Time-Dependent Evolving Null Horizons of a Dynamical Spacetime

Totally geodesic null hypersurfaces have been widely used in the study of isolated black holes. In this paper, we introduce a new quasilocal notion of a family of totally umbilical null hypersurfaces called evolving null horizons (ENH) of a dynamical spacetime, satisfied under an appropriate energy condition. We focus on a variety of examples of ENHs and in some cases establish their relation with event and isolated horizons. We also present two specific physical models of an ENH in a black hole spacetime. Beside the examples, for further study we propose two open problems on possible general existence of an ENH in a black hole spacetime and its canonical or unique existence. The results of this paper have ample scope of working on totally umbilical null hypersurfaces of Lorentzian and, in general, semiRiemannian manifolds.

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Generalized Robertson-Walker Space-Time Admitting Evolving Null Horizons Related to a Black Hole Event Horizon

International Scholarly Research Notices ◽

10.1155/2016/9312525 ◽

2016 ◽

Vol 2016 ◽

pp. 1-6

Author(s):

K. L. Duggal

Keyword(s):

Black Hole ◽

Event Horizon ◽

Space Time ◽

Time Dependent ◽

New Technique ◽

Open Problems ◽

Totally Umbilical ◽

Kinematic Condition ◽

A New Technique

A new technique is used to study a family of time-dependent null horizons, called “Evolving Null Horizons” (ENHs), of generalized Robertson-Walker (GRW) space-time (M¯,g¯) such that the metric g¯ satisfies a kinematic condition. This work is different from our early papers on the same issue where we used (1+n)-splitting space-time but only some special subcases of GRW space-time have this formalism. Also, in contrast to previous work, we have proved that each member of ENHs is totally umbilical in (M¯,g¯). Finally, we show that there exists an ENH which is always a null horizon evolving into a black hole event horizon and suggest some open problems.

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Regular black hole interior spacetime supported by three-form field

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09080-1 ◽

2021 ◽

Vol 81 (4) ◽

Author(s):

Mariam Bouhmadi-López ◽

Che-Yu Chen ◽

Xiao Yan Chew ◽

Yen Chin Ong ◽

Dong-han Yeom

Keyword(s):

Black Hole ◽

Energy Condition ◽

Null Energy Condition ◽

De Sitter ◽

Regular Black Hole ◽

Black Hole Spacetime ◽

Form Field ◽

Black Hole Interior ◽

Metric Function ◽

Geodesically Complete

AbstractIn this paper, we show that a minimally coupled 3-form endowed with a proper potential can support a regular black hole interior. By choosing an appropriate form for the metric function representing the radius of the 2-sphere, we solve for the 3-form field and its potential. Using the obtained solution, we construct an interior black hole spacetime which is everywhere regular. The singularity is replaced with a Nariai-type spacetime, whose topology is $$\text {dS}_2 \times \text {S}^2$$ dS 2 × S 2 , in which the radius of the 2-sphere is constant. So long as the interior continues to expand indefinitely, the geometry becomes essentially compactified. The 2-dimensional de Sitter geometry appears despite the negative potential of the 3-form field. Such a dynamical compactification could shed some light on the origin of de Sitter geometry of our Universe, exacerbated by the Swampland conjecture. In addition, we show that the spacetime is geodesically complete. The geometry is singularity-free due to the violation of the null energy condition.

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