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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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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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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155 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 ...
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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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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,...
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398 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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351 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 ...
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191 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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68 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. ...
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314 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 ...
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94 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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91 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 ...
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313 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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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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235 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 ...
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149 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 ...
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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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124 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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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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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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164 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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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 ...
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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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386 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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147 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}_{,\...
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115 views

White Hole Formation [duplicate]

How does a white hole form in nature if it were to exist? No knowledge of general relativity or advanced mathematics but doing a researching a physics project and need a basic explanation.
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284 views

What am I missing in this thought experiment about a black hole?

I've got a problem setting up a general relativity (GR) thought experiment. Thanks for your help! I'm the observer, in a lab that is falling through the event horizon of a black hole, observing a ...
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121 views

Definition of “nonlinear” in the context of perturbation of gravity

What exactly is the definition of a nonlinear perturbation when applied to a background spacetime metric? I have seen so called "linear perturbations" which look like $$ds^2 = -(1+2\Phi)dt^2 +a^2(1+...
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3answers
971 views

Are quantum mechanics and general relativity predictions of string theory, or were they built into the theory from the start?

Are quantum mechanics and general relativity predictions of string theory, or were they built into the theory from the start? If the former, why aren't tests of GR and QM considered simultaneous tests ...
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1answer
259 views

Spin connection and covariant derivative [closed]

How to prove explicitly (i.e., to don't postulate it) that by including Lorentz indices $a$ the covariant derivative $D_{\mu}$ looks like $$ D_{\mu}A^{\nu a} = \partial_{\mu}A^{\nu a} + \Gamma^{\nu}_{\...
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109 views

Hawking radiation (black hole evaporation) [duplicate]

I understand that one of the simplified ways of looking at Hawking radiation is a pair of virtual particles close to the event horizon (but outside of it). The particle with negative energy falls into ...
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159 views

Question on Einstein's derivation of the equation of the geodesic line?

While reading one of the original paper on general relativity written by Albert Einstein, titled the foundations of general relativity, I came across the following passage in pages 167-168, or pages ...
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100 views

What does this Hodge dual symbol $\star_3$ mean?

We know that in this $$\star {f(...)}$$ the $\star$ represents the Hodge dual. But in this: $\star_3 f(...)$ what does specifically the $\star_3$ symbol mean?
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How much of General relativity follows from the invariance of $c$ and an escape velocity?

Just supposing Einstein hadn't come up with his idea of the equivalence principle, leaving him blind for a while. Would he still have been able to come up with General Relativity just using the ...
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Schwarzschild Solution Convention

In looking at the components of the Schwarzschild Metric, one finds $ g_{00} = (1 - \frac{r_s}{r})c^2 $. Wikipedia states that $r$ is measured as the circumference, divided by $2π$, of a sphere ...
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Can a free falling observer localize the event horizon by calculations?

I'm think that in general relativity we can always pass the one curve in one coordinate system for another coordinate system. My intuition say that the free falling observer locate the event horizon ...
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Can a metric in General Relativity, Supergravity, String Theory, etc., be asymmetric?

Why is it that all problems I encountered until now have metrics that when represented in a matrix form turn out to be symmetric? Aren't there asymmetric matrices representing some metrics?
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Duality and 1 forms

How is a dual map defined if we are talking about partial derivatives and 1 forms?
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Is it correct to say that falling object are standing still?

As I was browsing youtube I came across the BBC video "Brian Cox visits the world's biggest vacuum chamber - Human Universe: Episode 4 Preview - BBC Two" He drops a bowling ball and a feather in a ...
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If a Killing vector field is timelike, can it be set to $\partial/\partial t$?

If one has a Killing vector that turned out to be a timelike Killing vector field because of negative norm. Can we set this Killing vector field equal to $\partial/\partial t$?
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Is $ds^2$ just a number or is it actually a quantity squared?

I originally thought $ds^2$ was the square of some number we call the spacetime interval. I thought this because Taylor and Wheeler treat it like the square of a quantity in their book Spacetime ...
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1answer
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Are the gravitational redshift and blueshift factors inverses of each other? [closed]

at a point in gravitational field assuming swcharzschild metric and the exact analysis. The other point in context is infinity. It would be helpful if you can provide citation/source of the answer/...
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1answer
156 views

Question about universe expansion

In general relativity, we cannot determine the global structure of the universe (since it is not flat), therefore all measurements and observations are only meaningful locally. In particular, we can ...
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50 views

Can someone clarify how many metrics exist that satisfy the EFEs?

As I currently understand it, there are two ways to work with the Einstein Field Equations: (1) exact solutions and (2) approximations that work under certain conditions. I also understand that ...
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3answers
233 views

Uniqueness or multiplicity of ADM masses for spacetime manifolds with more than one “end”?

The question is: What is the mathematical and/or physical basis for saying that a (static) spacetime manifold with more than one asymptotically flat region at infinity ("end") has a distinct ...
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157 views

What is the covariant basis around a Schwarzschild black hole? [closed]

First of all, I'm not interested in time for this question. So lets consider a 3-manifold whose metric is the spatial part of the Schwarzschild metric, so it has the event horizon and the singularity ...
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186 views

How does one calculate the full perihelion shift of Mercury, including perturbations from other planets?

I'm talking about the full calculation, including perturbations from other planets. I've seen the general relativistic correction done a half dozen times before, but I can't say that I've seen the ...
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Why do the Einstein field equations (EFE) involve the Ricci curvature tensor instead of Riemann curvature tensor?

I am just starting to learn general relativity. I don't understand why we use the Ricci curvature tensor. I thought the Riemann curvature tensor contains "more information" about the curvature. Why is ...
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How does Space-Time Cloak work?

Well, scientists have achieved Spacetime cloaking to make events fully disappear. Currently, it works only for a trillionth of a second, but here's real-world scenario from linked page: In theory, ...
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130 views

Relativity and Galaxy Rotation Speed

If time travels slower nearer gravity wells, why can't the galaxy rotation speeds being faster on the outer edges than the inner areas be explained by relativity? What necessitates dark matter?