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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Does the Komar mass density act like a four density?

The Komar mass is a means of measuring gravitational mass in spacetime. Via Wikipedia (https://en.wikipedia.org/wiki/Komar_mass) it is stated as (for a stationary metric): $$m=\int\rho d\mathrm{vol}=\...
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2answers
46 views

Space-Time Geometry that shortens time intervals?

So we've all heard of the concept of time dilation and length contraction (from both general and special relativity). Suppose we work with a metric of a black hole, and person A is far, far away and ...
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2answers
57 views

How can I slow down? Or, How can I speed up time? Reverse twin paradox

Everyone know the standard Twin Paradox. I have my clock synchronized here on Earth with my twin. I leave Earth, Travel for a time at 0.9c, turn around, come back at .9c and then my clock is slow ...
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57 views

On the definition of Lagrangian

I have a question about "the definition of Lagrangian" in spacetime manifold. In general relativity, the energy-stress tensor and the vacuum energy stress tensor can be written as below: $$T_{\nu\mu}=...
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1answer
56 views

What is the intuitive concept of the action of a relativistic point particle? [duplicate]

The action of a relativistic point particle is its negative rest energy along its worldline, the parameter being its own proper time. $$ S = - mc^2 \int d\tau $$ (see Wikipedia) Action is energy ...
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23 views

Why the action of a relativistic point particle is considered to be negative? [duplicate]

The action of a relativistic point particle is its negative rest energy along its worldline, the parameter being its own proper time. $$ S = - mc^2 \int d\tau $$ (see Wikipedia) Is there a ...
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4answers
785 views

Can general relativity be explained by equations describing a fabric of space embedded in a flat 5-dimensional Minkowski space?

Does such a set of equations exist or does our universe have an intrinsic curvature that can't be explained by an embedding in a flat Minkowski space of 1 higher dimension? Even if general relativity ...
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2answers
56 views

Does the expanding universe prove the theory of relativity wrong? [duplicate]

I recently read an article which said the the universe is expanding with a very high velocity, which is even a lot faster than the speed of light. So, doesn't this prove Einstein's theory wrong which ...
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1answer
55 views

Black Hole: mass density or energy density? [closed]

Recently, I read a quora post in which the OP asked the following question: Can a black hole be formed from accelerating a body and increasing its relativistic mass to the level of a Schwarzschild ...
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1answer
54 views

Effective Potential in General Relativity

I would like to clarify a concept about the Effective Potential in General Relativity when the kinetic energy term is not unitary. Suppose (in spherical coordinates) one has a generic line element of ...
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2answers
134 views

How exactly does string theory make general relativity and quantum mechanics compatible?

Correct me if I'm wrong, but the reason that quantum mechanics and general relativity are incompatible is because the quantum foam at Planck scales renders space-time discontinuous and doesn't allow ...
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78 views

Showing $m_I = m_g$ follows from the equivalence principle

The inertial mass of an object is defined as its resistance to acceleration by $\vec{F}_{net} = m_I\vec{a}$. The gravitational mass of an object is defined as the scaling of the gravitational force an ...
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58 views

Counting the number of linearly independent Killing vectors for some N-dimensional geometry of space

In symmetric spaces(for spacetimes of Einsteinian General Relativity) we would like to find the vector space of Killing vectors($\xi^{(n)}_\mu(x)$) for the given metric tensor($g_{\mu\nu})$ at some ...
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17 views

The “force” of gravity is an illusion: things follow geodesics in space-time warped by mass-energy - can other forces be explained by similar models? [duplicate]

As I understand it, the force of gravity between two objects is not really a force, but appears to be so. It behaves in such a way that the Newtonian force explanation works in many cases, but the ...
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2answers
77 views

Expanding Universe [closed]

So an expanding universe has the metric $$ds^2 = g_{\mu \nu} dx^\mu dx^\nu = -dt^2 + a(t) ( dr^2+r^2 d\Omega^2)$$ where $d\Omega^2 = d\theta^2 + \sin^2\theta d\varphi^2$ as the usual spherical ...
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2answers
72 views

What exactly is the relationship between gravity and acceleration?

