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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Where does the energy of a photon trying to escape a black hole go?

I've heard "light cannot escape a black hole" explained several ways. One is that if a photon inside the event horizon tries to escape a black hole it loses energy to gravity. As it loses energy its ...
0
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0answers
19 views

How are negative energy orbits around a Black Hole defined?

I have read several times that within the ergosphere or a Kerr Black Hole, it is possible to have particles that have an orbital energy value of less than 0. However, I do not understand the concept ...
0
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1answer
77 views

At what speeds does time dilations start to occur?

My question is, is it possible for time dilation to occur at a speed less than that of speed of light?
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1answer
63 views

When and where to check the formal definition of a manifold

In most texts on GR we are first introduced to a formal and rigorous definition of a manifold. We then learn the point that in GR "any coordinate system" might be used for the 4D spacetime metric. ...
3
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1answer
37 views

$f^{\prime}(R)=0$ in $f(R)$ gravity

Suppose in a certain $f(R)$ gravity theory, $f^{\prime}(R)=0$ for some finite value of $R$. (e.g. let $f(R)=R+\alpha R^2$ with $\alpha<0$. $f^{\prime}(R)=0$ at $R=-\frac{1}{2\alpha}$.) Also ...
3
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2answers
586 views

Producing gravitational waves in labs

Can gravitational waves be created on very small region of vacuum with quadruple movement of atom or subatomic particles?
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1answer
83 views

Smallest thing ever measured and quantum mechanic bs [closed]

Is it possible to prove in 2016 that the universe is made up of more discrete units than say an atom or quark? What is the smallest thing we have been able to measure, like not theorize about, but ...
-3
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0answers
38 views

General theory of relativity proves beginning of the universe? [duplicate]

As I'm not a physics student, i only have some basic idea about how the theory works. As Hawking quoted in his book - "A brief history of time " Roger Penrose and I showed that Einstein’s ...
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3answers
60 views

Space time curvature and gravity [duplicate]

Is Space time curvature responsible for gravity or Gravity responsible for the curvature in space-time.
1
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1answer
46 views

Orthogonal of tangent vector in Rindler coordinates

For 2D space time from $(t,x)$ to $(u,v)$ the transformation are $$t = u \sinh(v)$$$$x=u\cosh(v)$$ Asking to show that two families of curves $u = \textrm{constant}$ and $v = \textrm{constant}$ ...
0
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0answers
38 views

Proper Distance and Coordinate Distance in General Relativity

When I started studying general relativity,I was told that the coordinate distance is not covariant and it does not have any physical meaning.I realized that only the proper length is the ...
3
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0answers
19 views

Israel-Wilson-Perjés Solutions

I'm searching for a reference that gives explicitly the field strength (or at least the gauge fields) of the Israel-Wilson-Perjés Solution, using complex harmonic functions for the metric. In ...
4
votes
2answers
114 views

Why is the covariant derivative of the determinant of the metric zero?

This question, metric determinant and its partial and covariant derivative, seems to indicate $$\nabla_a \sqrt{g}=0.$$ Why is this the case? I've always learned that $$\nabla_a f= \partial_a f,$$ ...
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0answers
25 views

Inequivalent matter actions with the same stress-energy tensor in general relativity

In general relativity, suppose as usual that we have the following action for the matter fields \begin{equation} S_{\mathrm{matter}} = \int_M d^4 x \sqrt{-g} L_{\mathrm{matter}} , \end{equation} ...
3
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1answer
23 views

What is a quasar flux ratio anomaly?

In the context of strongly lensed, multiply-imaged quasar observations, I sometimes hear about "flux ratio anomalies". What are these? Why are they important?
1
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0answers
36 views

Gravity Theory Question [closed]

Three Questions: Is the Modern Five Dimension Theory of gravity an adaptation of Einstein's relativity theory? If so, can it allow us to accurately predict the movement, speed and direction of ...
1
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0answers
23 views

Orbital period and velocity around a Kerr black hole relative to fixed stars

I've been trying to make progress on some of the smaller pieces of this question about the environment around a Kerr black hole. In order to calculate the effects of special relativistic Doppler shift ...
0
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1answer
58 views

Straight lines in general relativity

This question stems from a possibly misguided attempt to understand General Relativity. I am about to leave High school for college, I do however have a rudimentary understanding of tensors, and I ...
-1
votes
1answer
79 views

Black holes shouldn't really exist? [duplicate]

General relativity states that for an observer sufficiently far from the gravitational field of a blackhole, the space time geodesic nearr the event horizon is so long that we should never observe an ...
0
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1answer
58 views

Do Gravitational Waves disprove superluminal Alcubierre drive?

