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Register a new userGravitational shockwave on the Kerr-AdS horizon
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Authors
Yoni BenTov
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I generalize the Dray-t Hooft gravitational shockwave to the Kerr-AdS background.
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It was recently observed that Kerr-AdS metrics with negative mass describe smooth spacetimes that have a region with naked closed time-like curves, bounded by a velocity of light surface. Such spacetimes are sometimes known as time machines. In this paper we study the BPS limit of these metrics, and find that the mass and angular momenta become discretised. The completeness of the spacetime also requires that the time coordinate be periodic, with precisely the same period as that which arises for the global AdS in which the time machine spacetime is immersed. For the case of equal angular momenta in odd dimensions, we construct the Killing spinors explicitly, and show they are consistent with the global structure. Thus in examples where the solution can be embedded in a gauged supergravity theory, they will be supersymmetric. We also compare the global structure of the BPS AdS$_3$ time machine with the BTZ black hole, and show that the global structure allows to have two different supersymmetric limits.
We use the isometric embedding of the spatial horizon of fast rotating Kerr black hole in a hyperbolic space to compute the quasi-local mass of the horizon for any value of the spin parameter $j=J/m^2$. The mass is monotonically decreasing from twice the ADM mass at $j=0$ to $1.76569m$ at $j=sqrt{3}/2$. It then monotonicaly increases to a maximum around $j=0.99907$, and finally decreases to $2.01966m$ for $j=1$ which corresponds to the extreme Kerr black hole.
By treating the black hole event horizon as a stochastic thermal fluctuating variable for small-large black hole phase transition, we investigate the dynamical process of phase transition for the Kerr AdS black holes on free energy landscape. We find that the extremal points of the off-shell Gibbs free energy correspond to physical black holes. For small-large black hole phase transition, the off-shell Gibbs free energy exhibits a double well behavior with the same depth. Contrary to previous research for the dynamics of phase transition for the Kerr-Newman AdS family black holes on free energy landscape, we find that there is a lower bound for the order parameter and the lower bound corresponds to extremal black holes. In particular, the off-shell Gibbs free energy is zero instead of divergent as previous work suggested for vanishing black hole horizon radius, which corresponds to the Gibbs free energy of thermal AdS space. The investigation for the evolution of the probability distribution for the phase transition indicates that the initial stable small (large) black hole tends to switch to stable large (small) black hole. Increasing the temperature along the coexistence curve, the switching process becomes faster and the probability distribution reaches the final stationary Boltzmann distribution at a shorter time. The distribution of the first passage time indicates the time scale of the small-large black hole phase transition, and the peak of the distribution becomes sharper and shifts to the left with the increase of temperature along the coexistence curve. This suggests that a considerable first passage process occurs at a shorter time for higher temperature.
We show that the Kerr-(Newman)-AdS$_4$ black hole will be shadowless if its rotation parameter is larger than a critical value $a_c$ which is not necessarily equal to the AdS radius. This is because the null hypersurface caustics (NHC) appears both inside the Cauchy horizon and outside the event horizon for the black hole with the rotation parameter beyond the critical value, and the NHC outside the event horizon scatters diffusely the light reaching it. Our studies also further confirm that whether an ultraspinning black hole is super-entropic or not is unrelated to the existence of the NHC outside the event horizon.
An exact hairy asymptotically locally AdS black hole solution with a flat horizon in the Einstein-nonlinear sigma model system in (3+1) dimensions is constructed. The ansatz for the nonlinear $SU(2)$ field is regular everywhere and depends explicitly on Killing coordinates, but in such a way that its energy-momentum tensor is compatible with a metric with Killing fields. The solution is characterized by a discrete parameter which has neither topological nor Noether charge associated with it and therefore represents a hair. A $U(1)$ gauge field interacting with Einstein gravity can also be included. The thermodynamics is analyzed. Interestingly, the hairy black hole is always thermodynamically favored with respect to the corresponding black hole with vanishing Pionic field.
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