Questions tagged [reissner-nordstrom-metric]

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What is $A'$ in the Reissner-Nordstrom metric?

So I was reading this paper on the Reissner-Nordstrom metric and on it they define $A$ as: But they don't define $A'$. Yet $A'$ still ends up in other equations like defining the Ricci tensors: So ...
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What unit of measurement are used for 𝑀 and 𝑟 in the Schwarzschild metric?

So I understand that đť‘€ in any metric solution stands for mass. But what unit of measurement do you use to define đť‘€?
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Does a charged particle respond to a charged black hole both gravitationally and electromagnetically?

The Reissner–Nordström metric is given by: $$ds^2= \Bigl( 1-\frac{r_s}{r}+\frac{r_Q^2}{r^2} \Bigr) c^2dt^2- \Bigl( 1-\frac{r_s}{r}+\frac{r_Q^2}{r^2} \Bigr)^{-1}dr^2-r^2d\Omega^2$$ Which is intuitive ...
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How is electric charge acting as a negative mass in general relativity?

In a NASA script on negative masses, there was the following statement: How is it understandable that, there, charge "acts negative on mass"? In general relativity, all kinds of energy ...
5 votes
2 answers
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Reissner–Nordström blackhole and irreducible mass

I'm learning the Reissner–Nordström metric and confused by the notion of irreducible mass $M_\text{irr}$. It is said that the "total mass" $M$ contains both the irreducible mass and the ...
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Question on Einstein Field Equations: charged black holes and fluids

Introduction Suppose then you're asked to find the metric of a charged black hole. Given a generic, static and spherically symmetric metric tensor, $\text{d}s^{2} = A(r)\text{d}t^{2} + B(r)\text{d}r^{...
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RN Black hole and an accelerated observer

If I use the spacetime geometry for the Reissner-Nordström case and try to see the black hole's effect on an accelerated charged observer nearby, can I use the covariant equation for a charge moving ...
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Are Reissner-Nordström black holes repulsive?

I'm not sure if I understand how the charged black holes work. The Reissner-Nordström metric is defined as $$ds^2=\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\right)dt^2-\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\...
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With how much energy can a charged black hole launch a electron away with?

Lets say with have a black hole with a strong negative charge, then a say a neutron falls towards it. Just before the neutron reaches the black hole's event horizon it undergoes beta decay, this ...
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Negative energy of infalling particle in a Reissner-Nordström black hole

If we have a Reissner-Nordström black hole with Q > 0, then what charge (positive or negative) must an infalling charged particle have in order for the particle to be able to obtain negative ...
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Why does a charged black hole affect the trajectories and event horizon for uncharged particles? [duplicate]

I can get electric charge affecting the behavior of quarks, charged leptons, W bosons, and photons since they interact electromagnetically. However, why would it affect uncharged particles like the ...
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How does the electric field of a Reissner-Nordstrom black hole exist outside its event horizon if nothing can escape the event horizon? [duplicate]

I am learning Reissner-Nordstrom black holes and I have learnt that the black hole contains a net charges. The static field due to it ( through the Energy Momentum tensor) exists even outside the ...
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How does Spherical Symmetry constraint the Components of the Vector Potential

I am a bit confused as to what form does the 4 vector potential and Electromagnetic field tensor $F_{\mu \nu}$ take in the presence of magnetic charges. I got confused in this while looking at the ...
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Why is trace of energy-momentum tensor not a good candidate for the source of gravity?

The reason why I think trace of energy-momentum tensor can't be the source is that, in a static weak field $p$<<$\rho$ $$T^{\mu}_{\mu} \approx T^{0}_{0} = -\rho$$ and if in one system I have ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...