Abstract

Abstract We investigate the phase space of multi-centered near-extremal configurations previously studied in arXiv:1108.5821 [1] and arXiv:1110.5641 [2] in the probe limit. We confirm that in general the energetically favored ground state of the multi-center potential, which can be a single or multi-center configuration, has the most entropy and is thus thermodynamically stable. However, we find the surprising result that for a subset of configurations, even though a single center black hole seems to be energetically favored, it is entropically not allowed (the resulting black hole would violate cosmic censorship). This disproves classical intuition that everything would just fall into the black hole if energetically favored. Along the way we highlight a shortcoming in the literature regarding the computation of the angular momentum coming from electromagnetic interaction in the probe limit and rectify it. We also demonstrate that static supertubes can exist inside ergoregions where ordinary point particles would be frame dragged.

Highlights

  • The Cvetic-Youm black hole [49,50,51] is a non-extremal, rotating three charge black hole of five-dimensional supergravity

  • We find that dynamical stability implies thermodynamic stability but not vice versa

  • One can establish that supertubes form locally stable bound states with the non-extremal black hole [1, 2, 31,32,33], which serve as testing grounds for more intricate bound states of black holes and black rings

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Summary

Angular momenta of a probe

We discuss the conserved angular momentum of a probe in a background with a magnetic field. The angular momentum depends on the background gauge potential, which is not gauge invariant. We discuss the procedure to find the correct gauge invariant conserved angular momentum. We explain the procedure in detail for a point particle in four dimensions (inspired by [46]), and generalize to a p-brane in arbitrary spacetime dimensions

Point particle in a magnetic field
Angular momentum from Noether procedure
Extended object in a magnetic field
A string in five dimensions
Background
Potential and angular momentum of a supertube
Comparison with the literature
Ergoregions for supertubes different from those of point particles
Phase space of supertube-black hole bound states
Parameter space
Scans of parameter space
Background with JΦ JΨ
Background with rotation in one plane
Conclusions
A Gauge parameters for a probe string
B The probe Hamiltonian and angular momentum
Probe Lagrangian We write the background metric as
Probe Hamiltonian
Probe angular momentum

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