Recent Trends in Lorentzian Geometry

Sánchez, Miguel; Ortega, Miguel; Romero, Alfonso

doi:10.1007/978-1-4614-4897-6

Cited by 2 publications

(3 citation statements)

References 39 publications

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“…However, we have to take care to avoid ill-defined expressions such as C ↓ * ( 5 ∇ A h B ), which is accomplished by appropriate algebraic decomposition of 5 ∇ A h B . Next, to obtain (20) we have used (4) while the final step which leads to (23) uses the behaviour of the 4D covariant derivative under conformal rescalings of the metric, 5 (h)…”

Section: The Expansionmentioning

confidence: 99%

“…Area inequalities bound the area A of stable MOTS in terms of quantities defined on the MOTS, namely charges and, in the axially symmetric case, angular momenta ( [22,23]). Here we first briefly recall the area inequalities for Einstein-Maxwell and EMD in 4D, and in a 5D vacuum.…”

Section: Area Inequalitiesmentioning

confidence: 99%

“…A further motivation comes from the area inequalities for stable MOTS [21][22][23]. Such inequalities have been found in particular for axially symmetric, stable 2D MOTS in 4D Einstein-Maxwell by Clement et al [24,25] and in 4D Einstein-Maxwell dilaton (EMD) theory by Yazadjiev [26].…”

Section: Introductionmentioning

confidence: 98%

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Marginally outer trapped surfaces in higher dimensions

Paetz¹,

Simon²

2013

Class. Quantum Grav.

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We review the basic setup of Kaluza–Klein theory, namely a five-dimensional vacuum with a cyclic isometry, which corresponds to Einstein–Maxwell-dilaton theory in four-dimensional spacetime. We first recall the behaviour of Killing horizons under bundle lift and projection. We then show that the property of compact surfaces of being (stably) marginally trapped is preserved under lift and projection provided the appropriate (‘Pauli’) conformal scaling is used for the spacetime metric. We also discuss and compare recently proven area inequalities for stable axially symmetric two-dimensional and three-dimensional marginally outer trapped surfaces.

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Section: The Expansionmentioning

confidence: 99%

Section: Area Inequalitiesmentioning

confidence: 99%

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Marginally outer trapped surfaces in higher dimensions

Paetz¹,

Simon²

2013

Class. Quantum Grav.

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Fermat Metrics

Masiello

2021

Symmetry

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In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.

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Recent Trends in Lorentzian Geometry

Cited by 2 publications

References 39 publications

Marginally outer trapped surfaces in higher dimensions

Marginally outer trapped surfaces in higher dimensions

Fermat Metrics

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