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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Is curvature space-time has impact on the object geometry

When we have e.g. metallic cube of dimensions 1x1x1m and we put it on the space without gravitational force the cube has equal 1x1x1m and we can use Euclidean geometry. But when this cube move on ...
3
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1answer
62 views

S-duality of Einstein-Maxwell-Dilaton theory

Consider theory with action $$S = \int d^D x \sqrt{-g} (R - \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2k!} e^{a \phi} F^2 _{[k]} ) $$ where $\phi$ is dilaton and $F_{[k]}$ is ...
4
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2answers
87 views

Path Integral Quantization in General Relativity

In Ref. 1 I have seen that the action must contain only the first derivative of the metric as required by the path integral approach. I don't understand why. I mean why the path integral approach of ...
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0answers
15 views

How does curved space make an obejct move toward Earth? [duplicate]

I think I understand how the equivalence principle shows how light can bend and therefore space must be curved. What I do not understand is how curved space makes an object move directly toward the ...
4
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0answers
201 views

How does one determine if a spacetime is globally hyperbolic?

A spacetime $M$ is said to be globally hyperbolic if it is strongly causal and if the sets $J^+(p)\cap J^-(q)$, for all $p,q\in M$, are compact. (For more information, see the Wiki article on causal ...
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0answers
46 views

Why are symmetrical structures highly stable?

What makes symmetrical structures(geometry) highly stable? It is perfect to say that the forces acting on a symmetrical structure is balanced and hence stable. But why is it so? To be more specific, ...
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2answers
2k views

Does the existence of “gravitational waves” (assuming they exist) imply that time exists as a 4th dimension in the universe? [closed]

I'm new to thinking about special and general relativity and I have no formal training as a physicist. However, I've been doing a bit of thinking about spacetime recently. I was wondering if ...
3
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1answer
47 views

Frame dragging resulting in an orbital plane?

In astrophysics today we talked about spinning black holes, ring singularities, and frame dragging. Is this also (to some degree) the cause of the milky way being as flat as it is? Does the spin of ...
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0answers
64 views

What is the metric at the center of a star? [duplicate]

If there is only one star in the universe then is the metric at the center of the star flat?
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1answer
40 views

Vierbeins in General Relativty; degrees of freedom?

I am self-learning GR. I want to ask if vierbeins $e^b_{\ \ \nu}$ need to satisfy any relations or if I am free to choose any type of vierbein I like So I have been looking into tetrads again. I ...
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0answers
23 views

Relativistic mass increment [duplicate]

Is the mass increment with an increase absolute velocity of a body, a direct consequence of energy to mass conversion
2
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1answer
127 views

Quotient space in the book The Large scale structure of space-time

On page 79, the author states One is thus concerned only with $\mathbf{Z}$ modulo a component parallel to $\mathbf{V}$, i.e. only with the projection of $\mathbf{Z}$ at each point $q$ into the ...
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3answers
138 views

Is time unidirectional because of 4th spatial dimension? [closed]

We heard about an expanding universe. Consider an expanding sphere. Consider the surface of the sphere as our 3 dimensional universe. Can time dimension be the radius $R$ of this sphere? And because ...
0
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2answers
117 views

In what other fields of physics does “math break down”? [closed]

I've heard numerous articles and videos state that when it comes to black holes and singularities our "math breaks down". Is there any other areas in physics where math similarly "breaks down", where ...
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2answers
79 views

What are world lines as opposed to arbitrary curves in spacetime?

In GR the spacetime manifold is equipped with a metric which makes it a Lorentzian manifold. It is the metric that is doing the separation of space and time (so that we end up with three dimensions of ...
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1answer
44 views

Einstein's Principle of Equivalence - Infinite Acceleration/Energy?

