Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities

The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of fields in curved backgrounds remains however a complicated task because of the highly intricate partial differential equations involved, especially when the space metric exhibits no symmetry. In this article, we provide --in a pedagogical way-- a general formalism to determine this dynamics at the semiclassical order. To this purpose, a generic expression for the semiclassical propagator is computed and the equation of motion for the probability four-current is derived. Those results underline a direct analogy between the computation of the propagator in general relativistic quantum mechanics and the computation of the propagator for stationary systems in non-relativistic quantum mechanics. A possible application of this formalism to curvature-induced quantum interferences is also discussed.Comment: New materials on gravitationally-induced quantum interferences has been adde

Exact Results for Evaporating Black Holes in Curvature-Squared Lovelock Gravity: Gauss-Bonnet Greybody Factors

Lovelock gravity is an important extension of General Relativity that provides a promising framework to study curvature corrections to the Einstein action, while avoiding ghosts and keeping second order field equations. This paper derives the greybody factors for D-dimensional black holes arising in a theory with a Gauss-Bonnet curvature-squared term. These factors describe the non-trivial coupling between black holes and quantum fields during the evaporation process: they can be used both from a theoretical viewpoint to investigate the intricate spacetime structure around such a black hole, and for phenomenological purposes in the framework of braneworld models with a low Planck scale. We derive exact spectra for the emission of scalar, fermion and gauge fields emitted on the brane, and for scalar fields emitted in the bulk, and demonstrate how the Gauss-Bonnet term can change the bulk-to-brane emission rates ratio in favour of the bulk channel in particular frequency regimes.Comment: 29 pages, Latex file, 11 figures, Data files (greybody factors) available at http://lpsc.in2p3.fr/ams/greybody/, typos corrected, references added, version to appear in Phys. Rev.

New black hole solutions in the string gravity with noncompact extra dimensions and their experimental search I

The Gauss-Bonnet invariant is one of the most promising candidates for a quadratic curvature correction to the Einstein action in expansions of supersymmetric string theory. We study these Gauss-Bonnet black holes (and their properties) which could be formed at future colliders if the Planck scale is of order a TeV, as predicted by some modern brane world models

Instability of the massive Klein-Gordon field on the Kerr spacetime

We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the $l = 1$, $m = 1$ state, for $M \mu \lesssim 0.5$. For a fast rotating hole ($a = 0.99$) we find a maximum growth rate of $\tau^{-1} \approx 1.5 \times 10^{-7} (GM/c^3)^{-1}$, at $M \mu \approx 0.42$. The physical implications are discussed.Comment: Added references. 27 pages, 7 figure

Bulk and Brane Decay of a (4+n)-Dimensional Schwarzschild-De-Sitter Black Hole: Scalar Radiation

In this paper, we extend the idea that the spectrum of Hawking radiation can reveal valuable information on a number of parameters that characterize a particular black hole background - such as the dimensionality of spacetime and the value of coupling constants - to gain information on another important aspect: the curvature of spacetime. We investigate the emission of Hawking radiation from a D-dimensional Schwarzschild-de-Sitter black hole emitted in the form of scalar fields, and employ both analytical and numerical techniques to calculate greybody factors and differential energy emission rates on the brane and in the bulk. The energy emission rate of the black hole is significantly enhanced in the high-energy regime with the number of spacelike dimensions. On the other hand, in the low-energy part of the spectrum, it is the cosmological constant that leaves a clear footprint, through a characteristic, constant emission rate of ultrasoft quanta determined by the values of black hole and cosmological horizons. Our results are applicable to "small" black holes arising in theories with an arbitrary number and size of extra dimensions, as well as to pure 4-dimensional primordial black holes, embedded in a de Sitter spacetime.Comment: 31 pages, latex file, data files available at http://lpsc.in2p3.fr/ams/greybody/ some clarifying comments and references added, typos corrected, version to appear in Phys. Rev.

Kerr-Gauss-Bonnet Black Holes: An Analytical Approximation

Gauss-Bonnet gravity provides one of the most promising frameworks to study curvature corrections to the Einstein action in supersymmetric string theories, while avoiding ghosts and keeping second order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for long, the Kerr-Gauss-Bonnet metric is missing. In this paper, a five dimensional Gauss-Bonnet approximation is analytically derived for spinning black holes and the related thermodynamical properties are briefly outlined.Comment: 5 pages, 1 figur

Anomaly-free vector perturbations with holonomy corrections in loop quantum cosmology

We investigate vector perturbations with holonomy corrections in the framework of loop quantum cosmology. Conditions to achieve anomaly freedom for these perturbations are found at all orders. This requires the introduction of counter-terms in the hamiltonian constraint. We also show that anomaly freedom requires the diffeomorphism constraint to hold its classical form when scalar matter is added although the issue of a vector matter source, required for full consistency, remains to be investigated. The gauge-invariant variable and the corresponding equation of motion are derived. The propagation of vector modes through the bounce is finally discussed.Comment: 16 pages, 1 figure. Matches version published in Class. Quantum Gra

Spherically symmetric Einstein-Maxwell theory and loop quantum gravity corrections

Effects of inverse triad corrections and (point) holonomy corrections, occuring in loop quantum gravity, are considered on the properties of Reissner-Nordstr\"om black holes. The version of inverse triad corrections with unmodified constraint algebra reveals the possibility of occurrence of three horizons (over a finite range of mass) and also shows a mass threshold beyond which the inner horizon disappears. For the version with modified constraint algebra, coordinate transformations are no longer a good symmetry. The covariance property of spacetime is regained by using a \emph{quantum} notion of mapping from phase space to spacetime. The resulting quantum effects in both versions of these corrections can be associated with renormalization of either mass, charge or wave function. In neither of the versions, Newton's constant is renormalized. (Point) Holonomy corrections are shown to preclude the undeformed version of constraint algebra as also a static solution, though time-independent solutions exist. A possible reason for difficulty in constructing a covariant metric for these corrections is highlighted. Furthermore, the deformed algebra with holonomy corrections is shown to imply signature change.Comment: 38 pages, 9 figures, matches published versio

Gauss-Bonnet Black Holes at the LHC : Beyond the Dimensionality of Space

The Gauss - Bonnet invariant is one of the most promising candidates for a quadratic curvature correction to the Einstein action in expansions of supersymmetric string theory. We study the evaporation of such Schwarzschild - Gauss - Bonnet black holes which could be formed at future colliders if the Planck scale is of order a TeV, as predicted by some modern brane world models. We show that, beyond the dimensionality of space, the corresponding coupling constant could be measured by the LHC. This opens new windows for physics investigation in spite of the possible screening of microphysics due to the event horizon.Comment: Accepted by Phys. Lett.