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The Stochastic Charge Effect for Asteroid-Mass Primordial Black Holes From Quantum Electrodynamics

Vasquez, Gabriel Alejandro
http://orcid.org/0000-0003-2635-503X
http://rave.ohiolink.edu/etdc/view?acc_num=osu1721483685206168

Abstract Details

2024, Doctor of Philosophy, Ohio State University, Physics.
Hawking radiation sets stringent constraints on Primordial Black Holes (PBHs) as a dark matter candidate in the M ~ 10 16 g regime based on the evaporation products such as photons, electrons, and positrons. This motivates the need for rigorous modeling of the Hawking emission spectrum. Using semi-classical arguments, Page [Phys. Rev. D 16, 2402 (1977)] showed that the emission of electrons and positrons is altered due to the black hole acquiring an equal and opposite charge to the emitted particle. The Poisson fluctuations of emitted particles cause the charge Z|e| to random walk, but since acquisition of charge increases the probability of the black hole emitting another charged particle of the same sign as the charge of the black hole, the walk is biased toward Z=0, and P(Z) approaches an equilibrium probability distribution with finite variance < Z2>. This thesis explores how this ``stochastic charge'' phenomenon arises from quantum electrodynamics (QED) on a Schwarzschild spacetime. We prove that (except for a small Fermi blocking term) the semi-classical variance < Z2> agrees with the variance of a quantum operator < 𝒵2>, where 𝒵 may be thought of as an ``atomic number'' that includes the black hole as well as charge near it (weighted by a factor of 2M/r). In QED, the fluctuations in < 𝒵2> do not arise from the black hole itself (whose charge remains fixed), but rather as a collective effect in the Hawking-emitted particles mediated by the long-range electromagnetic interaction. The rms charge < Z2> 1/2 asymptotes to 3.44 at small PBH masses M≲2x1016g, declining to 2.42 at M=5.2x1017g. Our construction also identifies which terms in the full QED Hamiltonian give rise to the stochastic charge effect, so that we can avoid ``double counting'' as we work toward a full calculation of the corrections to Hawking radiation at order O(α), where α ≈ 1/137 is the fine structure constant. As a secondary topic, we explore if resonances, quasi-bound states where the electron or positron is gravitationally bound to the black hole, alter the O(α) emission rate for both the photon and the electron/positron spectrum. We discovered transitions involving two resonant states, categorized colloquially as a bound-bound transition, are insignificant and are unable to be resolved when performing our integration across photon frequencies in order to derive the O(α) photon emission rate for dissipative interactions, processes that change the number of photons by one. We leave bound-free transitions, processes involving one resonant state and the other in a continuum, for future work. Additionally, we discovered the tunneling of resonant electrons and positrons through the potential barrier of the black hole plays a significant role towards altering the semi-classical electron and positron emission rate only for black holes within ~6x1021 MPlanck where MPlanck is the Planck mass. The next step of our work is to incorporate this absorption process and numerically calculate the change to the semi-classical emission rate as first derived by Page [Phys. Rev. D 16, 2402 (1977)].
Christopher Hirata (Advisor)
Eric Braaten (Committee Member)
Paul Martini (Committee Member)
John Beacom (Committee Member)
162 p.
Astrophysics; Physics

Recommended Citations

Citations

  • Vasquez, G. A. (2024). The Stochastic Charge Effect for Asteroid-Mass Primordial Black Holes From Quantum Electrodynamics [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1721483685206168

    APA Style (7th edition)

  • Vasquez, Gabriel. The Stochastic Charge Effect for Asteroid-Mass Primordial Black Holes From Quantum Electrodynamics. 2024. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1721483685206168.

    MLA Style (8th edition)

  • Vasquez, Gabriel. "The Stochastic Charge Effect for Asteroid-Mass Primordial Black Holes From Quantum Electrodynamics." Doctoral dissertation, Ohio State University, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=osu1721483685206168

    Chicago Manual of Style (17th edition)

osu1721483685206168
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© 2024, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.