# Tag Info

Accepted

### Is the size of a black hole singularity smaller than a fundamental particle?

The very short answer to this is: We have no idea. General relativity predicts that the singularity of a Schwarzschild black hole (which I assume is what you mean by "actual black hole") is ...
• 1,906

### Is the size of a black hole singularity smaller than a fundamental particle?

While @paulina's answer: we don't know is correct, because quantum gravity is not understood, I'll answer for a classical Schwarzschild blackhole as described by Kip Thorne. The size is zero, however ...
• 35.4k

### Is the size of a black hole singularity smaller than a fundamental particle?

We know that black hole is infinitely densed. More exactly: The theory of general relativity predicts that the center of a black hole is infinitely dense. This theory predicts very well everything ...
• 40.1k
Accepted

### Two contradictory derivations of Killing equation

As an overall comment, I stress that conservation of $Q$ is valid for the Killing vector $\xi$ if the considered curve is a geodesic. Let us come to the issue. First of all, generally speaking, the ...
• 73.8k

### Two contradictory derivations of Killing equation

Both approaches are fine. In the first approach, the analysis is done at the coordinate/component level of the equations. Simply asking the question how does $Q$ very with $\tau$ if we write ...
• 12.4k
1 vote

### Hawking Temperature of the BTZ Black Hole

Another option for finding the Hawking temperature of the BTZ black hole is by the formalism of the surface gravity $\kappa$ which connected to the Hawking temperature via: $$T_H=\frac{\kappa}{2\pi}$$ ...
1 vote
Accepted

### Cause of Coordinate Acceleration in Free Fall

The acceleration on a particle following a geodesic is defined by the Christoffel symbols which are in turn defined in terms of the metric. More properly, all inertially-moving objects not affected by ...
• 596
1 vote

### Trying to understand a visualization of contravariant and covariant bases

Given the metric tensor for the basis vectors A = \begin{bmatrix}\mathbf e_1 \cdot \mathbf e_1 & \mathbf e_1 \cdot \mathbf e_2 \\ \mathbf e_2 \cdot \mathbf e_1 & \mathbf e_2 \cdot \mathbf ...
1 vote

### Two contradictory derivations of Killing equation

I think the problem lies in the notation. I guess Tong is treating the components $\xi_\mu$ as scalars for which we have $\frac{\mathrm{d}}{\mathrm{d}\tau}=u^\alpha\partial_\alpha$. And the ...
• 426
1 vote

### What is the gravitational field of a hole in an infinite perfect crystal?

... overdensity attracts underdensity and underdensity repels overdensity ... Yes, in an empty universe a pair of matched positive and negative masses initially at rest would be self-accelerating ...
• 15.8k

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