Phase transitions and critical behavior of black branes in canonical ensemble

We study the thermodynamics and phase structure of asymptotically flat non-dilatonic as well as dilatonic black branes in a cavity in arbitrary dimensions ($D$). We consider the canonical ensemble and so the charge inside the cavity and the temperature at the wall are fixed. We analyze the stability of the black brane equilibrium states and derive the phase structures. For the zero charge case we find an analog of Hawking-Page phase transition for these black branes in arbitrary dimensions. When the charge is non-zero, we find that below a critical value of the charge, the phase diagram has a line of first-order phase transition in a certain range of temperatures which ends up at a second order phase transition point (critical point) as the charge attains the critical value. We calculate the critical exponents at that critical point. Although our discussion is mainly concerned with the non-dilatonic branes, we show how it easily carries over to the dilatonic branes as well.Comment: 37 pages, 6 figures, the validity of using the effective action discussed, references adde

Phase structure of black branes in grand canonical ensemble

This is a companion paper of our previous work [1] where we studied the thermodynamics and phase structure of asymptotically flat black $p$-branes in a cavity in arbitrary dimensions $D$ in a canonical ensemble. In this work we study the thermodynamics and phase structure of the same in a grand canonical ensemble. Since the boundary data in two cases are different (for the grand canonical ensemble boundary potential is fixed instead of the charge as in canonical ensemble) the stability analysis and the phase structure in the two cases are quite different. In particular, we find that there exists an analog of one-variable analysis as in canonical ensemble, which gives the same stability condition as the rather complicated known (but generalized from black holes to the present case) two-variable analysis. When certain condition for the fixed potential is satisfied, the phase structure of charged black $p$-branes is in some sense similar to that of the zero charge black $p$-branes in canonical ensemble up to a certain temperature. The new feature in the present case is that above this temperature, unlike the zero-charge case, the stable brane phase no longer exists and `hot flat space' is the stable phase here. In the grand canonical ensemble there is an analog of Hawking-Page transition, even for the charged black $p$-brane, as opposed to the canonical ensemble. Our study applies to non-dilatonic as well as dilatonic black $p$-branes in $D$ space-time dimensions.Comment: 32 pages, 2 figures, various points refined, discussion expanded, references updated, typos corrected, published in JHEP 1105:091,201

A deep 1.4 GHz survey of the J1030 equatorial field: a new window on radio source populations across cosmic time

We present deep L-Band observations of the equatorial field centered on the z=6.3 SDSS QSO, reaching a 1 sigma sensitivity of ~2.5 uJy at the center of the field. We extracted a catalog of 1489 radio sources down to a flux density of ~12.5 uJy (5 sigma) over a field of view of ~ 30' diameter. We derived the source counts accounting for catalog reliability and completeness, and compared them with others available in the literature. Our source counts are among the deepest available so far, and, overall, are consistent with recent counts' determinations and models. We detected for the first time in the radio band the SDSS J1030+0524 QSO (26 +/- 5 uJy). We derived its optical radio loudness R_O = 0.62 +/- 0.12, which makes it the most radio quiet AGN at z >~ 6 discovered so far and detected at radio wavelengths. We unveiled extended diffuse radio emission associated with the lobes of a bright FRII radio galaxy located close to the center of the J1030 field, which is likely to become the future BCG of a protocluster at z=1.7. The lobes' complex morphology, coupled with the presence of X-ray diffuse emission detected around the FRII galaxy lobes, may point toward an interaction between the radio jets and the external medium. We also investigated the relation between radio and X-ray luminosity for a sample of 243 X-ray-selected objects obtained from 500 ks Chandra observations of the same field, and spanning a wide redshift range (0 ~< z ~< 3). Focused on sources with a spectroscopic redshift and classification, we found that sources hosted by ETG and AGN follow Log(L_R)/Log(L_X) linear correlations with slopes of ~0.6 and ~0.8, respectively. This is interpreted as a likely signature of different efficiency in the accretion process. Finally, we found that most of these sources (>~87%) show a radio-to-X-ray radio loudness R_X < -3.5, classifying these objects as radio quiet.Comment: 18 pages, 15 figures, 5 table. Accepted for publication in A&

