arXiv subjects

George Tsoupros

Publications and source records attributed to George Tsoupros.

12 recordsLinked to original sources

arXiv2024

Across-Horizon Propagation and Infinite Time-Dilation: An Independent Approach to Hawking Radiation

The conformal scalar propagator as an explicit function of the Schwarzschild black-hole space-time has been established in the preceding three projects. The present project examines the precise relation which that propagator has to the amplitude the Schwarzschild black hole emit a scalar particle in a particular mode of positive energy. It is thereby established that the effect of infinite time-dilation on the event horizon results in both, the thermal radiation in the background of a static exterior space-time geometry and the detraction from thermality if energy-conservation is properly imposed as a constraint on scalar propagation. The derivation of the latter signifies an equivalent approach to the result of Parikh and Wilczek from the semi-classical perspective of the distant observer. From that perspective for that matter, Hawking radiation emerges in both contexts as the exclusive consequence of infinite time-dilation on the event horizon. These results are consistent with Hawking radiation as the exclusive consequence of the causal structure of the Schwarzschild black-hole space-time both, in a static exterior geometry and in such dynamical exterior geometry as energy-conservation signifies. The extension of the thermal case to other spin-fields and black-hole geometries is discussed.

hep-th↗

arXiv2013

Conformal Scalar Propagation and Hawking Radiation

The construction of the conformal scalar propagator which has been obtained in the preceding two projects as an analytic function of the Schwarzschild black-hole space-time is completed with a boundary condition imposed by the physical context through contour integration in the exterior vicinity of the event horizon. It is shown that, as a consequence of the semi-classical character which the emitted quanta have in that exterior vicinity, the particle production by the Schwarzschild black hole which was formally established in the preceding project is identical to thermal Hawking radiation. By extension, it is established that such a particle production corresponds to a spectrum which detracts from thermality by the amount predicted by Parikh and Wilczek if energy conservation is properly imposed as a constraint on scalar propagation. The results obtained herein support the case made by S. Hawking on the relation between quantum propagation and observation of particles produced by a black hole.

hep-th↗

arXiv2011

Conformal Scalar Propagation inside the Schwarzschild Black Hole

The analytic expression obtained in the preceding project for the massless conformal scalar propagator in the Hartle-Hawking vacuum state for small values of the Schwarzschild radial coordinate above $ r = 2M$ is analytically extended into the interior of the Schwarzschild black hole. The result of the analytical extension coincides with the exact propagator for a small range of values of the Schwarzschild radial coordinate below $ r = 2M$ and is an analytic expression which manifestly features its dependence on the background space-time geometry. This feature as well as the absence of any assumptions and prerequisites in the derivation render this Hartle-Hawking scalar propagator in the interior of the Schwarzschild black-hole geometry distinct from previous results. The two propagators obtained in the interior and in the exterior region of the Schwarzschild black hole are matched across the event horizon. The result of that match is a massless conformal scalar propagator in the Hartle-Hawking vacuum state which is shown to describe particle production by the Schwarzschild black hole.

hep-th↗

arXiv2010

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 $ <ϕ^2(x)>$ 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.

hep-th↗

arXiv2004

Conformal Anomalies for Interacting Scalar Fields on Curved Manifolds with Boundary

The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit calculations are given for those contributions to the conformal anomaly which emerge as a result of free scalar propagation as well as from scalar self-interactions up to second order in the scalar self-coupling. The renormalisation-group behaviour of the theory is, subsequently, exploited in order to advance the evaluation of the conformal anomaly to third order in the scalar self-coupling. In effect, complete contributions to the theory's conformal anomaly are evaluated up to fourth-loop order.

hep-th↗

arXiv2004

Conformal Anomaly for Free Scalar Propagation on Curved Bounded Manifolds

The trace anomaly for free propagation in the context of a conformally invariant scalar field theory defined on a curved manifold of positive constant curvature with boundary is evaluated through use of an asymptotic heat kernel expansion. In addition to their direct physical significance the results are also of relevance to the holographic principle and to Quantum Cosmology.

