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# Astrophysics/Hawking radiation on Kerr black hole

Question
Dear Mr. Stahl

I have already learn about hawking radiation (please correct me if i'm wrong). I have learnt that the pair creation of particles hold in event horizon. By the way it must be occurs also in Kerr (rotating) Black Hole. But as i know, this kind of black holes have two event horizon for positive and negative solution. So my question today:

Where exactly this pair creation proceed? In positive solution of event horizon or negative, or in ergoregion?

Thank you so much. Nice to see you

Ergosphere around a Ke
Hello,

First, I am not sure how much you already know. Are you taking a course on black holes, or simply pursuing this out of curiosity? Are you using some specific textbook? It would be good to know these things to know the level at which to address your questions.

I think when you refer to rotating Kerr holes and "two event horizons" you are referring to what manifests as a result of a process known as frame-dragging. We know that general relativity predicts that a rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. The effect is to produce a region of space-time called the "ergosphere".

For the case of the rotating Kerr black hole then, the effect is to produce an intermediary region with an outer boundary called the 'ergosurface' and an interior 'outer' event horizon. In other words, one arrives at an oblate spheroid shape with its "poles" coinciding with the event horizon proper, but wider and diverging about the equator. The crude diagram attached seeks to capture this.

A much mnore sophisticated diagram (which actually shows the inner and outer event horizon) can be found at the site below:

http://www.daviddarling.info/encyclopedia/E/ergosphere.html

I take your "positive" and "negative" solutions to refer to what are obtained from the outer and inner event horizons, respectively.

Now as to your question, the answer assumes you know or are somewhat familiar with "the Penrose process". In this process, 2 pre-existing particles exchange energy in the region called the ergosphere - which is exactly the shaded region I've indicated in my diagram. This is apart from either 'outer' or 'inner' event horizons and is the only region within which (macroscopic) masses of positive and negative energy can co-exist.

The process only applies to a rotating hole because, obviously, if the rotation were to somehow stop the ergosphere would cease to exist (i.e. no more frame dragging) and thence pair production would not occur.

In contrast, Hawking radiation (the phenomenon associated with black hole "evaporation" at the quantum level) can occur at the outer horizon itself - so can apply equally to a rotating (Kerr) or non-rotating black hole.

In this case, Hawking radiation, we apply the energy-time uncertainty principle, whereby:

(delta E) (delta t) >  h/ 2π

where h is the Planck constant of action.

Given quantum (vacuum) fluctuations of time on the order of 10^-44 or less pairs of particles can then appear for an instant as a result, with attendant energy such that:

(delta E) ~  (h/2π)/ (delta t) ~ (h/2π) / (10^-44 s)

In effect, paritcle-antiparticle pairs are thereby being created all the time and destroyed. The latter, i.e. destruction, is so very rapid that the pairs aren't visible at everyday scales of observation hence we give them the name "virtual pairs". But under the conditions at the (outer) horizon a virtual pair becomes a real pair.

Hopefully, you are able to follow this and it makes sense!
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Astrophysics

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#### Philip A. Stahl

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I specialize in stellar and solar astrophysics. Can answer questions pertaining to these areas, including: stellar structure and evolution, HR diagrams, binary systems, collapsars (black holes, neutron stars) stellar atmospheres and the spectroscopic analysis of stars – as well as the magnetohydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions. No nonsense questions accepted, i.e. pertaining to astrology, or 'UFOs' or overly speculative questions: 'traveling through or near black holes, worm holes, time travel etc. Absolutely NO questions based on the twaddle at this Canadian site: http://members.shaw.ca/warmbeach/FAQ.htm purporting to show a "new physics". Do not waste my time or yours by wasting bandwidith with reference to such bunkum.

##### Experience

Have constructed computerized stellar models; MHD research. Gave workshops in astrophysics (stellar spectroscopy, analysis) at Harry Bayley Observatory, Barbados. More than twenty years spent in solar physics research, including discovery of SID flares. Developed first ever consistent magnetic arcade model for solar flares incorporating energy dissipation and accumulation. Developed first ever loop-based solar flare model using double layers and incorporating cavity resonators. (Paper presented at Joint AGU/AAS Meeting in Baltimore, MD, May 1994)

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American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.

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Papers appearing in Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France). Books: 'Fundamentals of Solar Physics', 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level', 'Astronomy & Astrophysics: Notes, Problems and Solutions', 'Modern Physics: Notes, Problems and Solutions'

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B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.

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Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society. Barbados Astronomical Society award for service (1977-91) as Journal editor.

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Caribbean Examinations Council (as advisor, examiner), Barbados Astronomical Society (as Journal Editor 1977-91), Trinidad & Tobago Astronomical Society (as consultant on courses, methods of instruction, and guest speaker).