Particle/antiparticle annihilation problem near blackholes

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During the Big Bang, particle and antiparticle pairs formed and mostly annihilated, with a small fraction surviving to contribute to the universe's structure. At the event horizon of a black hole, virtual particles can escape as Hawking radiation, raising questions about energy conservation if a particle escapes without its antiparticle. The discussion explores whether this scenario necessitates changes in the properties of the black hole. It suggests that such anomalies could be represented using Feynman diagrams, linking the escaping particle to the black hole. The implications of these interactions on black hole characteristics and energy conservation remain a key focus.
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So around the time of the Big Bang, Particle and antiparticle pairs were created and annihilated. I believe one out of every 100 million(?) particle pairs actually didn't have an accompanying antiparticle, and survived the maelstrom, giving us the galaxies and stars we have today.

Now, at the EH of a black hole, where virtual particles escape from the black-hole as hawking radiation, if one of these anomalies occur, where the particle is able to escape, and have no antiparticle accompanying it, what properties of the black hole have to change in order to preserve the conservation of energy? Is there any change at all to the black hole?
 
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I think that what you call an anomaly should be described by a Feynman diagram. And that one of its legs should be linked to the BH.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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