hep-th↗

arXiv2003

Perturbative Evaluation of Interacting Scalar Fields on a Curved Manifold with Boundary

The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the theory to second order in the scalar self-coupling pursued herein involves explicit calculations of up to third loop-order and reveals that, in addition to the renormalisation of the scalar self-coupling and scalar field, the removal of all divergences necessitates the introduction of conformally non-invariant counterterms proportional to $ RΦ^2$ and $ KΦ^2$ in the bare scalar action as well as counterterms proportional to $ RK^2$, $ R^2$ and $ RK$ in the gravitational action. The substantial backreaction effects and their relevance to the renormalisation procedure are analysed.

hep-th↗

arXiv2002

Perturbative Evaluation of the Effective Action for a Self-Interacting Conformal Field on a Manifold with Boundary

In a series of three projects a new technique which allows for higher-loop renormalisation on a manifold with boundary has been developed and used in order to assess the effects of the boundary on the dynamical behaviour of the theory. Commencing with a conceptual approach to the theoretical underpinnings of the, underlying, spherical formulation of Euclidean Quantum Field Theory this overview presents an outline of the stated technique's conceptual development, mathematical formalism and physical significance.

hep-th↗

arXiv2002

Spherical Formulation for Diagramatic Evaluations on a Manifold with Boundary

The mathematical formalism necessary for the diagramatic evaluation of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The evaluation of quantum corrections to the effective action past one-loop necessitates diagramatic techniques. Diagramatic evaluations and higher loop-order renormalisation can be best accomplished on a Riemannian manifold of constant curvature accommodating a boundary of constant extrinsic curvature. In such a context the stated evaluations can be accomplished through a consistent interpretation of the Feynman rules within the spherical formulation of the theory for which the method of images allows. To this effect, the mathematical consequences of such an interpretation are analyzed and the spherical formulation of the Feynman rules on the bounded manifold is, as a result, developed.

hep-th↗

arXiv2002

Perturbative Evaluation of the Zero-Point function for Self-Interacting Scalar Field on a Manifold with Boundary

The character of quantum corrections to the gravitational action of a conformally invariant field theory for a self-interacting scalar field on a manifold with boundary is considered at third loop-order in the perturbative expansion of the zero-point function. Diagramatic evaluations and higher loop-order renormalisation can be best accomplished on a Riemannian manifold of constant curvature accommodating a boundary of constant extrinsic curvature. The associated spherical formulation for diagramatic evaluations reveals a non-trivial effect which the topology of the manifold has on the vacuum processes and which ultimately dissociates the dynamical behaviour of the quantised field from its behaviour in the absence of a boundary. The first surface divergence is evaluated and the necessity for simultaneous renormalisation of volume and surface divergences is shown.

hep-th↗

arXiv2000

Radiative Contributions to the Effective Action of Self-Interacting Scalar Field on a Manifold with Boundary

The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature the boundary of which is characterised by constant extrinsic curvature. An extension of the spherical formulation in the presence of a boundary is attained through use of the method of images. Contrary to the consolidated vanishing effect in maximally symmetric space-times the contribution of the massless "tadpole" diagram no longer vanishes in dimensional regularisation. As a result, conformal invariance is broken due to boundary-related vacuum contributions. The evaluation of one-loop contributions to the two-point function suggests an extension, in the presence of matter couplings, of the simultaneous volume and boundary renormalisation in the effective action.

hep-th↗

arXiv1998

Scaling Behaviour of Conformal Fields in Curved Three-dimensional Space

The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field. The analysis of the theory's scaling behaviour reveals that scalar-loop effects contribute to the conformal anomaly only at advanced orders allowing for a range of relevant energy scales which extend to those comparable to the non-perturbative scale of Planck mass.

gr-qc↗