A new spin on the Weak Gravity Conjecture

Abstract

The mild form of the Weak Gravity Conjecture states that quantum or higher-derivative corrections should decrease the mass of large extremal charged black holes at fixed charge. This allows extremal black holes to decay, unless protected by a symmetry (such as supersymmetry). We reformulate this conjecture as an integrated condition on the effective stress tensor capturing the effect of quantum or higher-derivative corrections. In addition to charged black holes, we also consider rotating BTZ black holes and show that this condition is satisfied as a consequence of the c-theorem, proving a spinning version of the Weak Gravity Conjecture. We also apply our results to a five-dimensional boosted black string with higher-derivative corrections. The boosted black string has a BTZ×S2 near-horizon geometry and, after Kaluza-Klein reduction, describes a four-dimensional charged black hole. Combining the spinning and charged Weak Gravity Conjecture we obtain positivity bounds on the five-dimensional Wilson coefficients that are stronger than those obtained from charged black holes alone.

QED positivity bounds

“…In practice, for our considerations it is better to utilize the improved positivity bounds since the former is dominated by the branch put at 4m 2 and the latter at a much higher scale. These bounds can be motivated on entropic grounds [44][45][46][47] or in other setups [48][49][50][51]. Recently, the procedure of applying directly the positivity bounds to the t-channel removed amplitude was argued to be justified by a compactification argument in [42].…”

Extremal bifurcations of rotating AdS4 black holes

“…The work of [41][42][43][44] implies now that there exists a quantum-corrected black hole with the same mass and angular momentum as the small, "exotic" black hole we have considered, but with a still higher entropy. Taking all this together, we conclude that there is no thermodynamic obstruction to the bifurcation of extremal AdS 4 -Kerr-Newman black holes to a pair consisting of a "survivor", together with this quantum-corrected black hole.…”

“…We will show that this is always so. It follows that, since including the effect of higherdimension operators increases the entropy [41][42][43][44] relative to classical expectations, the second law ensures that, if the conjectured decay channel for the original black hole exists, that black hole will always decay through the emission of a quantum-corrected black hole. This is so even when the original black hole is so massive as to be "classical".…”

“…In short, the entropy of quantumcorrected black holes is "larger than expected", and of course this is welcome if one hopes to show, using the second law, that extremal bifurcation actually takes place. 4 However, while it is certainly important and encouraging that the entropy shift computed in [41][42][43][44] is "in the right direction, 5 " the actual value of the shift depends on Wilson JHEP12(2021)155 coefficients which are known only in principle. Therefore, even if we can construct an expression for the entropy of the quantum-corrected emitted black hole, as in [36,37], we will not be able to extract an explicit numerical value for it.…”

“…The calculations in[41][42][43] are concerned exclusively with (AdS)-Reissner-Nordström black holes. However, the entropy shift is positive also when the emitted object is AdS4-Kerr and has a smaller mass than classical Censorship allows in that case: see[44] 5. See however[45]; work remains to be done before one can claim that the WGC is fully understood in the string-theoretic embedding, particularly for rotating black holes.…”