#### Title

Auto-stabilised Electron

#### Document Type

Article

#### Publication Date

11-12-2018

#### Keywords

fsc2020

#### Abstract

We include effects of self-gravitation in the self-interaction of single electrons with the electromagnetic field. When the effect of gravitation is included there is an inevitable cut-off of the k">kk-vector - the upper limit is finite. The inward pressure of the self-gravitating field balances the outward pressure of self-interaction. Both pressures are generated by self-interactions of the electron with two fields - the vacuum electromagnetic field and the self-induced gravitational field. Specifically we demonstrate that gravitational effects must be included to stabilize the electron. We use the Einstein equation to perform an exact calculation of the bare mass and electron radius. We find a close-form solution. We find the electron radius re=9.2α/4πℏG/c3=9.2α/4πlP≈10−36">re=9.2α/4π−−−−√ℏG/c3−−−−−√=9.2α/4π−−−−√lP≈10−36re=9.2α/4πℏG/c3=9.2α/4πlP≈10−36m, where ℓP=ℏG/c3">ℓP=ℏG/c3−−−−−√ℓP=ℏG/c3 is the Planck length educed from first principles. We find that the electromagnetic and gravitational fields merge at (8/3)α/4πℏc/G=(8/3)α/4π mP=1017">(8/3)α/4π−−−−√ℏc/G−−−−√=(8/3)α/4π−−−−√ mP=1017(8/3)α/4πℏc/G=(8/3)α/4π mP=1017 GeV in terms of the Planck mass mP">mPmP. The unified field depends on e">ee and G">GG alone, independent of ℏ">ℏℏ; the unified field is continuous. Renormalisation is accomplished by requiring continuity of the interior and exterior metrics at re">rere.

We include effects of self-gravitation in the self-interaction of single electrons with the electromagnetic field. When the effect of gravitation is included there is an inevitable cut-off of the k">kk-vector - the upper limit is finite. The inward pressure of the self-gravitating field balances the outward pressure of self-interaction. Both pressures are generated by self-interactions of the electron with two fields - the vacuum electromagnetic field and the self-induced gravitational field. Specifically we demonstrate that gravitational effects must be included to stabilize the electron. We use the Einstein equation to perform an exact calculation of the bare mass and electron radius. We find a close-form solution. We find the electron radius re=9.2α/4πℏG/c3=9.2α/4πlP≈10−36">re=9.2α/4π−−−−√ℏG/c3−−−−−√=9.2α/4π−−−−√lP≈10−36re=9.2α/4πℏG/c3=9.2α/4πlP≈10−36m, where ℓP=ℏG/c3">ℓP=ℏG/c3−−−−−√ℓP=ℏG/c3 is the Planck length educed from first principles. We find that the electromagnetic and gravitational fields merge at (8/3)α/4πℏc/G=(8/3)α/4π mP=1017">(8/3)α/4π−−−−√ℏc/G−−−−√=(8/3)α/4π−−−−√ mP=1017(8/3)α/4πℏc/G=(8/3)α/4π mP=1017 GeV in terms of the Planck mass mP">mPmP. The unified field depends on e">ee and G">GG alone, independent of ℏ">ℏℏ; the unified field is continuous. Renormalisation is accomplished by requiring continuity of the interior and exterior metrics at re">rere.

#### DOI

doi.org/10.1142/S0217751X20400242

#### Publication Information

Karim, Munawar (2018). "Auto-stabilised Electron." *International Journal of Modern Physics A *35.02n03.

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## Comments

This article is part of the SPECIAL ISSUE — Selected papers from the Tenth Alexander Friedmann International Seminar on Gravitation and Cosmology, Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg, Russia, 24–28 June 2019 Editors: V. M. Mostepanenko and E. N. Velichko.