I am not a physicist. But... does the rate at which gravitational waves travel set an upper limit to the "speed" of a ship propelled with Alcubierre drive? Or does it present a relativistic trick ...
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0answers
24 views

How is time evolution done in numerical GR?

Suppose we're simulating what happens when a fairly massive object falls into a black hole. Say the object starts far away, so that the initial condition is that the metric is the Schwarzschild metric ...
1
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0answers
71 views

Euler-Lagrange equations in General Relativity

When obtaining the Euler Lagrange equations for a scalar field with higher order derivatives in curved space is it the same to use $$ -\partial_\nu\partial_\mu\frac{\partial \sqrt{-g} ...
3
votes
3answers
133 views

Do gravitational waves affect light?

Gravity "bends" light, predicted with theory of relativity and subsequently observed: how does gravity and gravitational waves achieve this effect, and shouldn't this effect be present wherever ...
1
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0answers
21 views

Why '1+log slicing condition' and 'Gamma Driver Shift Condition' were successful in black hole simulations?

The 1+log slicing and Gamma driver shift conditions are I want to know if there is a specific reason why these conditions were used most for Black Hole simulations in Numerical Relativty. And how ...
15
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0answers
144 views

Curvature Invariants in General Relativity and Singularities

Suppose that I want to check if a given metric is singular or not. I'm interested in curvature singularities, not coordinate singularities, so I can look to scalars made with Ricci, Riemann and Weyl ...
5
votes
4answers
96 views

Would time speed up near a large body of negative mass relative to observers in micro gravity?

Time tends to slow down near objects with large amounts of positive mass relative to observers in micro gravity. Considering that negative mass is the opposite of normal mass and would time tend to ...
2
votes
1answer
61 views

Why does the 'sticky bead argument' for (gravitational waves carrying energy) work?

Throughout much of the 20th century there was debate about whether Gravitational Waves were real, and whether or not they carrier energy and could be detected. It is often presented that Feynman's ...
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1answer
37 views

Causal structure, time orientability and equivalence classes

Quoting from this Wikipedia article, if $(M,g)$ is a Lorentzian manifold then the tangent vectors at each point in the manifold can be classified into three different types. Using a $(+,-,-,-)$ metric ...
1
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1answer
55 views

Does a singularity appear the instant a black hole is formed? [duplicate]

Imagine a very heavy (tens of solar masses) star in its final moments before collapsing to form a black hole. The gravitational force exerted by the weight of the star overcomes the neutron degeneracy ...
3
votes
1answer
77 views

Diffeomorphism invariance and geodesic action

I'm trying to understand the role of diffeomorphism and isometry invariance in the geodesic action in GR: $$ S = \int_{\tau_1}^{\tau_2} \! d\tau~ g_{ab}(x(\tau)) \frac{dx^a}{d\tau} \frac{dx^a}{d\tau} ...
5
votes
1answer
91 views

Proportionality Constant in Einstein Field Equations

The Einstein Field Equations: $$G_{ab}~=~8\pi T_{ab}.$$ I am familiar with how to obtain the $8\pi$ proportionality factor through correspondence with Newtonian gravity, but am wondering if this ...
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0answers
32 views

Force needed to hold particle at Killing horizon

I'm trying to understand the force required to hold a particle near the event horizon of a black hole. In particular I'm trying to fill in some details of Carroll's text around equations 6.15 to 6.17. ...
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0answers
37 views

Can Bose-Einstein Condensates reflect gravitational waves?

This is a question based on the paper by Raymond Chiao in 2002 where it is stated: One of the conceptual tensions between quantum mechanics (QM) and general relativity (GR) arises from the clash ...
3
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0answers
37 views

Can gravitational waves observed far from a black hole tell us anything about the multipole moments of a dynamical horizon?

In a paper by Ashtekar et al in 2013 on the approach to the final state to a stationary black hole they study the evolution of the multipole moments of dynamical horizons, which relax away (except for ...
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0answers
43 views

Gravity modeled by warping of spacetime or by field field theory?