I know that one of Einstein's key steps towards General Relativity was the realization that gravity and acceleration were related. I understand the free-falling elevator analogy, but the relationship ...
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0answers
15 views

Flat Universe and Evolving Geometry [duplicate]

I have heard in multiple locations that in the case of a flat universe, the universe is infinite. This seems to present multiple issues: a) If a flat universe were infinite, would would the space of ...
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2answers
48 views

Does the concept of curved spacetime for spatial distances hold only inside of the observable universe?

What is the spatial distance of two stars, if each of them is outside of the observable universe of the other? Even by the means of a thought experiment, we could not synchronize the two clocks of ...
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1answer
44 views

Time dilation along a curved path

I was thinking about Einstein's elevator, more specifically, a box, say with one side labeled A and the opposite labeled B. On side A, a laser sends pulses of light to side B at equal time intervals. ...
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4answers
125 views

Visualizing gravity

When you see graphics trying to help people visualize what gravity in Einstein's relativity "looks" like it will often be a mostly two-dimensional plane with a concave warp where a massive object is ...
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9 views

How to calculate the lensing amplification of the weak field images in schwartzchild metric?

In Strong field limit of black hole gravitational lensing, Bozza et al state (without proof) that the amplification of each weak field image is given by $$ \mu_{wfi}=\frac{1}{\beta}\sqrt{\frac{2\,D_{...
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50 views

Extrinsic Curvature variation

I have seen the post Explicit Variation of Gibbons-Hawking-York Boundary Term on variation of Gibbons-Hawking term, that was really helpful, however, I have problem evaluating $\delta K$ and getting ...
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27 views

Removing temperature from black hole

Suppose I take the metric of a three dimensional AdS-Schwarzschild black brane (Note not actually a black hole!): $ds^2 = \frac{L^2 dr^2}{r^2 W} + \frac{r^2}{L^2} \left[ - W dt^2 + dz^2 + dx^2 \right]...
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4answers
110 views

What's the definition of distance in curved space-time in general relativity?

While I'm learning general relativity, the definition of the distance really confuses me. For example, we observe the distance between the Earth and the Sun (usually by a transit of Venus), what does ...
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25 views

How dense is the material in the core of a black hole? [duplicate]

If I would like to find out the answer of this question, I get two different one: The material is collapsed into a tiny dot. This density is called planck density, and it is so dense, all of the ...
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18 views

Theory of relativity [duplicate]

I’ve been reading about Einstein’s Theory of Relativity, specifically the segment on gravity being explained as consequence of spacetime being curved by mass. I can understand the concept of object ...
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26 views

Black Hole mass

Where is the material that has past the event horizon of a black hole stored/kept? Does it become pure energy once it passes the event horizon? Does the singularity at the center of the black hole ...
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0answers
21 views

How to determine the three-velocity measured by a single observer?

In this question the issue of extracting the three-velocity of a test particle in some frame arose. The answer provided by @PaulT and in this paper (arXiv) seems to me to give rise to ambiguity when ...
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3answers
105 views

What is the connection between inertial/gravitational mass and relativity?

In Einstein/Infield 's The Evolution of Physics (32-35) the authors establish that inertial mass and gravitational mass are the same and then connect this to relativity.Throughout these pages I was ...
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1answer
49 views

Does fusion continue to happen as a star collapses into a black hole (beyond our view)?

I know that we can't actually see a black hole form, because of time dilation, and we would see a frozen image just before the final collapse past the event horizon, slowly redshifting to nothing... ...
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1answer
65 views

Computation of photon trajectory near a black hole [closed]

I've been given the task to represent the trajectory of a photon near a Schwarzschild Black hole. I've read the physics behind it, and I've derived the equation of photon orbit near a schwarzschild ...
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1answer
68 views

What is the difference between Quantum Gravity, Loop Quantum Gravity, Quantum Geometrodynamics, and Relativistic Quantum Mechanics? [closed]

What is the difference between Quantum Gravity, Loop Quantum Gravity, Quantum Geometrodynamics, and Relativistic Quantum Mechanics? As far as I know, they are all theories made to unify QM and GR. But ...
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1answer
61 views

Form of the geodesic equation

I have been studying the basics of general relativity with Hartle's Gravity. He presents the geodesic equation as $$ \frac{d^2x^{{\mu}}}{ds^2}=-{\Gamma}^{{\mu}}_{{\alpha}{\beta}}\frac{dx^{{\alpha}}}{...
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28 views

Capacitors in space [closed]

I'm new here and I have a question for all of you. What happens to a capacitor in open space? There are different kind of them, which one of these is better to use there? And... We know that if we ...
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0answers
38 views

Acting for a covariant derivative on charged spinor [closed]

For field, theory what i know $i.e$,complex scalar QED \begin{align} D_\mu \phi = \partial_{\mu} \phi - i Q A_{\mu} \phi \end{align} and \begin{align} D_\mu \phi^{\dagger} = \partial_{\mu} \phi^{\...
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2answers
371 views

Photon pair production at relativistic speeds?

