weak gravity conjecture

black hole spacetimes | vanishing angular momentum | positive angular momentum |
---|---|---|

vanishing charge | Schwarzschild spacetime | Kerr spacetime |

positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |

The *weak gravity conjecture* is a conjecture (Arkani-Hamed, Motl, Nicolis, Vafa 06) often summarized as saying that for gravity or quantum gravity to be consistent, the force of the field gravity must be weaker than that of any of the gauge field forces, in suitable units.

More precisely, what is argued in (AH-M-N-V 06, section 2) is that there alwayst must be “elementary particles” for which the ratio $m/{\vert q\vert}$ of their mass over their gauge field charge (e.g. electric charge, magnetic charge) is smaller than one: $m/{\vert q\vert} \lt 1$ (in natural units).

The argument for this in (AH-M-N-V 06, section 2.2) is the following. The extremal (BPS state) bound for charged black holes is that their mass $M$ *exceeds or equals* their charge ${\vert Q\vert}$, $M/{\vert Q\vert} \geq 1$. Now via black hole radiation any black hole is supposed to eventually decay by radiating away elementary particle quanta. If there were no elementary particle with $m/{\vert q\vert} \leq 1$, so the argument goes, then by radiating away particles with $m/{\vert q\vert} \gt 1$ the black hole would eventually lose all its mass, while still having some non-vanishing charge left. But such “black hole remnants” have been argued to lead to inconsistency (Susskind 96)

The weak gravity conjecture was originally motivated from string theory, which is argued to validate the “weak gravity” assumption.

In (AH-M-N-V 06, section 4) it is argued that the closed superstring excitattion states in heterotic string theory KK-compactified on to 4d satisfy the condition $m/{\vert q\vert} \lt 1$:

In 2015 Cumrun Vafa has argued that the weak gravity conjecture implies the cosmic censorship hypothesis: The latter turns out to be generally false, even in in 4 dimensions (Crisford-Santos 17), but there are arguments that configurations violating it also violate the assumption of “weak gravity”.

Subsequent calculations by Santos and Crisford supported Vafa’s hunch; the simulations they’re running now could verify that naked singularities become cloaked in black holes right at the point where gravity becomes the weakest force. (Wolchover, June 20 2017)

The statement is due to

- Nima Arkani-Hamed, Lubos Motl, Alberto Nicolis, Cumrun Vafa,
*The String Landscape, Black Holes and Gravity as the Weakest Force*, JHEP 0706:060,2007 (arXiv:hep-th/0601001)

with reference to arguments in

- Leonard Susskind,
*Trouble For Remnants*(arXiv:hep-th/9501106)

Further discussion includes

- Clifford Cheung, Junyu Liu, Grant N. Remmen,
*Proof of the Weak Gravity Conjecture from Black Hole Entropy*(arXiv:1801.08546)

Last revised on February 8, 2018 at 01:06:56. See the history of this page for a list of all contributions to it.