A deep 1.4 GHz survey of the J1030 equatorial field: A new window on radio source populations across cosmic time

We present deep L-Band observations of the equatorial field centered on the z = 6.3 Sloan Digital Sky Survey (SDSS) quasar (QSO). This field is rich of multiwavelength photometry and spectroscopy data, making it an ideal laboratory for galaxy evolution studies. Our observations reach a 1σ sensitivity of ~2.5 μJy at the center of the field. We extracted a catalog of 1489 radio sources down to a flux density of ~12.5 μJy (5σ) over a field of view of ~ 30′ diameter. We derived the source counts accounting for catalog reliability and completeness, and compared them with others available in the literature. Our source counts are among the deepest available so far, and, overall, are consistent with recent counts'determinations and models. They show a slight excess at flux densities ~50 μJy, possibly associated with the presence of known overdensities in the field. We detected for the first time in the radio band the SDSS J1030+0524 QSO (26 ± 5 μJy, 8σ significance level). For this object, we derived an optical radio loudness RO = 0.62±0.12, which makes it the most radio quiet among active galactic nuclei (AGN) discovered so far at z ≳ 6 and detected at radio wavelengths. We unveiled extended diffuse radio emission associated with the lobes of a bright Fanaroff-Riley type II (FRII) radio galaxy located close to the center of the J1030 field, which is likely to become the future brightest cluster galaxy of a protocluster at z = 1.7. The lobes'complex morphology, coupled with the presence of X-ray diffuse emission detected around the FRII galaxy lobes, may point toward an interaction between the radio jets and the external medium. We also investigated the relation between radio and X-ray luminosity for a sample of 243 X-ray-selected objects obtained from 500 ks Chandra observations of the same field, and spanning a wide redshift range (0 ≲ z ≲ 3). Focused on sources with a spectroscopic redshift and classification, we found that sources hosted by early-type galaxies and AGN follow log(LR)/log(LX) linear correlations with slopes of ~0.6 and ~0.8, respectively. This is interpreted as a likely signature of different efficiency in the accretion process. Finally, we found that most of these sources (≳87%) show a radio-to-X-ray radio loudness RX ≲ -3.5, classifying these objects as radio quiet

Thermodynamics of d-dimensional charged rotating black brane and AdS/CFT correspondence

We compute the Euclidean actions of a $d$-dimensional charged rotating black brane both in the canonical and the grand-canonical ensemble through the use of the counterterms renormalization method, and show that the logarithmic divergencies associated with the Weyl anomalies and matter field vanish. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta, and the electric charge, and show that these quantities satisfy the first law of thermodynamics. Using the conserved quantities and the Euclidean actions, we calculate the thermodynamics potentials of the system in terms of the temperature, angular velocities, and electric potential both in the canonical and grand-canonical ensembles. We also perform a stability analysis in these two ensembles, and show that the system is thermally stable. This is commensurate with the fact that there is no Hawking-Page phase transition for a black object with zero curvature horizon. Finally, we obtain the logarithmic correction of the entropy due to the thermal fluctuation around the equilibrium.Comment: REVTEX4, 15 pages, 1 figur

Holographic phase diagram of quark-gluon plasma formed in heavy-ions collisions

The phase diagram of quark gluon plasma (QGP) formed at a very early stage just after the heavy ion collision is obtained by using a holographic dual model for the heavy ion collision. In this dual model colliding ions are described by the charged shock gravitational waves. Points on the phase diagram correspond to the QGP or hadronic matter with given temperatures and chemical potentials. The phase of QGP in dual terms is related to the case when the collision of shock waves leads to formation of trapped surface. Hadronic matter and other confined states correspond to the absence of trapped surface after collision. Multiplicity of the ion collision process is estimated in the dual language as area of the trapped surface. We show that a non-zero chemical potential reduces the multiplicity. To plot the phase diagram we use two different dual models of colliding ions, the point and the wall shock waves, and find qualitative agreement of the results.Comment: 33 pages, 14 figures, typos correcte