I've recently read "Fields of Color" by Rodney Brooks who states that there are currently two ways of understanding the phenomenon of gravity. One involves a warping of 4D spacetime a la Einstein, ...
0
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1answer
75 views

Does a black hole really slow down time?

When an object gets pulled into a black hole it seems to slow and stop, but could it be possibly be because the speed of light that hit the object and came back was slowing down as the object got ...
4
votes
0answers
81 views

Can a rotating black hole have a donut-shaped event horizon? [closed]

It is conjectured that a rotating black hole has at its center a ring-shaped singularity. Thus, at the center of the ring-shaped singularity the gravitational field must be zero (similar to ...
-3
votes
0answers
40 views

Beyond gravitational waves- what now? [duplicate]

Now that the existence of gravitational waves has been established, what is the position regarding the incompatibility of general relativity and quantum mechanics in the creation of matter? Has this ...
6
votes
1answer
73 views

Signification of “finite but unbounded universe”?

I recently read Einstein's book about relativity and he says that his theory predicts the shape of the universe. It would be finite but unbounded. But how is this possible? What's the difference ...
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0answers
34 views

Does energy produce a gravitational force [duplicate]

$E=mc^2$. From this, I would assume that any form of energy (not just rest-mass energy, but kinetic energy as well) would produce a gravitational force. Am I being too naive in my application of ...
8
votes
1answer
143 views

Acceleration of particle “held in place” at $x = 1$ [closed]

The metric components in a two-dimensional spacetime are given in terms of the coordinates $(t, x)$ by$$ds^2 = -\cosh x\,dt^2 + dx^2.$$Consider a particle that is "held in position" at $x = 1$. What ...
4
votes
4answers
188 views

Distance in General relativity

I read a few lines about general relativity and one of the first equations is the one defining the eigentime of a time - like curve. But observers should also be able to measure length, right? So is ...
1
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0answers
45 views

Gauge invariance in gravitational field

I have read that the linearized equation for the metric fluctuations $h_{\mu\nu}$, namely: $$ \partial^2h^{\mu\nu}-\partial_{\alpha}(\partial^{\mu}h^{\nu\alpha}+\partial^{\nu}h^{\mu\alpha}) ...
0
votes
0answers
35 views

GR - curve (in)completeness & (in)extendibility

Seeking clarification of the distinction between completeness of geodesics/extendibility of curves in GR spacetimes? (Confirm: not the geodesic completeness of a spacetime but the completeness of an ...
0
votes
1answer
54 views

Information from inside a black hole

Now I'm hardly a physicist, but I am pretty interested in it. I was thinking about black holes and the movie Interstellar, and if you've seen it, then one of the central points about it is that they ...
1
vote
0answers
60 views

Relation between second covariant derivative of Killing vector and Riemann tensor [closed]

I need to prove that $$D_\mu D_\nu \xi^\alpha = - R^\alpha_{\mu\nu\beta} \xi^\beta$$ where D is covariant derivative and R is Riemann tensor. $\xi$ is a Killing vector. I have proved that $$D_\mu ...
0
votes
0answers
35 views

Help needed to understand Kerr coordinate transformation

The (uncharged) Kerr metric for a black hole of mass $M$ and angular momentum $Ma$ takes the form $$ds^{2} = \Sigma\Big(\frac{dr^{2}}{\Delta} + d\theta^{2}\Big) + (r^{2} + a^{2})\text{sin}^{2}\theta ...
1
vote
1answer
57 views

Rotational relativity? Is there an universal frame of reference for rotation?

So, there is obviously no such thing as an universal frame of reference for velocity. According to the relativity theory, there is no difference between two observers moving with respect to each ...
1
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1answer
22 views

Deriving Electromagnetism energy-stress tensor in GR [closed]

Please find the mistake in the following calculations. We have $L=-F^{\mu\nu}F_{\mu\nu}$, and try to derive the energy-stress tensor using $\delta(-g)^{1/2}=\frac{1}{2}(-g)^{1/2}g^{\mu\nu}\delta ...
6
votes
1answer
106 views

Two “Robertson-Walker observers,” velocity of baseball as seen by second observer right before it's caught?

The spacetime metric of a spatially flat ($k = 0$) radiation dominated FLRW universe is given by$$ds^2 = -dT^2 + T[dx^2 + dy^2 + dz^2].$$Consider two "Robertson-Walker observers," i.e., observers with ...