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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333 views

Infinitesimal transformations for a relativistic particle

The action of a free relativistic particles can be given by $$S=\frac{1}{2}\int d\tau \left(e^{-1}(\tau)g_{\mu\nu}(X)X^\mu(\tau)X^\nu(\tau)-e(\tau)m^2\right).$$ If we then make an infinitesimal ...
3
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1answer
126 views

Distance between two galaxies of different redshift

Let $Q_1$ and $Q_2$ two different objects in the Universe (we can think to two galaxies or quasars), that we observe from the Earth at different angular position $(\alpha_1,\delta_1)$, ...
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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.
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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 ...
2
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1answer
74 views

What is the utility of ADM decomposition of the space-time metric?

I know it's one of the possibility of quantization of gravitational field's degree of freedom but it is introduced also in other situation. My question is what is the use for this kind of ...
5
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2answers
267 views

Non-trivial scalar quantity

Is there any scalar quantity made of only the Christoffel symbols, determinant of a metric and tensors, not derivatives? In other words, can we construct a scalar quantity which cannot be written in ...
6
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2answers
383 views

Wave packet in curved spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
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2answers
100 views

Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?
2
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1answer
121 views

Two spherically symmetric shells of matter collapsing into a black hole

Suppose I have a thin spherically symmetric shell of matter of (rest) mass $M$ that collapses to form a black hole, and later a second thin spherical shell of mass (rest) $M'$, concentric to the ...
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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} ...
14
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1answer
232 views

What happened to the black hole firewall theory?

What happened to the black hole firewall theory? Back in 2012, some physicists apparently came up with strong evidence that one of three things must be wrong for black holes to work the way we thought ...
3
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1answer
24 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?
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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 ...
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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 ...
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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
60 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 ...
0
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1answer
59 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 ...
10
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1answer
365 views

How long can a particle survive inside of the horizon of a black hole?

By examining the causal structure of a Schwarzschild black hole, one can see that a particle in region II is unable to escape to $r=\infty$. Such diagrams do not show, however, how long a particle ...
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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 ...
10
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1answer
365 views

Would warp bubbles emit gravitational Cerenkov radiation in general relativity?

Inspired by the gravtiomagnetic analogy, I would expect that just as a charged tachyon would emit normal (electromagetic) Cerenkov radiation, any mass-carrying warp drive would emit gravitational ...
3
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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 ...
5
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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 ...
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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} ...
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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 ...
2
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1answer
64 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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0answers
147 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 ...
2
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1answer
194 views

Deriving the Poisson bracket relation of the Ashtekar variables

I'm trying to figure out how to calculate the orthogonality of Ashtekar variables with respect to the ADM hypersurface metric and conjugate momentum. $$\{{A_a}^i(x), {E^b}_j(y)\} = 8 \pi \beta ...
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3answers
747 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
0
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1answer
38 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 ...
5
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1answer
93 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
129 views

The integration of Einstein's equations [closed]

Einstein's equation is $$G_{\mu\nu} + \Lambda g_{\mu\nu} = {8 \pi G \over c^4} T_{\mu\nu}$$ where $G_{\mu\nu} = R_{\mu\nu} - (1/2)g_{\mu\nu}\,R$ is the Einstein tensor, which combines the Ricci ...
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1answer
2k views

General Relativity: Christoffel symbol identity

I want to show that $$\Gamma ^{\mu}_{\mu \nu}=\partial _\nu (\ln \sqrt{|g|}) .$$ (Here $|g|$ denotes the determinant of the metric.) Working out the left hand side:\begin{align} \Gamma ^{\mu}_{\mu ...
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2answers
934 views

Einstein Equation at the Singularity. Understanding the Dr. Michio Kaku's explanation

I'm trying to understand what Dr. Michio Kaku is exaplaining in this video: http://www.youtube.com/watch?v=hydDhUNvva8 I'm just able to rewrite this two equations. I think I've probably made ​​some ...
1
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1answer
143 views

Ernst potential from Kaluza-Klein reduction of axisymmetric space-time

Following appendix A of "Ergoregions in Magnetised Black Hole Spacetimes" by G. W. Gibbons, A. H. Mujtaba and C. N. Pope, starting from the Lagrangian $$\mathcal{L} = \hat{R} - ...
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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
39 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 ...
4
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1answer
79 views

What gauge field can be constructed from Lorentz symmetry?

You can take a global symmetry and promote it to a local gauge symmetry by introducing an appropriate gauge field and upgrading the partial derivative to a covariant derivative. The photon field ...
8
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1answer
1k views

Geometry inside the event horizon

I'm trying to understand intuitively the geometry as it would look to an observer entering the event horizon of a Schwarszchild black hole. I would appreciate any insights or corrections to the above. ...
4
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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 ...
0
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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, ...
1
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2answers
86 views

Difference between gravity and standing on a platform accelerating upwards at 9.81 m/s^2

So, according to Einstein's theory of general relativity, gravity is not a force instead it is a consequence of objects with mass deforming spacetime, right? And so, according to him, there is no ...
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 ...
2
votes
2answers
192 views

Why is the mass of a Kerr black hole proportional to its 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 ...
4
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4answers
189 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 ...
5
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1answer
196 views

The cosmological constant as a Lagrange multiplier?

The cosmological constant $\Lambda$ can be introduced into the gravitational action like this : \begin{equation} S = \frac{1}{2 \kappa} \int_{\Omega} (R - 2 \Lambda) \sqrt{-g} \; d^4 x + \text{matter ...
6
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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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4answers
3k views

Are neutrinos affected by gravity?

Layman here, but EE and BS physics. I know that light is affected by gravity. But are neutrinos? During the collapse of a star into a neutron star, as the electrons join protons to form neutrons ...