Questions tagged [reissner-nordstrom-metric]
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Interpretation of $t$ coordinate for charged black hole in Kerr-Schild form
In GP coordinates, the $t$ coordinate matches the proper time of a free-falling observer starting at infinity with zero velocity. Now consider the Reissner–Nordström metric in Kerr–Schild form:
$$ g_\...
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Extremal Reissner-Nordström Black Holes and the Third Law
I am thinking about a way to design a process which makes a extremal Reissner-Nordström black hole out of a non extremal one, i.e. it would violate the third law of black hole thermodynamics.
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Maximal analytic extension of Robinson-Bertotti geometry
I want to find a maximal analytic extension of the Robinson-Bertotti metric given by
$$ds^2 = - \lambda^2 dt^2 +Q^2 \frac{d\lambda^2}{\lambda^2}+Q^2d\Omega_{S^2}^2.$$
Where $Q$ is a constant charge ...
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Does the no-hair theorem apply to non-stationary spacetimes?
Carroll (pg. 238) gives the follow statement of the no-hair theorem:
Stationary, asymptotically flat black hole solutions to general relativity coupled to electromagnetism that are nonsingular ...
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1answer
66 views
Time dilation in the Reissner-Nordström metric [closed]
According to Wikipedia, the formula for gravitational time dilation in the vicinity of a charged mass is:
$$\varsigma = \sqrt{|g^{t t}|} = \sqrt{\frac{r^2}{Q^2+(r-2 M) r}}$$
However, if I plug in $M=...
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1answer
79 views
Mass distribution inside inner horizon of a charged black hole
I am trying to understand the spatial geometry inside the inner horizon of a charged black hole. I assume the charge accumulates exactly on the inner horizon (https://jila.colorado.edu/~ajsh/bh/rn....
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1answer
157 views
What is the electromagnetic 4-vector potential in Reissner-Nordström coordinates?
If you have the usual Reissner-Nordström metric of a charged black hole, is the electromagnetic potential of the black hole still:
$$A_0(r,\theta,\phi) = \frac{Q}{r}$$
in these units?
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69 views
Can a Black hole only have negative EM charge?
I understand that Black holes can have EM charge, they can have EM fields around them.
But is that possible that a black hole has more positrons and protons inside it (or that these have more EM ...
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1answer
294 views
Irreducible mass of a charged black hole merger
The irreducible mass $ \rm m_{irr} $ of a black hole with charge $ \rm Q $ is (in natural units)
$$ \rm m_{irr} = \frac{r_{+}}{2} = \frac{M}{2} + \sqrt{\frac{M^2}{4} - \frac{Q^2}{4}} $$
which is ...
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1answer
105 views
Imaginary charge on black hole
I was wondering if one can put an imaginary charge on a black hole. What I mean is, take a Reissner-Nordstörm black hole and make the charge $Q$ and therefore also the imaginary potential pure ...
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106 views
What is the reason for $g_{tt}g_{rr}=-1$?
Both Reissner Nordstrom and Schwarzschild solutions in GR exhibit the property that $g_{tt}g_{rr}=-1$.
What can we deduce from this property in terms of the gravitational field?
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On destroying the horizon of a Reissner-Nordstrom black hole
Consider a Reissner-Nordstrom black hole with $Q<M$, so that it has a well defined event horizon, the metric for such a black hole is given by (for $\theta=0, and ~d\phi=0$):
$$ds^{2}~=~-g(r)dt^{2}+...
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87 views
Naked Singularities Out of Extremal Black Holes?
Consider a pair of identical extremal black holes at rest. It is a fact that they exert no net force on each other and remain in static equilibrium. Now, clearly, each of the black holes is in ...
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1answer
788 views
Why Do Extremal Black Holes Not Radiate?
This might be a "metaphysical" question with no actual physics content and if such is the case then I apologize. Actually, to figure out whether or not it is an actual physics question is one of the ...
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1answer
197 views
Correlation between gravitational and electromagnetic radiation from collision of Kerr-Newman black holes
When black holes collide, they produce a gravitational wave, as has been recently established by LIGO.
When a charge is accelerated, it creates an electromagnetic wave.
Does an accelerated massive ...
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2answers
413 views
Does the Reissner Nordstrom Metric Necessarily Represent a Charged Black-hole?
The Reissner Nordstrom metric
$$ds^2 = - \bigg(1-\dfrac{2M}{r}+\dfrac{4\pi Q^2}{r^2}\bigg)dt^2 + \dfrac{1}{\bigg(1-\dfrac{2M}{r}+\dfrac{4\pi Q^2}{r^2}\bigg)} dr^2 + r^2 d\Omega_2^2 $$
is a solution ...
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Temperature of R-N Black Hole by Euclideanising the Metric [closed]
How to derive the temperature of the Reissner–Nordstrom black hole by euclideanising the metric?
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397 views
Would two Reissner-Nordstrom black holes with like charges repel or attract?
A few related side questions:
If the two oppositely-charged Reissner Nordstrom black holes collide
would their charge be negated and result in a regular Schwarzschild black hole?
Would a positively-...
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2answers
97 views
Is it possible to turn a RN black hole with real r+- into one with naked singularity?
