Large entropy production inside black holes: a simple model

Particles dropped into a rotating black hole can collide near the inner horizon with enormous energies. The entropy produced by these collisions can be several times larger than the increase in the horizon entropy due to the addition of the particles. In this paper entropy is produced by releasing large numbers of neutrons near the outer horizon of a rotating black hole such that they collide near the inner horizon at energies similar to those achieved at the Relativistic Heavy Ion Collider. The increase in horizon entropy is approximately 80 per dropped neutron pair, while the entropy produced in the collisions is 160 per neutron pair. The collision entropy is produced inside the horizon, so this excess entropy production does not violate Bousso's bound limiting the entropy that can go through the black hole's horizon. The generalized laws of black hole thermodynamics are obeyed. No individual observer inside the black hole sees a violation of the second law of thermodynamicsComment: 10 page

Sequences of dipole black rings and Kaluza-Klein bubbles

We construct new exact solutions to 5D Einstein-Maxwell equations describing sequences of Kaluza-Klein bubbles and dipole black rings. The solutions are generated by 2-soliton transformations from vacuum black ring - bubble sequences. The properties of the solutions are investigated. We also derive the Smarr-like relations and the mass and tension first laws in the general case for such configurations of Kaluza-Klein bubbles and dipole black rings. The novel moment is the appearance of the magnetic flux in the Smarr-like relations and the first laws.Comment: 26 pages, 1 figur

Small Hairy Black Holes in Global AdS Spacetime

We study small charged black holes in global AdS spacetime in the presence of a charged massless minimally coupled scalar field. In a certain parameter range these black holes suffer from well known superradiant instabilities. We demonstrate that the end point of the resultant tachyon condensation process is a hairy black hole which we construct analytically in a perturbative expansion in the black hole radius. At leading order our solution is a small undeformed RNAdS black hole immersed into a charged scalar condensate that fills the AdS `box'. These hairy black hole solutions appear in a two parameter family labelled by their mass and charge. Their mass is bounded from below by a function of their charge; at the lower bound a hairy black hole reduces to a regular horizon free soliton which can also be thought of as a nonlinear Bose condensate. We compute the microcanonical phase diagram of our system at small mass, and demonstrate that it exhibits a second order `phase transition' between the RNAdS black hole and the hairy black hole phases.Comment: 68+1 pages, 18 figures, JHEP format. v2 : small typos corrected and a reference adde

Continuous Hawking-Page transitions in Einstein-scalar gravity

We investigate continuous Hawking-Page transitions in Einstein's gravity coupled to a scalar field with an arbitrary potential in the weak gravity limit. We show that this is only possible in a singular limit where the black-hole horizon marginally traps a curvature singularity. Depending on the subleading terms in the potential, a rich variety of continuous phase transitions arise. Our examples include second and higher order, including the Berezinskii-Kosterlitz-Thouless type. In the case when the scalar is dilaton, the condition for a continuous phase transition lead to (asymptotically) linear-dilaton background. We obtain the scaling laws of thermodynamic functions, as well as the viscosity coefficients near the transition. In the limit of weak gravitational interactions, the bulk viscosity asymptotes to a universal constant, independent of the details of the scalar potential. As a byproduct of our analysis we obtain a one-parameter family of kink solutions in arbitrary dimension d that interpolate between AdS near the boundary and linear-dilaton background in the deep interior. The continuous Hawking-Page transitions found here serve as holographic models for normal-to superfluid transitions.Comment: 35 pages + appendice

Shock waves in strongly coupled plasmas

Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong shocks are discontinuous within hydrodynamics and therefore probe the microscopics of the theory. In this paper we consider the case of the strongly coupled N=4 plasma whose microscopic description, applicable for scales smaller than the inverse temperature, is given in terms of gravity in an asymptotically $AdS_5$ space. In the gravity approximation, weak and strong shocks should be described by smooth metrics with no discontinuities. For weak shocks we find the dual metric in a derivative expansion and for strong shocks we use linearized gravity to find the exponential tail that determines the width of the shock. In particular we find that, when the velocity of the fluid relative to the shock approaches the speed of light $v\to 1$ the penetration depth $\ell$ scales as $\ell\sim (1-v^2)^{1/4}$. We compare the results with second order hydrodynamics and the Israel-Stewart approximation. Although they all agree in the hydrodynamic regime of weak shocks, we show that there is not even qualitative agreement for strong shocks. For the gravity side, the existence of shock waves implies that there are disturbances of constant shape propagating on the horizon of the dual black holes.Comment: 47 pages, 8 figures; v2:typos corrected, references adde

