The limits of Brans-Dicke spacetimes: a coordinate-free approach

Paiva, F. M.; Romero, C.

doi:10.1007/bf00759035

Cited by 38 publications

(31 citation statements)

References 15 publications

(26 reference statements)

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“…[35] for a discussion of the coordinate-dependence, and Refs. [26,27] for a coordinate-independent approach to the problem). A detailed study of the Brans solution requires considerations specific to this particular solution, which is not the main topic of the present paper, and will be the subject of a future work.…”

Section: Introductionmentioning

confidence: 99%

Illusions of general relativity in Brans-Dicke gravity

Faraoni

1999

Phys. Rev. D

114

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Contrary to common belief, the standard tenet of Brans-Dicke theory reducing to general relativity in the ω → ∞ limit is false when the trace of the matter energy-momentum tensor vanishes. The issue is clarified in a new approach using conformal transformations. The otherwise unaccountable limiting behavior of Brans-Dicke gravity is easily understood in terms of the conformal invariance of the theory when the sources of gravity have radiation-like properties. The rigorous computation of the asymptotic behavior of the Brans-Dicke scalar field is straightforward in this new approach.

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Section: Introductionmentioning

confidence: 99%

Illusions of general relativity in Brans-Dicke gravity

Faraoni

1999

Phys. Rev. D

114

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“…One away to solve this problem would be the use of the Cartan scalar techniques developed in [7,8] to find all limits of the concerning metric. The main difficulty is computational, since in the present case too many Cartan scalars are different from zero and they depend on more than one coordinate and parameter.…”

Section: Resultsmentioning

confidence: 99%

“…Later, [7] re-obtained these limits by using the Cartan scalar technique, and extended the results presenting new limits of the Schwarzschild metric and developing an approach to find all limits of a given spacetime (see also [8,15,16])…”

Section: The Geroch Limitsmentioning

confidence: 98%

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The Levi-Civita space–time as a limiting case of the γ space–time

Herrera

Paiva

Santos

1999

Journal of Mathematical Physics

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“…Kasner metric [27] and, strictly speaking, a coordinate-free approach [55][56][57] is needed to make limits rigorous.…”

Section: Isotropic Coordinatesmentioning

confidence: 99%

Stationary Black Holes in General Relativity

Faraoni

2015

Cosmological and Black Hole Apparent Horizons

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The noblest pleasure is the joy of understanding.-Leonardo da Vinci IntroductionBeginning with the Rindler horizons which appear for accelerated observers in Minkowski space without gravity, one comes quickly to acknowledge the presence of various types of horizons when gravity is introduced in spacetime: first one encounters black hole horizons and cosmological horizons. Then, studying classical and semiclassical black holes one is faced with inner, outer, Cauchy, and extremal horizons. The early literature on black holes and the works which developed black hole thermodynamics in the seventies had plenty to do with discussing stationary black holes and event horizons (e.g., [23,74,75]). Dynamical situations such as gravitational collapse, black hole evaporation due to Hawking radiation, and black holes interacting with non-trivial environments and exchanging mass-energy require that the concept of event horizon be generalized to some other construct with which it is possible to work. Conceivable dynamical situations include black holes accreting or expelling gravitating (i.e., non-test) matter; examples are Vaidya spacetimes, black holes immersed in a cosmological "background" other than de Sitter space, black holes emitting (and possibly also absorbing) Hawking radiation (which becomes significant in the last evolutionary stages with backreaction playing an important role), or black holes with variable mass because of other physical processes. If a black hole is placed in a non-trivial environment, its mass-energy should be also the internal energy which we need to account for in the first law of thermodynamics. This mass-energy must be defined carefully; usually it is identified with some quasi-local energy construct which is related to the notion of horizon. In these lectures we will use the Misner-Sharp-Hernandez mass in spherical symmetry and its generalization, the Hawking-Hayward quasi-local energy in the absence of spherical symmetry.Intuitively, an horizon is "a frontier between things observable and things unobservable" [64]. Inequivalent notions of black hole horizon abound in the technical literature and the terminology used features event,

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The limits of Brans-Dicke spacetimes: a coordinate-free approach

Abstract: We investigate the limit of Brans-Dicke spacetimes as ω → ∞ applying a coordinate-free technique. We obtain the limits of some known exact solutions. It is shown that these limits may not correspond to similar solutions in the general relativity theory.

Cited by 38 publications

References 15 publications

Illusions of general relativity in Brans-Dicke gravity

Illusions of general relativity in Brans-Dicke gravity

The Levi-Civita space–time as a limiting case of the γ space–time

Stationary Black Holes in General Relativity

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