Hello and thank you for your time. I've been wondering about Einstein's Equivalence Principle core idea. That is, from experiment alone, one cannot differentiate between a gravitational field and a ...
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0answers
22 views

A star starts at rest at infinity, how do you calculate the kinetic energy of the star when it crosses the event horizon of a black hole? [duplicate]

A star that begins very, very far away from a black hole (infinity) is brought in by the black hole's gravitational pull. How do you calculate the kinetic energy of the star as it passes the point ...
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1answer
54 views

Killing equation manipulation

Why does the killing equation $$K_{\mu;\nu}+ K_{\nu;\mu} = 0$$ equal $$K_{\mu,\nu}+ K_{\nu,\mu} -2\Gamma^{\rho}_{\mu\nu}K_{\rho} = 0 $$ when in general a covariant derivative $V_{\beta;\alpha} = ...
3
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1answer
128 views

Fermi-Propagated Jacobi equation in the book The Large scale structure of space-time

On page 81, equation (4.6), the author use the Fermi derivative to write the Jacobi equation \begin{equation} \tag{4.6} \frac{{D^2}_\text{F}}{\partial s^2} {}_{\bot}Z^a = ...
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0answers
24 views

Equation of state for a radiation fluid

Can anyone give me (point me to a reference of) a derivation of the equation of state for a radiation fluid: pressure = energy/3 Much thanks.
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1answer
94 views

The Lie derivative of the metric $g_{ab}$ and index notation

I don't quite know where to start this question. I'm essentially not understanding how to compute the Lie derivative of a given metric and vector. So I have the following definition: $$ ...
12
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3answers
1k views

How does gravity truly work? [duplicate]

I Am only 12 years old and I'm constantly wondering and trying understand how gravity really works. On YouTube everyone always talks about objects wrapping space time around themselves and uses the ...
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1answer
58 views

Extrinsic curvature components

I'm trying to understand how to derive the extrinsic curvature (in order to understand some calculation on fluid/gravity dynamics). But I hit a wall in my progress. I stuck at trying to verify the ...
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0answers
37 views

Gravity as a gauge theory - Cartan-Killing form?

First, let me state the form of Lagrangian for YM and GR \begin{align} L_{YM} = \alpha \textrm{tr}(F^2), \qquad L_{GR} = \beta R \end{align} I heard, YM is a gauge theory but GR isn't a really gauge ...
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1answer
157 views

Jacobi equation in the book The Large scale structure of space-time

On pp. 79, it is obvious that equation (4.2) \begin{equation} \frac{D}{\partial s}Z^a = {V^a}_{;\ b}Z^b \end{equation} holds, where $Z$ is the deviation vector and $V$ is the unit tangent vector along ...
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1answer
58 views

Does mass compress space-time?

My understanding of relativity explains that the presence of mass warps space-time so that light travelling through the warp follows at straight line but the warp itself is curved and therefore the ...
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3answers
217 views

How do we measure Schwarzschild coordinates?

In special relativity, we make a big fuss about setting up inertial frames of reference, and then constructing coordinate systems using networks of clocks and rulers. This gives an unambiguous ...
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3answers
159 views

Why is speed of light a constant while distance in space is not?

Disclaimer: I asked this at Astronomy.SE, but got no answer whatsoever, so I am trying my luck here. As you probably know current state-of-the art physics (i.e. gravitational waves, cosmic expansion) ...
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1answer
73 views

A question regarding $f(R)$ Lagrangians

Consider the class of Lagrangian known as $f(R)$ Lagrangians where the Lagrangian is some function $f(R)$, \begin{equation} S=\int\sqrt{g}d^4x\ f(R) \end{equation} assuming there are no (or ...
3
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0answers
32 views

Disappearing galaxies [duplicate]

According to the cosmological model of the expanding universe, the distant (diametrally opposite) galaxies have bigger and bigger relative comoving speed, and this speed (which is not a relative speed ...
3
votes
3answers
133 views

Is General Relativity compatible with relative speeds bigger than $c$ between two inertial frames?

My question is motivated by a remark done by Tegmark in his book "Our Mathematical Universe". He says that GRT does not prove that relative speeds between material points are always smaller than c. It ...
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1answer
53 views

Gravitational Waves and LIGO [closed]

Last month, we as a species did something remarkable. We detected the presence of gravitational waves. While we all are celebrating and excited about the newest discovery of mankind. I could use ...
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0answers
80 views

Absolute direction of time [closed]

As Universe is expanding into emptyness, we think that flow of time is forward. This means that expansion is directed forward in time. Even though we don't know for sure whether this expansion will be ...
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1answer
45 views

Since Alcubierre drive moves a flat region of space, does it mean that space acts lika a liquid? [closed]

