Universal charge-mass relation: From black holes to atomic nuclei

Abstract

The cosmic censorship hypothesis, introduced by Penrose forty years ago, is one of the corner stones of general relativity. This conjecture asserts that spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. The elimination of a black-hole horizon is ruled out by this principle because that would expose naked singularities to distant observers. We test the consistency of this prediction in a gedanken experiment in which a charged object is swallowed by a charged black hole. We find that the validity of the cosmic censorship conjecture requires the existence of a charge-mass bound of the form $q\le {\mu }^{2/3}{E}_c^{-1/3}$, where $q$ and $\mu$ are the charge and mass of the physical system respectively, and $E_c$ is the critical electric field for pair-production. Applying this bound to charged atomic nuclei, one finds an upper limit on the number $Z$ of protons in a nucleus of given mass number $A$: $Z\le Z^{\ast }={\alpha }^{-1/3}{A}^{2/3}$, where $\alpha =e^2/\hslash$ is the fine structure constant. We test the validity of this novel bound against the $(Z,A)$-relation of atomic nuclei as deduced from the Weizsäcker semi-empirical mass formula.

5 pages

References in corpus (14)

• Bohr's Correspondence Principle and The Area Spectrum of Quantum Black Holes
• Overcharging a Black Hole and Cosmic Censorship
• Weak Cosmic Censorship: As Strong as Ever
• Cosmic Censorship: As Strong As Ever
• Gravitational Collapse and Cosmic Censorship
• Cosmic Censorship, Area Theorem, and Self-Energy of Particles
• Best Approximation to a Reversible Process in Black-Hole Physics and the Area Spectrum of Spherical Black Holes
• Energy conservation for point particles undergoing radiation reaction
• Black hole polarization and new entropy bounds
• Return of the quantum cosmic censor
• Universal Charge-Radius Relation for Subatomic and Astrophysical Compact Objects
• Stability of the Black Hole Horizon and the Landau Ghost
• Cosmic Censorship: The Role of Quantum Gravity
• Black-Hole Polarization and Cosmic Censorship

Cited by in corpus (12)

• On charged boson stars
• Strong cosmic censorship in charged black-hole spacetimes: As strong as ever
• Cosmic Censorship: Formation of a Shielding Horizon Around a Fragile Horizon
• Charged massive scalar field configurations supported by a spherically symmetric charged reflecting shell
• The charged black-hole bomb: A lower bound on the charge-to-mass ratio of the explosive scalar field
• Marginally bound resonances of charged massive scalar fields in the background of a charged reflecting shell
• Slowly decaying resonances of charged massive scalar fields in the Reissner-Nordström black-hole spacetime
• Charge-mass ratio bound and optimization in the Parikh-Wilczek tunneling model of Hawking radiation
• Universal lower bound on orbital periods around central compact objects
• Hawking radiation as irreversible tunneling through self-interaction
• On a Nonlinear Newtonian Gravity and Charging a Black Hole
• The quantum mass gap of extremal black holes