Boundary Conditions and Unitarity: the Maxwell-Chern-Simons System in AdS_3/CFT_2

We consider the holography of the Abelian Maxwell-Chern-Simons (MCS) system in Lorentzian three-dimensional asymptotically-AdS spacetimes, and discuss a broad class of boundary conditions consistent with conservation of the symplectic structure. As is well-known, the MCS theory contains a massive sector dual to a vector operator in the boundary theory, and a topological sector consisting of flat connections dual to U(1) chiral currents; the boundary conditions we examine include double-trace deformations in these two sectors, as well as a class of boundary conditions that mix the vector operators with the chiral currents. We carefully study the symplectic product of bulk modes and show that almost all such boundary conditions induce instabilities and/or ghost excitations, consistent with violations of unitarity bounds in the dual theory.Comment: 50+1 pages, 6 figures, PDFLaTeX; v2: added references, corrected typo

Gravitational Chern-Simons Lagrangians and black hole entropy

We analyze the problem of defining the black hole entropy when Chern-Simons terms are present in the action. Extending previous works, we define a general procedure, valid in any odd dimensions both for purely gravitational CS terms and for mixed gauge-gravitational ones. The final formula is very similar to Wald's original formula valid for covariant actions, with a significant modification. Notwithstanding an apparent violation of covariance we argue that the entropy formula is indeed covariant.Comment: 39 page

Setting limits on Effective Field Theories: the case of Dark Matter

The usage of Effective Field Theories (EFT) for LHC new physics searches is receiving increasing attention. It is thus important to clarify all the aspects related with the applicability of the EFT formalism in the LHC environment, where the large available energy can produce reactions that overcome the maximal range of validity, i.e. the cutoff, of the theory. We show that this does forbid to set rigorous limits on the EFT parameter space through a modified version of the ordinary binned likelihood hypothesis test, which we design and validate. Our limit-setting strategy can be carried on in its full-fledged form by the LHC experimental collaborations, or performed externally to the collaborations, through the Simplified Likelihood approach, by relying on certain approximations. We apply it to the recent CMS mono-jet analysis and derive limits on a Dark Matter (DM) EFT model. DM is selected as a case study because the limited reach on the DM production EFT Wilson coefficient and the structure of the theory suggests that the cutoff might be dangerously low, well within the LHC reach. However our strategy can also be applied to EFT's parametrising the indirect effects of heavy new physics in the Electroweak and Higgs sectors

The temperature and entropy of CFT on time-dependent backgrounds

We express the AdS-Schwarzschild black-hole configuration in coordinates such that the boundary metric is of the FLRW type. We review how this construction can be used in order to calculate the stress-energy tensor of the dual CFT on the FLRW background. We deduce the temperature and entropy of the CFT, which are related to the temperature and entropy of the black hole. We find that the entropy is proportional to the area of an apparent horizon, different from the black-hole event horizon. For a dS boundary we reproduce correctly the intrinsic temperature of dS space.Comment: 19 pages, major revision, several comments added, version to appear in JHE

On The Phase Structure and Thermodynamic Geometry of R-Charged Black Holes

We study the phase structure and equilibrium state space geometry of R-charged black holes in $D = 5$, 4 and 7 and the corresponding rotating $D3$, $M2$ and $M5$ branes. For various charge configurations of the compact black holes in the canonical ensemble we demonstrate new liquid-gas like phase coexistence behaviour culminating in second order critical points. The critical exponents turn out to be the same as that of four dimensional asymptotically AdS black holes in Einstein Maxwell theory. We further establish that the regions of stability for R-charged black holes are, in some cases, more constrained than is currently believed, due to properties of some of the response coefficients. The equilibrium state space scalar curvature is calculated for various charge configurations, both for the case of compact as well as flat horizons and its asymptotic behaviour with temperature is established.Comment: 1 + 33 pages, LaTeX, 25 figures. References adde