: $T^{\mu\nu}$ is the flux of four-momentum $p^{\mu}$ across a surface of constant $x^{\nu}$. Here's an ...
3
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3answers
346 views

It's established that universal energy is not constant. But is the net change positive or negative?

Dark energy is density is constant and that's something like 75% of the universe, so I am pretty sure that the net change must be positive. But photons redshift and so loose energy. I assume other ...
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0answers
128 views

What is static mass increase effect predicted by General relativity?

According to wikipedia, static mass increase is predicted by Einstein's General Relativity. In the book 'The Meaning of Relativity' by Einstein, inertia will increase when the object is near a ...
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0answers
37 views

Is energy-momentum of curvature a boundary/holographic density?

Since the beginnings of General Relativity, we have had this awkward, unholy separation of the universe in marble versus wood. divergence of the stress-energy momentum holds at all points of space-...
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0answers
90 views

Does the curvature of spacetime by gravity affect homogeneity and isotropy of the space of the universe?

The FLRW metric starts with the assumption of homogeneity and isotropy of space.(Wikipedia) FLRW metrics of the universe have no or only very weak curvature - It is curved space. In contrast, ...
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2answers
168 views

Gravity: Is there curved space besides curved spacetime?

Wikipedia: Curved spaces play an essential role in General Relativity where gravity is often visualized as curved space. Is the Wikipedia article "curved space" talking about curved space or ...
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0answers
37 views

Assigning an asymptotic power to the volume form?

I was reading about the covariant theory of asymptotic symmetries in this review: http://arxiv.org/abs/hep-th/0111246 I have a question about eq. (1.8), but before I ask I should describe what the ...
36
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5answers
7k views

Shine a beam of light horizontally, drop a stone from same height - would both hit the ground at the same time?

If a beam of light was shone horizontally, and simultaneously a stone was dropped from the same height, would they both hit the ground a the same time? Of course on Earth they would not, but let's ...
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1answer
396 views

Are the Jacobi equation and the geodesic deviation equation related?

On page 111 in his book Riemannian Geometry, Manfredo Do Carmo states what he calls the Jacobi equation \begin{equation} \frac{D^2J}{dt^2} + R(\gamma'(t),J(t))\gamma'(t) = 0 \end{equation} ...
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1answer
154 views

Stress-Energy Tensor Integral Identity [closed]

I'm attempting to work a problem in Schutz's A First Course in General Relativity, and I'm running into something curious with tensor indices. The problem states: Use the Identity $T^{\mu\nu}_{,\...