Semiclassical (Quantum Field Theory) and Quantum (String) de Sitter Regimes: New Results

We compute the quantum string entropy S_s(m, H) from the microscopic string density of states rho_s (m,H) of mass m in de Sitter space-time. We find for high m, a {\bf new} phase transition at the critical string temperature T_s= (1/2 pi k_B)L c^2/alpha', higher than the flat space (Hagedorn) temperature t_s. (L = c/H, the Hubble constant H acts at the transition as producing a smaller string constant alpha' and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT Hawking-Gibbons) de Sitter temperature T_sem = hbar c /(2\pi k_B L). We find a new formula for the full de Sitter entropy S_sem (H), as a function of the usual Bekenstein-Hawking entropy S_sem^(0)(H). For L << l_{Planck}, ie. for low H << c/l_Planck, S_{sem}^{(0)}(H) is the leading term, but for high H near c/l_Planck, a new phase transition operates and the whole entropy S_sem (H) is drastically different from the Bekenstein-Hawking entropy S_sem^(0)(H). We compute the string quantum emission cross section by a black hole in de Sitter (or asymptotically de Sitter) space-time (bhdS). For T_sem ~ bhdS << T_s, (early evaporation stage), it shows the QFT Hawking emission with temperature T_sem ~ bhdS, (semiclassical regime). For T_sem ~ bhdS near T_{s}, it exhibits a phase transition into a string de Sitter state of size L_s = l_s^2/L}, l_s= \sqrt{\hbar alpha'/c), and string de Sitter temperature T_s. Instead of featuring a single pole singularity in the temperature (Carlitz transition), it features a square root branch point (de Vega-Sanchez transition). New bounds on the black hole radius r_g emerge in the bhdS string regime: it can become r_g = L_s/2, or it can reach a more quantum value, r_g = 0.365 l_s.Comment: New original materia

Semiclassical (QFT) and Quantum (String) anti - de Sitter Regimes: New Results

We compute the quantum string entropy S_s(m, H) from the microscopic string density of states of mass m in Anti de Sitter space-time. For high m, (high Hm -->c/\alpha'), no phase transition occurs at the Anti de Sitter string temperature T_{s} which is higher than the flat space (Hagedorn) temperature t_{s}. (the Hubble constant H acts as producing a smaller string constant and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT) Anti de Sitter temperature scale . We compute the quantum string emission by a black hole in Anti de Sitter space-time (bhAdS). In the early evaporation stage, it shows the QFT Hawking emission with temperature T_{sem~bhAdS}, (semiclassical regime). For T_{sem~bhAdS}--> T_{s}, it exhibits a phase transition into a Anti de Sitter string state. New string bounds on the black hole emerge in the bhAdS string regime. We find a new formula for the full (quantum regime included) Anti de Sitter entropy S_{sem}, as a function of the usual Bekenstein-Hawking entropy S_{sem}^(0). For low H (semiclassical regime), S_{sem}^(0) is the leading term but for high H (quantum regime), no phase transition operates, in contrast to de Sitter space, and the entropy S_{sem} is very different from the Bekenstein-Hawking term S_{sem}^(0).Comment: Comments 26 pages; no figure

Monitoring of Rehabilitation of Degraded Rangelands

The Algerian steppe covers an area of about 20 million ha, and is the barrier between the desert and the Mediterranean region. With more than 20 million sheep, overgrazing is an important issue resulting in continued degradation of the natural resources (Nedjraoui and Bedrani 2008). Trials of the rehabilitation of these ecosystems were undertaken in a participatory process with farmers complemented by some detailed monitoring of the responses in experimental plots (Hammouda 2009; Bouchareb 2012). This study reports on some results of the ecological monitoring and evaluation for a participatory project, in the steppe of South Algiers, conducted by a multidisciplinary team

Semiclassical (QFT) and Quantum (String) Rotating Black Holes and their Evaporation: New Results

Combination of both quantum field theory (QFT) and string theory in curved backgrounds in a consistent framework, the string analogue model, allows us to provide a full picture of the Kerr-Newman black hole and its evaporation going beyond the current picture. We compute the quantum emission cross section of strings by a Kerr-Newmann black hole (KNbh). It shows the black hole emission at the Hawking temperature T_{sem} in the early evaporation and the new string emission featuring a Hagedorn transition into a string state of temperature T_ s at the last stages. New bounds on the angular momentum J and charge Q emerge in the quantum string regime. The last state of evaporation of a semiclassical KNbh is a string state of temperature T_s, mass M_s, J = 0 = Q, decaying as a quantum string into all kinds of particles.(There is naturally, no loss of information, (no paradox at all)). We compute the microscopic string entropy S_s(m, j) of mass m and spin mode j. (Besides the usual transition at T_s), we find for high j, (extremal string states) a new phase transition at a temperature T_{sj} higher than T_s. We find a new formula for the Kerr black hole entropy S_{sem}, as a function of the usual Bekenstein-Hawking entropy . For high angular momentum, (extremal J = GM^2/c), a gravitational phase transition operates and the whole entropy S_{sem} is drastically different from the Bekenstein-Hawking entropy. This new extremal black hole transition occurs at a temperature T_{sem J} higher than the Hawking temperature T_{sem}.Comment: New articl