The deep Chandra survey in the SDSS J1030+0524 field

We present the X-ray source catalog for the ∼479 ks Chandra exposure of the SDSS J1030+0524 field, which is centered on a region that shows the best evidence to date of an overdensity around a z > 6 quasar, and also includes a galaxy overdensity around a Compton-thick Fanaroff-Riley type II (FRII) radio galaxy at z = 1.7. Using wavdetect for initial source detection and ACIS Extract for source photometry and significance assessment, we create preliminary catalogs of sources that are detected in the full (0.5-7.0 keV), soft (0.5-2.0 keV), and hard (2-7 keV) bands, respectively. We produce X-ray simulations that mirror our Chandra observation to filter our preliminary catalogs and achieve a completeness level of > 91% and a reliability level of ∼95% in each band. The catalogs in the three bands are then matched into a final main catalog of 256 unique sources. Among them, 244, 193, and 208 are detected in the full, soft, and hard bands, respectively. The Chandra observation covers a total area of 335 arcmin2 and reaches flux limits over the central few square arcmins of ∼3 × 10-16, 6 × 10-17, and 2 × 10-16 erg cm-2 s-1 in the full, soft, and hard bands, respectively This makes J1030 field the fifth deepest extragalactic X-ray survey to date. The field is part of the Multiwavelength Survey by Yale-Chile (MUSYC), and is also covered by optical imaging data from the Large Binocular Camera (LBC) at the Large Binocular Telescope (LBT), near-infrared imaging data from the Canada France Hawaii Telescope WIRCam (CFHT/WIRCam), and Spitzer IRAC. Thanks to its dense multi-wavelength coverage, J1030 represents a legacy field for the study of large-scale structures around distant accreting supermassive black holes. Using a likelihood ratio analysis, we associate multi-band (r, z, J, and 4.5  μm) counterparts for 252 (98.4%) of the 256 Chandra sources, with an estimated reliability of 95%. Finally, we compute the cumulative number of sources in each X-ray band, finding that they are in general agreement with the results from the Chandra Deep Fields.We acknowledge the referee for a prompt and constructive report. We acknowledge financial contribution from the agreement ASI-INAF n. 2017-14-H.O. We thank P. Broos for providing great support for the analysis of our simulations with AE, and H. M. Günther for the support provided for using MARX. We also thank B. Luo for providing us the log(N)–log(S) of the 7Ms CDF-S. FV acknowledges financial support from CONICYT and CASSACA through the Fourth call for tenders of the CAS-CONICYT Fund, and CONICYT grants Basal-CATA AFB-170002. DM and MA acknowledge support by grant number NNX16AN49G issued through the NASA Astrophysics Data Analysis Program (ADAP). Further support was provided by the Faculty Research Fund (FRF) of Tufts University

Global embeddings of scalar-tensor theories in (2+1)-dimensions

We obtain (3+3)- or (3+2)-dimensional global flat embeddings of four uncharged and charged scalar-tensor theories with the parameters B or L in the (2+1)-dimensions, which are the non-trivially modified versions of the Banados-Teitelboim-Zanelli (BTZ) black holes. The limiting cases B=0 or L=0 exactly are reduced to the Global Embedding Minkowski Space (GEMS) solution of the BTZ black holes.Comment: 19 pages, 2 figure

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics...Comment: 51 single column pages, 19 postscript figures, 2 tables, GRG tex style; minor corrections added; final version appearing in General Relativity and Gravitatio

Higher dimensional flat embeddings of (2+1) dimensional black holes

We obtain the higher dimensional global flat embeddings of static, rotating, and charged BTZ black holes. On the other hand, we also study the similar higher dimensional flat embeddings of the (2+1) de Sitter black holes which are the counterparts of the anti-de Sitter BTZ black holes. As a result, the charged dS black hole is shown to be embedded in (3+2) GEMS, contrast to the charged BTZ one having (3+3) GEMS structure.Comment: 16pages, revtex, no figures, to appear in Phys. Rev.