The Alcubierre drive would move a patch of flat space through space and, leaving exotic matter aside, is mathematically correct. Does that means that space-time is not a "solid" lattice i.e. not ...
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0answers
47 views

Using geodesic deviation for freely falling particles when gravitational waves comes through

Suppose we have a gravitational wave which gives us the following metric $$ds^2=-dt^2+(1+h_+\cos(\omega(t-z)))dx^2+(1-h_+\cos(\omega(t-z)))dy^2+dz^2$$ I want to calculate the time it takes for a ...
0
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1answer
48 views

In General relativity, what is the meaning of flow of $x$ momentum in $x$ direction or pressure in $x$ direction? [duplicate]

I found this interesting paper on Arxiv devoted to explaining Einstein's field equations in simple English. The author, JC Baez, does this by considering a group of small spherical balls in ...
2
votes
1answer
86 views

How much the notion of force is discarded in modern physics? [closed]

Suppose that we are not allowed to use the notion of force to describe nature. My understanding of general relativity says that won't be a problem because the Einstein field equation doesn't involve ...
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0answers
57 views

Complex tetrad vs. Real metric

I asked this question almost a month ago on mathoverflow (http://mathoverflow.net/q/228138/) but received no response. I thought I could have better luck here: I have a question on the relationship ...
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0answers
29 views

Binary black hole system, near-field geodesics and post-newtonian formalism

I am interested in simulating the following system: Particle trajectory near one black hole (around 6-10 Schwarzschild radius) in the presence of another black hole (more than 50 Schwarzschild radius ...
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2answers
82 views

Standing wave on a circle [closed]

Suppose that we have a standing wave on a circle. I heard that by gradually increasing the radius of the circle, the wavelength will also increase to keep the standing wave. Is it right? If yes, ...
3
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0answers
26 views

Lense-Thirring Precession of short GRBs

Stone et al. 2014 have proposed that the jet resulting from the merger of a black hole (BH) and neutron star (NS) may precess due to Lense Thirring torques A large rotating mass e.g. the Earth, can ...
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0answers
54 views

Einstein's Equations [closed]

Can one please explain tensors, specifically stress energy tensors and its application in Einstein's Equations? I am a beginner cosmology learner and want to know the meaning and significance of ...
2
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2answers
73 views

Merging and Splitting of Black Holes [duplicate]

We know that two black holes can merge to form a single black hole with the release of vast amounts of energy. Can the reverse happen? That is can it happen that large energy is supplied to a black ...
3
votes
1answer
86 views

Is it possible to integrate a function over a null hypersurface?

For $f$ a compactly supported function on a spacetime $(\mathcal{M},g)$, one may define its integral over $\mathcal{M}$ by $$f\longmapsto \int_\mathcal{M}\star f,$$ where $\star$ is the Hodge star of ...
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0answers
106 views

Did the LIGO measure gravitomagnetic waves as well?

I think of gravitomagnetism as as the "magnetic" portion of gravity, with gravity being the "electric" portion. Since gravity ("electric") seems to affect space (which the LIGO could detect) what ...
3
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1answer
115 views

Effect of general relativity on Newton's second law

Let's say I have some object, like a long pole, that is 30 km long with non-zero mass $m$. One end is resting on the Earth's surface and it is sticking straight up, perpendicular to the surface. ...
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3answers
217 views

Two “devil's advocate” questions related to LIGO measurement results interpretation

"If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things." Rene Descartes Laymen like me typically refers to Wikipedia ...
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3answers
94 views

How is Space-Time produced? [closed]

The parable of the ant walking on the surface of a balloon tells us that as the balloon expands, more of surface is created, hence more place for the ant to walk. Space-Time is also in the same ...
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2answers
84 views

How do you know what kind of space(time) you have when solving the Einstein Field Equations?

I'm experimenting with the EFE, and I ''invented'' a metric; a diagonal non-zero metric, and I discovered that the Riemann tensors are equal to zero which implies the Einstein tensor $G_{mn}$ equals ...
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1answer
30 views

Is there energy density arising from expansion velocity?

I'm taking a first course in cosmology, and I'm having a conflict of intuitions when it comes to the relative motion of objects arising from the growth of the scale factor. Intuition 1: The growth of ...