English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This work offers a didactical introduction to the calculations andgeometrical properties of a static, spherically symmetric spacetime foliated byhyperboloidal time surfaces. We discuss the various degrees of freedominvolved, namely the height function, responsible for introducing thehyperboloidal time coordinate, and a radial compactification function. Acentral outcome is the expression of the Trautman-Bondi mass in terms of thehyperboloidal metric functions. Moreover, we apply this formalism to a class ofwave equations commonly used in black-hole perturbation theory. Additionally,we provide a comprehensive derivation of the hyperboloidal minimal gauge,introducing two alternative approaches within this conceptual framework: thein-out and out-in strategies. Specifically, we demonstrate that the heightfunction in the in-out strategy follows from the well-known tortoise coordinateby changing the sign of the terms that become singular at future null infinity.Similarly, for the out-in strategy, a sign change also occurs in the tortoisecoordinate's regular terms. We apply the methodology to the followingspacetimes: Singularity-approaching slices in Schwarzschild, higher-dimensionalblack holes, black hole with matter halo, and Reissner- Nordstr\"om-de Sitter.From this heuristic study, we conjecture that the out-in strategy is bestadapted for black hole geometries that account for environmental or effectivequantum effects.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics