International Journal of Modern Physics D

This paper presents a non-string-theoretic calculation of the microcanonical entropy of relic integer-spin Hawking radiation, at fixed total energy E, from an evanescent, neutral, non-rotating four-dimensional black hole. The only conserved macroscopic quantity is the total energy E which, for a black hole that evaporates completely, is the total energy of the relic radiation. Through a boundary-value approach, in which data for massless, integer-spin perturbations are set on initial and final space-like hypersurfaces, the statistical-mechanics problem becomes, in effect, a one-dimensional problem, with the "volume" of the system determined by the real part of the time separation at spatial infinity — the variable conjugate to the total energy. We count the number of field configurations on the final space-like hypersurface that have total energy E, assuming that initial perturbations are weak. We find that the density of states resembles the well-known Cardy formula. The Bekenstein–Hawking entropy is recovered if the real part of the asymptotic time separation is of the order of the semi-classical black-hole lifetime. We thereby obtain a statistical interpretation of black-hole entropy. Corrections to the microcanonical entropy are computed, and we find agreement with other approaches in terms of a logarithmic correction to the black-hole area law, which is universal (independent of black-hole parameters). This result depends crucially upon the discreteness of the energy levels. We discuss the similarities of our approach with the transition from the black-hole to the fundamental-string regime in the final stages of black-hole evaporation. In addition, we find that the squared coupling, g², which regulates the transition from a black hole to a highly-excited string state, and vice versa, can be related to the angle, δ, in the complex-time plane, through which we continue analytically the time separation at spatial infinity. Thus, in this scenario, the strong-coupling regime corresponds to a Euclidean black hole, while the physical limit of a Lorentzian space–time (the limit as δ → 0₊) corresponds to the weak-coupling regime. This resembles the transition of a black hole to a highly-excited string-like state, which subsequently decays into massless particles, thereby avoiding the naked singularity.

We study Einstein gravity minimally coupled to a scalar field in a static, spherically symmetric space–time in four dimensions. Black hole solutions are shown to exist for a phantom scalar field whose kinetic energy is negative. These "scalar black holes" have an infinite horizon area and zero Hawking temperature and are termed "cold black holes" (CBHs). The relevant explicit solutions are well known in the massless case (the so-called anti-Fisher solution), and we have found a particular example of a CBH with a nonzero potential V(ϕ). All CBHs with V(ϕ) ≢ 0 are shown to behave near the horizon, quite similarly to those with a massless field. The above solutions can be converted by a conformal transformation to Jordan frames of a general class of scalar–tensor theories of gravity, but CBH horizons in one frame are in many cases converted to singularities in the other, which gives rise to a new type of conformal continuation.

This paper deals with the role of anisotropy and inhomogeneity of space–time in quasi-spherical gravitational collapse. The effect of the initial area radius has been studied in characterizing the final state of collapse. Both dust and fluid with anisotropic pressure are considered as the collapsing matter. The results are presented in the form of propositions.

The goal of this paper is to investigate the final stage of the black-hole-evaporation process in the framework of Lorentz-violating modified dispersion relations (MDRs). As a consequence of MDRs, the high energy sector of the underlying field theory does not decouple from the low energy sector — a phenomenon known as UV/IR mixing. In the absence of exact supersymmetry, we derive an MDR which shows UV/IR mixing by a novel energy dependence. Then we investigate the effects of this type of MDRs on the thermodynamics of a radiating noncommutative Schwarzschild black hole. The final stage of black hole evaporation obtained in this framework is compared with existing pictures.

We introduce a new model for dark energy in the Universe in which a small cosmological constant is generated by ordinary electromagnetic vacuum energy. The corresponding virtual photons exist at all frequencies but switch from a gravitationally active phase at low frequencies to a gravitationally inactive phase at higher frequencies via a Ginzburg–Landau type of phase transition. Only virtual photons in the gravitationally active state contribute to the cosmological constant. A small vacuum energy density, consistent with astronomical observations, is naturally generated in this model. We propose possible laboratory tests for such a scenario based on phase synchronization in superconductors.

If global supersymmetry is broken by gaugino condensation in the hidden sector of the heterotic superstring theory after compactification, then the auxiliary field F_B of the modulus B ≡ (B_r, B_i) attains a finite value, while that of the dilaton A ≡ (A_r, A_i) vanishes, F_A = 0, the Goldstone fermion being the modulino , the spin-½ component of the complex chiral supermultiplet . The Goldstone boson of the scale symmetry that is broken when the radius of the internal space is fixed at a constant value is B_r, which is determined from the goldstino Lagrangian, compared term by term with the superstring Lagrangian, including higher-derivative gravitational terms and , after linking the space–time curvature to the energy–momentum tensor of the goldstino via the Einstein equations. This non-linear formulation of supersymmetry, due to Volkov and Akulov, is expressed in terms of the goldstino alone, whose Lagrangian contains a negative cosmological constant, which can be cancelled by the super-Higgs mechanism of Deser and Zumino to make the gravitino massive and break supersymmetry at the level GeV, while . Here, the modulus has been scaled to the Hagedorn value for the heterotic superstring theory, , and A_r, identified with the inverse square of the tree-level gauge coupling, has been scaled to the calculation in the minimal supersymmetric standard model due to Weinberg, that g^-2 = 1.39 at the unification mass M_X = 2.2 × 10¹⁶ GeV, assuming three generations of elementary particles and two Higgs doublets. In the presence of gravitino condensation in the internal space, however, there is an arbitrary additional contribution to the cosmological constant, facilitating reduction of m_s to ~ 100 TeV, say, and m_3/2 to ~ 1 eV.

The heterotic superstring theory is formulated on the world sheet h_ab(τ,σ), in a flat space–time background , by combining a 26-dimensional left-moving sector, consisting only of bosonic fields , with a 10-dimensional right-moving sector, consisting of bosonic fields and Majorana–Weyl fermionic fields ψ^A(τ - σ), the string coordinates in 10-dimensional space–time being the sum and the right-moving sector supersymmetric due to the decoupling of left- and right-moving modes for closed strings. Here, we generalize the background to a curved space–time ĝ_AB(X^C). The equation of motion for X^A(τ,σ), given by Short, is then a non-linear modification of the linear wave equation □X^A = 0 which yields decoupled left- and right-moving sectors in flat space–time. The linearity of the transverse modes can be maintained, however, if the metric, after reduction to four dimensions, is allowed to depend only upon co-moving time t ∝ X⁰, although it can be anisotropic, g_ij = g_ij(X⁰). Specializing to the isotropic, Friedmann cosmological space–time ds² = dt² - r²(t) dx², where the radius function of the three-space dx², assumed flat, is r(t), with d ln r/dt = 2/3γt for a perfect-fluid source whose pressure and energy-density are related by p = (γ - 1)ρ, we find that the string coordinates X^α(τ,σ)(α = 1,2,3), multiplied by the overall prefactor r ≡ t^2/3γ, are purely oscillatory only in Minkowski space or for the value γ = 2/3. This result is equivalent to requiring that the Nordström energy-density ρ_N ≡ (3γ - 2)ρ vanish. The case ρ = 2/3 corresponds to a space–time generated by an ensemble of cosmic strings, including the superstrings themselves in a self-consistent solution containing no other matter, and defines the Milne universe. The string is only world-sheet-supersymmetric if ρ_N = 0, that is if ρ = 0 or γ = 2/3.

