Conformal Scalar Propagation on the Schwarzschild Black-Hole Geometry

The vacuum activity generated by the curvature of the Schwarzschild black-hole geometry close to the event horizon is studied for the case of a massless, conformal scalar field. The associated approximation to the unknown, exact propagator in the Hartle-Hawking vacuum state for small values of the radial coordinate above $r = 2M$ results in an analytic expression which manifestly features its dependence on the background space-time geometry. This approximation to the Hartle-Hawking scalar propagator on the Schwarzschild black-hole geometry is, for that matter, distinct from all other. It is shown that the stated approximation is valid for physical distances which range from the event horizon to values which are orders of magnitude above the scale within which quantum and backreaction effects are comparatively pronounced. An expression is obtained for the renormalised $$ in the Hartle-Hawking vacuum state which reproduces the established results on the event horizon and in that segment of the exterior geometry within which the approximation is valid. In contrast to previous results the stated expression has the superior feature of being entirely analytic. The effect of the manifold's causal structure to scalar propagation is also studied.Comment: 34 pages, 2 figures. Published on line on October 16, 2009 and due to appear in print in Gen.Rel.Gra

Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes

Analytical approximations for ${}$ and ${}$ of a quantized scalar field in static spherically symmetric spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state. The expressions for ${}$ and ${}$ are divided into low- and high-frequency parts. The contributions of the high-frequency modes to these quantities are calculated for an arbitrary quantum state. As an example, the low-frequency contributions to ${}$ and ${}$ are calculated in asymptotically flat spacetimes in a quantum state corresponding to the Minkowski vacuum (Boulware quantum state). The limits of the applicability of these approximations are discussed.Comment: revtex4, 17 pages; v2: three references adde

Vacuum polarization in two-dimensional static spacetimes and dimensional reduction

We obtain an analytic approximation for the effective action of a quantum scalar field in a general static two-dimensional spacetime. We apply this to the dilaton gravity model resulting from the spherical reduction of a massive, non-minimally coupled scalar field in the four-dimensional Schwarzschild geometry. Careful analysis near the event horizon shows the resulting two-dimensional system to be regular in the Hartle-Hawking state for general values of the field mass, coupling, and angular momentum, while at spatial infinity it reduces to a thermal gas at the black-hole temperature.Comment: REVTeX 4, 23 pages. Accepted by PRD. Minor modifications from original versio

Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes

We study the renormalized stress-energy tensor (RSET) for static quantum states on (n+1)-dimensional, static, spherically symmetric black holes. By solving the conservation equations, we are able to write the stress-energy tensor in terms of a single unknown function of the radial co-ordinate, plus two arbitrary constants. Conditions for the stress-energy tensor to be regular at event horizons (including the extremal and ``ultra-extremal'' cases) are then derived using generalized Kruskal-like co-ordinates. These results should be useful for future calculations of the RSET for static quantum states on spherically symmetric black hole geometries in any number of space-time dimensions.Comment: 9 pages, no figures, RevTeX4, references added, accepted for publication in General Relativity and Gravitatio

Method to compute the stress-energy tensor for the massless spin 1/2 field in a general static spherically symmetric spacetime

A method for computing the stress-energy tensor for the quantized, massless, spin 1/2 field in a general static spherically symmetric spacetime is presented. The field can be in a zero temperature state or a non-zero temperature thermal state. An expression for the full renormalized stress-energy tensor is derived. It consists of a sum of two tensors both of which are conserved. One tensor is written in terms of the modes of the quantized field and has zero trace. In most cases it must be computed numerically. The other tensor does not explicitly depend on the modes and has a trace equal to the trace anomaly. It can be used as an analytic approximation for the stress-energy tensor and is equivalent to other approximations that have been made for the stress-energy tensor of the massless spin 1/2 field in static spherically symmetric spacetimes.Comment: 34 pages, no figure

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A second fourth-order ordinary differential equation for the general Fourier coefficent is derived from an integral representation of the coefficient, and both differential equations are shown to be equivalent. Series solutions for the various Fourier coefficients are also given, mostly in terms of Legendre functions and Bessel/Hankel functions. These are derived from the closed form hypergeometric solutions or an integral representation, or both. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented

Fluctuations of an evaporating black hole from back reaction of its Hawking radiation: Questioning a premise in earlier work

This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole. We explain how the stochastic gravity formalism can be a useful tool for that purpose within a low-energy effective field theory approach to quantum gravity. As an explicit example we apply it to the study of the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in earlier work on spherically-symmetric induced fluctuations, is carefully analyzed and found to be invalid. Our analysis suggests the existence of an infinite amplitude for the fluctuations of the horizon as a three-dimensional hypersurface. We emphasize the need for understanding and designing operational ways of probing quantum metric fluctuations near the horizon and extracting physically meaningful information.Comment: 10 pages, REVTeX; minor changes, a few references added and a brief discussion of their relevance included. To appear in the proceedings of the 10th Peyresq meeting. Dedicated to Rafael Sorkin on the occasion of his 60th birthda

The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets

This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics

Signatures of the slow solar wind streams from active regions in the inner corona

Some of local sources of the slow solar wind can be associated with spectroscopically detected plasma outflows at edges of active regions accompanied with specific signatures in the inner corona. The EUV telescopes (e.g. SPIRIT/CORONAS-F, TESIS/CORONAS-Photon and SWAP/PROBA2) sometimes observed extended ray-like structures seen at the limb above active regions in 1MK iron emission lines and described as "coronal rays". To verify the relationship between coronal rays and plasma outflows, we analyze an isolated active region (AR) adjacent to small coronal hole (CH) observed by different EUV instruments in the end of July - beginning of August 2009. On August 1 EIS revealed in the AR two compact outflows with the Doppler velocities V =10-30 km/s accompanied with fan loops diverging from their regions. At the limb the ARCH interface region produced coronal rays observed by EUVI/STEREO-A on July 31 as well as by TESIS on August 7. The rays were co-aligned with open magnetic field lines expanded to the streamer stalks. Using the DEM analysis, it was found that the fan loops diverged from the outflow regions had the dominant temperature of ~1 MK, which is similar to that of the outgoing plasma streams. Parameters of the solar wind measured by STEREO-B, ACE, WIND, STEREO-A were conformed with identification of the ARCH as a source region at the Wang-Sheeley-Arge map of derived coronal holes for CR 2086. The results of the study support the suggestion that coronal rays can represent signatures of outflows from ARs propagating in the inner corona along open field lines into the heliosphere.Comment: Accepted for publication in Solar Physics; 31 Pages; 13 Figure