Uniqueness Theorem for Black Hole Space-Times with Multiple Disconnected Horizons

We show uniqueness of stationary and asymptotically flat black hole space-times with multiple disconnected horizons and with two rotational Killing vector fields in the context of five-dimensional minimal supergravity (Einstein-Maxwell-Chern-Simons gravity). The novelty in this work is the introduction in the uniqueness theorem of intrinsic local charges measured near each horizon as well as the measurement of local fluxes besides the asymptotic charges that characterize a particular solution. A systematic method of defining the boundary conditions on the fields that specify a black hole space-time is given based on the study of its rod structure (domain structure). Also, an analysis of known solutions with disconnected horizons is carried out as an example of an application of this theorem.Comment: 28 pages, 5 figures. v3: Further improvements on uniqueness theorem, Lemma introduced for clarity of derivation, new quantities introduced to treat special case with zero flux, refs. added, typos fixe

Uniqueness and nonuniqueness of the stationary black holes in 5D Einstein-Maxwell and Einstein-Maxwell-dilaton gravity

In the present paper we investigate the general problem of uniqueness of the stationary black solutions in 5D Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling parameter containing the Einstein-Maxwell gravity as a particular case. We formulate and prove uniqueness theorems classifying the stationary black hole solutions in terms of their interval structure, electric and magnetic charges and the magnetic fluxes. The proofs are based on the nonpositivity of the Riemann curvature operator on the space of the potentials which imposes restrictions on the dilaton coupling parameter.Comment: 21 pages, LaTe

Black hole mass and angular momentum in topologically massive gravity

We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.Comment: 20 pages, references added, version to appear in Classical and Quantum Gravit

A General Black String and its Microscopics

Using G2(2) dualities we construct the most general black string solution of minimal five-dimensional ungauged supergravity. The black string has five independent parameters, namely, the magnetic one-brane charge, smeared electric zero-brane charge, boost along the string direction, energy above the BPS bound, and rotation in the transverse space. In one extremal limit it reduces to the three parameter supersymmetric string of five-dimensional minimal supergravity; in another extremal limit it reduces to the three parameter non-supersymmetric extremal string of five-dimensional minimal supergravity. It also admits an extremal limit when it has maximal rotation in the four-dimensional transverse space. The decoupling limit of our general black string is a BTZ black hole times a two sphere. The macroscopic entropy of the string is reproduced by the Maldacena-Strominger-Witten CFT in appropriate ranges of the parameters. When the pressureless condition is imposed, our string describes the infinite radius limit of the most general class of black rings of minimal supergravity. We discuss implications our solution has for extremal and non-extremal black rings of minimal supergravity.Comment: 35 pages; 3 figures; v2 section 4.1.1 rewritten + minor changes + ref adde

All Vacuum Near-Horizon Geometries in DD-dimensions with (D−3)(D-3) Commuting Rotational Symmetries

We explicitly construct all stationary, non-static, extremal near horizon geometries in $D$ dimensions that satisfy the vacuum Einstein equations, and that have $D-3$ commuting rotational symmetries. Our work generalizes [arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been given in $D=4,5$. But our method is different from theirs and relies on a matrix formulation of the Einstein equations. Unlike their method, this matrix formulation works for any dimension. The metrics that we find come in three families, with horizon topology $S^2 \times T^{D-4}$, or $S^3 \times T^{D-5}$, or quotients thereof. Our metrics depend on two discrete parameters specifying the topology type, as well as $(D-2)(D-3)/2$ continuous parameters. Not all of our metrics in $D \ge 6$ seem to arise as the near horizon limits of known black hole solutions.Comment: 22 pages, Latex, no figures, title changed, references added, discussion of the parameters specifying solutions corrected, amended to match published versio

G2 Dualities in D=5 Supergravity and Black Strings

Five dimensional minimal supergravity dimensionally reduced on two commuting Killing directions gives rise to a G2 coset model. The symmetry group of the coset model can be used to generate new solutions by applying group transformations on a seed solution. We show that on a general solution the generators belonging to the Cartan and nilpotent subalgebras of G2 act as scaling and gauge transformations, respectively. The remaining generators of G2 form a sl(2,R)+sl(2,R) subalgebra that can be used to generate non-trivial charges. We use these generators to generalize the five dimensional Kerr string in a number of ways. In particular, we construct the spinning electric and spinning magnetic black strings of five dimensional minimal supergravity. We analyze physical properties of these black strings and study their thermodynamics. We also explore their relation to black rings.Comment: typos corrected (26 pages + appendices, 2 figures