This is probably an obvious question, but I don't see it answered anywhere. Imagine we have an object in the Universe that is traveling, relative to the Milkyway at about .99999999999999999999999999c ...
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2answers
85 views

Can a black hole fall into another black hole's innermost stable orbit?

Can a black hole, in principle, fall into another black hole's innermost stable circular orbit?
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0answers
28 views

Fast moving black hole with low rest mass [duplicate]

Sorry for probably very stupid questions but.. If the massive body with small mass (one of the twins, for example) accelerates until the speed close to the speed of light, the mass of this body as ...
4
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3answers
140 views

Textbook on Differential Geometry for General Relativity [duplicate]

I'm going to start self-studying General Relativity from Sean Caroll's Spacetime and Geometry: An Introduction to General Relativity. I'd like to have a textbook on Differential Geometry/Calculus on ...
3
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1answer
47 views

Can an inhabitant of a spacetime region measure its curvature tensor?

So, lets say that I am an ant living on a 2-D spherical surface that is stretching to the equator...like half a sphere. I can not describe this surface in terms of the outside coordinates only someone ...
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2answers
51 views

Local frame of reference

I am currently simulating particle trajectories in Kerr spacetime numerically with $M=1$ and $a=1$. In the picture above, I am calculating the geodesic in Boyer-Lindquist coordinates. I was messing ...
3
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1answer
114 views

Geometrical point of view of the harmonic constraints ($\Delta g_{ij}=0$) in General Relativity

What does it mean, from the geometrical point of view, use (in General Relativity) of the constraints on the metric tensor's coefficients such that $\Delta g_{ij}=0$? (where $\Delta$ is the Beltrami-...
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0answers
56 views

Hughston, Todd General Relativity Problem 5.2

Hey everyone I am trying to solve the following problem in Hughston Tod: A manifold is endowed with a connection such that $$(\nabla_a\nabla_b-\nabla_b\nabla_a)V_c=T^d_{ab}\nabla_d V_c $$ For any ...
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0answers
21 views

Difference or relation between ADM mass, Brown-York Quasi-local mass, Komar mass

Can you give me some explanations for difference or relation between ADM mass, Quasi-Local mass and Komar mass? What i know about is there is some relation between ADM mass and Quasi-local mass. (i....
2
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1answer
50 views

Nambu-Goto and Polyakov Actions

This might be a little bit of a technical question, so bear with me. Ok, so from string theory we know that the action for a relativistic string is found from the worldsheet when we embed the string ...
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113 views

Metric transformation, polygons and gravitons

I'm trying to understand the paper by Hitchin called: ''Polygons and gravitons". I'm stuck at page 471. At this point, he does some computations and obtains a metric: $$ \gamma dz d\bar{z}+\...
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1answer
62 views

Position / velocity / acceleration vs time graphs when falling towards a black hole

In Newtonian physics, as far as I understand it, for a small object falling towards a massive object, the graphs of position, speed and acceleration vs time look like this: (If the massive object ...
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1answer
50 views

Can molecules/atoms/any subatomic particle cause space time curvature?

Space-time curvature is caused by huge objects in space like black holes, merging black holes, or planets. This curvature is what causes gravity. Can molecules cause at least a really tiny curve ?
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136 views

View of the sky from inside a black hole

Consider an observer located at radius $r_o$ from a Schwarzschild black hole of radius $r_s$. The observer may be inside the event horizon ($r_o < r_s$). Suppose the observer receives a light ray ...
5
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Confusion with conclusion to positive mass theorem

I am trying to understand the positive mass theorem as it is presented in the survey paper by Corvino and Pollack http://arxiv.org/abs/1102.5050 I am fundamentally confused by the structure of their ...