Let's say we initially have a RN black hole that has $Q^2<M^2$ where $Q$ and $M$ are its charge and mass respectively. Now if a particle goes into the blackhole is it possible for the new charge ...
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407 views
Electromagnetic tensor trouble understanding
I'm running into trouble understanding what is going wrong, fooling around with the maxwell equations in tensor form, and playing with Cartesian and spherical coordinates.
To be more clear, I'm ...
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360 views
Einstein Maxwell Lagrangian
If I take the Lagrangian
\begin{eqnarray} L= \frac{1}{2} R *1 - \frac{1}{2} F\wedge *F
\end{eqnarray}
I found $$ds^2 = -(1-\frac{2M}{R} +\frac{Q^2}{2r^2} )dt^2 + (1-\frac{2M}{R} +\frac{Q^2}{2r^2}...
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Physical interpretation of the Reissner-Nordstrom metric for the special case
In the Reissner-Nordstrom metric
$$ \mathrm ds^2 = \left(1 - \frac{2GM}{r} + \frac{GQ^2}{4\pi\epsilon_0 r^2}\right)~\mathrm dt^2 - \left(1 - \frac{2GM}{r} + \frac{GQ^2}{4\pi\epsilon_0 r^2}\right)^{-1}...
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1answer
130 views
Does the cosmic censorship conjecture limit the charge/mass ratio for particles?
For charged black holes, supposing true the cosmic censorship conjecture, this inequality must be verified (in natural units):
$GM^2 > Q^2$
Where of course $M$ and $Q$ are the mass and charge of ...
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2answers
408 views
Does the charge of a black hole affect its space-time geometry?
Does a black-hole of a given mass and angular momentum have the same space-time geometry regardless of its charge? I'm pretty sure that an electric field can accelerate a charged particle but doesn't ...
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2answers
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Derivation for the temperature of Reissner-Nordström (charged) black hole
A lot of the text for this is from "How does one correctly interpret the behavior of the heat capacity of a charged black hole?" but this concerns a different question. The Reissner-Nordström black ...
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1answer
362 views
Physical interpretation of the Reissner-Nordstrom metric
The Reissner-Nordstrom metric (in spherical coordinates and c = 1) differs from the Schwarzschild metric in a additive term $$\frac{GQ^2}{4\pi\epsilon_0 r^2}$$, so the metric is
$$ds^2 = \left(1 - \...
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What is the difference between Reissner-Nordstrom (RN) black hole and dyonic black hole?
A RN black hole is a black hole with electric charge, and a dyonic black hole with both electric charge and magnetic charge.
My Questions:
Is the above statement correct?
Is the charges the unique ...
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3answers
567 views
Physical motivation for mathematically extending solutions to Einstein's equations
Sorry if this question gets a little long; I want to explain why I'm asking it.
The usual Schwarzchild metric
$$ds^2 = -\left(1-\frac{2M}{r}\right) dt^2 + \left(1-\frac{2M}{r}\right)^{-1} dr^2 + r^2(...
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What is unstable about the wormhole in the Reissner-Nordström solution?
In the conformal diagram for the Reissner-Nordström solution (included below), the inner horizon of the black hole leads to a wormhole which has a singularity, but it is possible to exit it through a ...
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329 views
Singularities in the Reissner–Nordström metric
I am doing a presentation on black holes but I'm having trouble finding information on the Reissner–Nordström metric. From the metric
$$\textrm{d}s^2=\left(1-\frac{R_S}{r}+\frac{R_Q^2}{r^2}\right)c^2\...
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1answer
208 views
EM Field tensor of a point charge [closed]
If I say the Reissner-Nordstrom metric
$$
ds^2=-\left(1-\frac{2m}{r}+\frac{e^2}{r^2}\right)\text d t^2 + \left( 1-\frac{2m}{r}+\frac{e^2}{r^2}\right)^{-1}\text d r^2 + r^2 \text d \Omega^2
$$
is the ...
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353 views
Reissner-Nordström Black Holes
The Reissner-Nordström black holes are described by the metric,
\begin{align}
ds^2 = -\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\right)dt^2 + \frac{1}{1-\frac{2M}{r}+\frac{Q^2}{r^2}}+r^2d\Omega^2
\end{...
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Do black holes have charges?
Do black holes have charges? If so, how would they be measured? Also, does electricity behave the same way? Black holes affect photons, which are carriers of EM radiation, so do black holes have any ...
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Diving into a charged (Reissner-Nordstrom) Black hole
Apparently there are two event horizons in this type of black hole, where the second one is known as the Cauchy horizon. According to Carroll, if you go into the first one, you will fall until you ...
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Can a nearly-extremal black hole be stable against Schwinger vacuum breakdown?
I was doing some basic algebra to estimate the range of possible masses $M$ and electric charge $Q$ for a nearly extremal Reissner-Noström black hole. I want to see if the logic is correct
the ...
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2answers
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Is the Hawking radiation of a charged black hole thermal?
Suppose you have a Schwarzschild black hole of mass $M$ and angular parameter $a = 0$ (no rotation).
Question: is it possible to throw a charge $Q$ at a faster rate than it will be re-radiated? Will ...
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2answers
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What role does electrical charge play in black holes?
Not having studied General Relativity, I have sometimes been puzzled by references to the behaviour for "classic" black holes — as they are popularly portrayed — as being true for black ...
