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Results tagged with black-holes
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user 336260
A black hole is a region of spacetime from which nothing can escape. More formally, the future light cone of any observer within the black hole is completely contained in the black hole, and the black hole region is not within the past light cone of any observer that goes to spatial infinity in an infinite amount of time.
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Carter-Robinson Theorem
There are uniqueness theorems that classify Black holes according to its mass, angular momentum and charge. One of the theorem is Carter-Robinson theorem which has many assumptions and then it says ax …
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Angular velocity of stationary observer
I am studying Kerr metric in Boyer Lindquist coordinates and having trouble in understanding the components of angular velocity of stationary observer with constant r and $\theta$ motion w.r.t externa …
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Past null horizon
What are past null horizons and future null horizons? Are they the same as past event horizons and future event horizons? The literature on Black Holes often uses these terms but I don’t get it. Pleas …
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Significance of simultaneous transformation of $t$ and $\phi$ in kerr metric
The Kerr metric in Boyer-Lindquist coordinate is invariant under simultaneous transformations $t \rightarrow -t$ and $\phi \rightarrow -\phi$ but not invariant if we apply one transformation only. Wha …
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How to derive Smarr formula for Kerr Black Hole?
Following is the Smarr formula for Kerr Black Hole
$$M=\frac{\kappa A}{4\pi}+2 \Omega J $$
where $\kappa, \Omega$, $J$ and $A$ are surface gravity, angular velocity, angular momentum and surface area …
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Why is the Einstein Field Equation relevant in the area theorem?
I am studying Area theorem and the first assumption is as follows :
If Einstein equation holds satisfy null energy condition...
I don't understand in general, what does it mean to satisfy Einstein e …
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End points of event horizon
I am reading The Nature of Space and Time by S. W. Hawking. In the last paragraph on page 16 he said that:
event horizon may have past end points but don't have any future end points
I understand th …
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Why domain of Kerr black hole includes negative values for $r$ coordinate?
I understand the domain of $t$ is all real numbers but mathematically, how to prove the domain of $r$ coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two dis …
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What are regular event horizons?
I am studying uniqueness theorems of Black Holes and I often see the word "regular event horizon" instead only event horizon. Many textbooks and literature do not define this term. Please explain what …
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Problem in deriving Killing equation
I am studying derivation of Killing equation by Wald (also reading some other literature) but having some problem in understanding the math.
Let $\chi ^a$ is killing vector on the horizon
$$\chi _{[a …
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