We examine the effect of large extra dimensions on black hole seeded vacuum decay using the Randall-Sundrum model as a prototype for warped extra dimensions. We model the braneworld black hole by a tidal solution, and solve the Higgs equations of motion for the instanton on the brane. Remarkably, the action of the static instanton can be shown to be the difference in the bulk areas of the seed and remnant black holes, and we estimate these areas assuming the black holes are small compared to the bulk AdS radius. Comparing to the Hawking evaporation rate shows that small black hole seeds preferentially catalyse vacuum decay, thus extending our previous results to higher dimensional braneworld scenarios. The parameter ranges do not allow for Standard Model Higgs decay from collider black holes, but they can be relevant for cosmic ray collisions.

We study a critical limit in which asymptotically-AdS black holes develop maximal conical deficits and their horizons become non-compact. When applied to stationary rotating black holes this limit coincides with the "ultraspinning limit" and yields the Superentropic black holes whose entropy was derived recently and found to exceed the maximal possible bound imposed by the Reverse Isoperimetric Inequality [1,2]. To gain more insight into this peculiar result, we study this limit in the context of accelerated AdS black holes that have unequal deficits along the polar axes, hence the maximal deficit need not appear on both poles simultaneously. Surprisingly, we find that in the presence of acceleration, the critical limit becomes smooth, and is obtained simply by taking various upper bounds in the parameter space that we elucidate. The Critical black holes thus obtained have many common features with Superentropic black holes, but are manifestly not superentropic. This raises a concern as to whether Superentropic black holes actually are superentropic 1 . We argue that this may not be so and that the original conclusion is likely attributed to the degeneracy of the resulting first law.Keywords: black hole thermodynamics, accelerated black holes, reverse isoperimetric inequality 1 We use the upper case Superentropic to indicate the specific black hole solution, and lower case superentropic to indicate the property that entropy violates the Reverse Isoperimetric Inequality.

We examine the effect of large extra dimensions on vacuum decay in the Randall–Sundrum (RS) braneworld paradigm. We assume the scalar field is confined to the brane, and compute the probability for forming an “anti-de Sitter” (AdS) bubble inside a critical flat RS brane. We present the first full numerical solutions for the brane instanton considering two test potentials for the scalar field. We explore the geometrical impact of thin and thick bubble walls, and compute the instanton action in a range of cases. We conclude by commenting on a more physically realistic potential relevant for the Standard Model Higgs. For bubbles with large backreaction, the extra dimension has a dramatic effect on the tunnelling rate, however, for the weakly backreacting bubbles more relevant for realistic Standard Model potentials, the extra dimension has little impact.