We analyze the dynamical implications of an exponential Lagrangian density for the gravitational field, as referred to an isotropic FRW Universe. Then, we discuss the features of the generalized de Sitter phase, predicted by the new Friedmann equation. The existence of a consistent de Sitter solution arises only if the ratio between the vacuum energy density and that associated with the fundamental length of the theory acquires a tantalizing negative character. This choice allows us to explain the present Universe dark energy as a relic of the vacuum-energy cancellation due to the cosmological constant intrinsically contained in our scheme. The corresponding scalar-tensor description of the model is addressed too, and the behavior of the scalar field is analyzed for both negative and positive values of the cosmological term. In the first case, the Friedmann equation is studied both in vacuum and in the presence of external matter, while, in the second case, the quantum regime is approached in the framework of "repulsive" properties of the gravitational interaction, as described in recent issues in loop quantum cosmology. In particular, in the vacuum case, we find a pure non-Einsteinian effect, according to which a negative cosmological constant provides an accelerating de Sitter dynamics, in the region where the series expansion of the exponential term does not hold.

In two previous articles [Phys. Rev. D71 (2005) 124307 (gr-qc/0503007) and Phys. Rev. D76 (2006) 0440241 (gr-qc/0607001)] we have discussed several "algorithmic" techniques that permit one (in a purely mechanical way) to generate large classes of general-relativistic static perfect fluid spheres. Working in Schwarzschild curvature coordinates, we used these algorithmic ideas to prove several "solution-generating theorems" of varying levels of complexity. In the present article we consider the situation in other coordinate systems. In particular, in general diagonal coordinates we shall generalize our previous theorems, in isotropic coordinates we shall encounter a variant of the so-called "Buchdahl transformation," and in other coordinate systems (such as Gaussian polar coordinates, Synge isothermal coordinates, and Buchdahl coordinates) we shall find a number of more complex "Buchdahl-like transformations" and "solution-generating theorems" that may be used to investigate and classify the general-relativistic static perfect fluid sphere. Finally, by returning to general diagonal coordinates and making a suitable ansatz for the functional form of the metric components, we place the Buchdahl transformation in its most general possible setting.

In singularity-generating space–times both the outgoing and the ingoing expansions of null geodesic congruences θ⁺ and θ^- should become increasingly negative without bound, inside the horizon. This behavior leads to geodetic incompleteness, which in turn predicts the existence of a singularity. In this work we inquire whether, in gravitational collapse, space–time can sustain singularity-free trapped surfaces, in the sense that such a space–time remains geodetically complete. As a test case, we consider a type D space–time of Dymnikova which is Schwarzschild-like at large distances and consists of a fluid with a p = -ρ equation of state near r = 0. By following both the expansion parameters θ⁺ and θ^- across the horizon and into the black hole, we find that both θ⁺ and θ⁺θ^- have turning points inside the trapped region. Further, we find that deep inside the black hole there is a region, 0 ≤ r < r₀ (which includes the black hole center), which is not trapped. Thus the trapped region is bounded from both outside and inside. The space–time is geodetically complete, a result which violates a condition for singularity formation. It is inferred that, in general, if gravitational collapse were to proceed with a p =-ρ fluid formation, the resulting black hole might be singularity-free.

We present the analysis of the quadrupole phases of the Internal Linear Combination map, ILC(I) and (III), derived by the WMAP team (one- and three-year data release). This approach allows us to see the global trend of non-Gaussianity of the quadrupoles for the ILC(III) map through phase correlations with the foregrounds. Significant phase correlations are found between the ILC(III) quadrupole and the WMAP foreground phases for the K-W band: the phases of the ILC(III) quadrupole ξ_2,1, ξ_2,2 and those of the foregrounds at K–W bands Φ_2,1, Φ_2,2 display significant symmetry: ξ_2,1 + Φ_2,1 ≃ ξ_2,2 + Φ_2,2, which is a strong indication that the morphology of the ILC(III) quadrupole is a mere reflection of that the foreground quadrupole through coupling. To clarify this issue we exploit the symmetry of the CMB power, which is invariant under permutation of the index m = 1 ⇔ 2. By simple rotation of the ILC(III) phases with the same angle we reach the phases of the foreground quadrupole. We discuss possible sources of phase correlation and come to the conclusion that the phases of the ILC(III) quadrupole reflect most likely systematic effects such as changing of the gain factor for the three-year data release with respect to the one-year, rather than manifestation of the primordial non-Gaussianity.