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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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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30 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 ...
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1answer
63 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 ...
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1answer
88 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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1answer
73 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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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 ...
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74 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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3answers
141 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 ...
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25 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 ...
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154 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 ...
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4answers
139 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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1answer
77 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
41 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 ...
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1answer
58 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 ...
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1answer
126 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} ...
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1answer
98 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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37 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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42 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 ...
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43 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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47 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, ...
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1answer
78 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 ...
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84 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 ...
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1answer
74 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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36 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 ...
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1answer
144 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 ...
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4answers
190 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 ...
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47 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}) ...
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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 ...
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1answer
57 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 ...
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0answers
65 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 ...
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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 ...
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1answer
65 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 ...
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1answer
27 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 ...
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1answer
129 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 ...
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2answers
203 views

Can you have black holes in your black holes?

Inspired by Are we inside a black hole?, can you have a black hole such that other black holes are in them? In particular, the event horizon of the larger black hole should completely enclose the ...
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2answers
110 views

Where do I begin in order to study relativity? [duplicate]

I am in high school now and I want to get the basic idea of what relativity. Can anyone suggest me a book or website for it? I am also curious about the mathematics behind it. Is it possible for me to ...
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1answer
43 views

Solving systems of equations using Levi-Civita and index notation?

I'm doing some self-studying out of Hughston and Tod's Introduction to General Relativity and I stumbled upon a few problems asking me to solve systems of equations using Levi-Civita and index ...
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19 views

Simple Question About Repulsive Potential Field Time Dilation

A space-time with a point mass gravitational potential given by $\Phi(r)$ has a metric described by, $$ds^2=-\left(1+\cfrac{2 \cdot \Phi(r)}{c^2} \right) \cdot c^2 \cdot dt^2+\left(1-\cfrac{2 \cdot ...
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1answer
74 views

Does Alcubierre drive allow time travel? [closed]

In Alcubierre drive, one can travel apparently faster than the speed of light by "compressing" space in front in the direction of travel. So let's say we have a stationary observer at point A, and an ...
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2answers
89 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 ...
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2answers
61 views

Wald's General Relativity, section 6.3 Page 144

I cannot understand how he reaches the conclusion in equation 6.3.36 and 6.3.37; even the terminology is somewhat confusing. This is a problem of bending of light under gravitational field. This is ...
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2answers
66 views

Power of blueshifted light falling on observer in circular orbit around Schwarzschild black hole

This answer explains that the time dilation for an observer in a circular orbit around a Schwarzschild black hole, relative to a distant observer at rest relative to the black hole, is given by the ...
3
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1answer
91 views

The dimension of the energy-momentum tensor and the Einstein-Hilbert action

I have been thinking recently what will happen if one uses the energy momentum tensor of the Dirac field as a source in the Einstein Field equations. It is well known that in this case $$ ...
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0answers
33 views

Einstein-Infeld-Hoffman-Lagrangian for a Test-Particle as Limit of Schwarzschild-Geodesic

Consider a test particle of mass $m$ which is in orbit around a spherical-symmetric body with mass $M$. It therefore has a position as described by the coordinates $r,\phi$, and its motion can be ...
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2answers
95 views

Are gravitational force and gravitational time dilation proportional?

Particles in gravitational fields are subject to gravitational time dilation. The closer a particle is near a gravitational source, the slower is running its clock. I would like to know more about the ...
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2answers
56 views

Bending of Light in General Relativity using Perturbation

It is standard textbook calculation (e.g. Schutz's First Course in General Relativity page 294) that we can find a total angular change in light deflection due to gravity to be ...
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1answer
241 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 ...
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1answer
47 views

Coordinate form of divergence of anti-symmetric tensor field [closed]

just a quick question on something that might save me a little bit of time and effort. In a general curved metric, the divergence of a vector field, $A^\mu$, can be written as: $ \nabla_\mu A^\mu = ...
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1answer
56 views

Classical Limit of Schwarzschild Metric

The orbit of a test particle orbiting a black hole can be described by the Lagrangian $$\mathcal{L} = -\frac{1}{2}\left(-\left(1-\frac{2 G m}{c^2 r}\right) \dot{t}^2 + \left(1-\frac{2 G m}{c^2 ...
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2answers
91 views

Gravity and spacetime bending [duplicate]

Something that puzzles me if gravity is just bending of space time near a mass then what is gravitational force? If say two massive bodies were perfectly at rest relative to each other they would ...