<i>The Wave Equation on a Curved Space-Time</i>

Friedlander, F. G.; Jang, Pong Soo

doi:10.1063/1.3023428

Cited by 259 publications

(516 citation statements)

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“…Since the considered spacetimes are equipped, by definitions, with metrics and thus preferred volume measures, here we assume that distributions of D (M × M ) work on smooth compactly-supported scalar fields of D(M ) := C ∞ 0 (M ) as in [Fr75] instead of smooth compactly-supported scalar densities as in [Hör71]. As is well known this choice is pure matter of convention since the two points of view are equivalent.…”

Section: 2mentioning

confidence: 99%

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Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

Moretti

2008

Commun. Math. Phys.

109

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Abstract. This paper continues the analysis of the quantum states introduced in previous works and determined by the universal asymptotic structure of four-dimensional asymptotically flat vacuum spacetimes at null infinity M . It is now focused on the quantum state λM , of a massless conformally coupled scalar field φ propagating in M . λM is "holographically" induced in the bulk by the universal BMS-invariant state λ defined on the future null infinity + of M . It is done by means of the correspondence between observables in the bulk and those on the boundary at future null infinity discussed in previous papers. This induction is possible when some requirements are fulfilled, in particular whenever the spacetime M and the associated unphysical one,M , are globally hyperbolic and M admits future time infinity i + . λM coincides with Minkowski vacuum if M is Minkowski spacetime. It is now proved that, in the general case of a curved spacetime M , the state λM enjoys the following further remarkable properties. (i) λM is invariant under the (unit component of the Lie) group of isometries of the bulk spacetime M .(ii) λM fulfills a natural energy-positivity condition with respect to every notion of Killing time (if any) in the bulk spacetime M : If M admits a time-like Killing vector, the associated one-parameter group of isometries is represented by a strongly-continuous unitary group in the GNS representation of λM . The unitary group has positive self-adjoint generator without zero modes in the one-particle space. In this case λM is a so-called regular ground state. (iii) λM is (globally) Hadamard in M and thus it can be used as starting point for perturbative renormalisation procedure of QFT of φ in M .

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Section: 2mentioning

confidence: 99%

“…First of all we prove that λ M individuates a distribution in D (M ×M ), i.e. it is continuous in the relevant weak topology [Fr75] whenever the spacetime (M, g) is a vacuum asymptotically flat at null infinity spacetime and admits future temporal infinity i + . We give also a useful explicit expression for the distribution.…”

Section: 2mentioning

confidence: 99%

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

Moretti

2008

Commun. Math. Phys.

109

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“…Using (2.1) and (2.4), the n-th order perturbation components obey decoupled wave equations 5) where the source on the right hand side is generated by the lower order perturbations, and can be computed explicitely order by order. The general integral solution of (2.5) can be written using the Green's function method (see Theorem 6.3.1 of [22])…”

Section: Higher Order Shock Wave Perturbation Theorymentioning

confidence: 99%

Radiation from aD-dimensional collision of shock waves: Higher-order setup and perturbation theory validity

et al. 2013

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The collision of two D-dimensional, ultra-relativistic particles, described in General Relativity as Aichelberg-Sexl shock waves, is inelastic. In first order perturbation theory, the fraction of the initial centre of mass energy radiated away was recently shown to be 1/2 − 1/D. Here, we extend the formalism to higher orders in perturbation theory, and derive a general expression to extract the inelasticity, valid non-perturbatively, based on the Bondi mass loss formula. Then, to clarify why perturbation theory captures relevant physics of a strong field process in this problem, we provide one variation of the problem where the perturbative framework breaks down: the collision of ultra-relativistic charged particles. The addition of charge, and the associated repulsive nature of the source, originates an extra radiation burst, which we argue to be an artifact of the perturbative framework, veiling the relevant physics.

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“…The term in δ R (Γ) describes a contribution to the Green function from φ waves propagating along the light cone (Γ = 0), while the term Θ R (−Γ) describes the contribution to G R from tails of φ propagating inside the light cone (Γ < 0). The functions Σ(x ′ , x) and W (x ′ , x) are mere coefficients which (at least in principle) are determined once the spacetime metric is fixed [54,55]. The Einstein equivalence principle is imposed as follows on the physics of the field φ: when the spacetime manifold is progressively approximated by its tangent space (i.e.…”

Section: What Is the Value Of ξ ?mentioning

confidence: 99%

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Faraoni

2001

International Journal of Theoretical Physics

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Nonminimal coupling of the inflaton field to the Ricci curvature of spacetime is generally unavoidable, and the paradigm of inflation should be generalized by including the corresponding term ξRφ 2 /2 in the Lagrangian of the inflationary theory. This paper reports on the status of the programme of generalizing inflation. First, the problem of finding the correct value (or set of values) of the coupling constant ξ is analyzed; the result has important consequences for the success or failure of inflationary scenarios. Then, the slow-roll approximation to generalized inflation is studied. Both the unperturbed inflating universe models and scalar/tensor perturbations are discussed, and open problems are pointed out.

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The Wave Equation on a Curved Space-Time

Cited by 259 publications

References 0 publications

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

Radiation from aD-dimensional collision of shock waves: Higher-order setup and perturbation theory validity

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