Quasi-local mass near the singularity, the event horizon and the null infinity of black hole spacetimes

Characterizing black holes by means of classical event horizon is a global concept because it depends on future null infinity. This means, to find black hole region and event horizon requires the notion of the entire spacetime which is a teleological concept. With this as a motivation, we use local approach as a complementary means of characterizing black holes. In this paper we apply Gauss divergence and covariant divergence theorems to compute the fluxes and the divergences of the appropriate null vectors in Vaidya spacetime and thus explicitly determine the existence of trapped and marginally trapped surfaces in its black hole region.

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STRINGS FROM BLACK HOLES

International Journal of Modern Physics D ◽

10.1142/s0218271892000173 ◽

1992 ◽

Vol 01 (02) ◽

pp. 355-361 ◽

Cited By ~ 6

Author(s):

ICHIRO ODA

Keyword(s):

Black Holes ◽

Black Hole ◽

Event Horizon ◽

Zero Mode ◽

Center Of Mass ◽

Two Dimensional ◽

Null Infinity ◽

Four Dimensions ◽

Surface Fluctuation ◽

Future Null Infinity

It is shown that surface fluctuation of the event horizon of black holes in four dimensions which have been previously studied by ’t Hooft can be understood in terms of the topological two-dimensional string. This interpretation is valid at the lowest order, with respect to the magnitude of the radial momentum per magnitude of the transverse momentum, when particles near the event horizon fall into the black hole and from which particles then emit to future null infinity, owing to the Hawking radiation. This implies that in such a kinematical regime only the zero mode, that is, the center-of-mass momentum of the Euclidean string, propagates on the surface of the event horizon.

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Quasinormal Modes in Extremal Reissner–Nordström Spacetimes

Communications in Mathematical Physics ◽

10.1007/s00220-021-04137-4 ◽

2021 ◽

Author(s):

Dejan Gajic ◽

Claude Warnick

Keyword(s):

Wave Equation ◽

Event Horizon ◽

Hilbert Spaces ◽

Quasinormal Modes ◽

Meromorphic Continuation ◽

De Sitter ◽

Null Infinity ◽

Asymptotically Flat ◽

Black Hole Spacetimes ◽

New Framework

AbstractWe present a new framework for characterizing quasinormal modes (QNMs) or resonant states for the wave equation on asymptotically flat spacetimes, applied to the setting of extremal Reissner–Nordström black holes. We show that QNMs can be interpreted as honest eigenfunctions of generators of time translations acting on Hilbert spaces of initial data, corresponding to a suitable time slicing. The main difficulty that is present in the asymptotically flat setting, but is absent in the previously studied asymptotically de Sitter or anti de Sitter sub-extremal black hole spacetimes, is that $$L^2$$ L 2 -based Sobolev spaces are not suitable Hilbert space choices. Instead, we consider Hilbert spaces of functions that are additionally Gevrey regular at infinity and at the event horizon. We introduce $$L^2$$ L 2 -based Gevrey estimates for the wave equation that are intimately connected to the existence of conserved quantities along null infinity and the event horizon. We relate this new framework to the traditional interpretation of quasinormal frequencies as poles of the meromorphic continuation of a resolvent operator and obtain new quantitative results in this setting.

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A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström

Communications in Mathematical Physics ◽

10.1007/s00220-020-03857-3 ◽

2020 ◽

Vol 380 (1) ◽

pp. 323-408

Author(s):

Yannis Angelopoulos ◽

Stefanos Aretakis ◽

Dejan Gajic

Keyword(s):

Black Hole ◽

Wave Equation ◽

Event Horizon ◽

Scattering Theory ◽

Physical Space ◽

Extremal Black Hole ◽

Null Infinity ◽

Interior Region ◽

Exterior Region ◽

Black Hole Interior

Abstract It is known that sub-extremal black hole backgrounds do not admit a (bijective) non-degenerate scattering theory in the exterior region due to the fact that the redshift effect at the event horizon acts as an unstable blueshift mechanism in the backwards direction in time. In the extremal case, however, the redshift effect degenerates and hence yields a much milder blueshift effect when viewed in the backwards direction. In this paper, we construct a definitive (bijective) non-degenerate scattering theory for the wave equation on extremal Reissner–Nordström backgrounds. We make use of physical-space energy norms which are non-degenerate both at the event horizon and at null infinity. As an application of our theory we present a construction of a large class of smooth, exponentially decaying modes. We also derive scattering results in the black hole interior region.

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Stable circular orbits in Kaluza-Klein black hole spacetimes

Physical Review D ◽

10.1103/physrevd.103.124004 ◽

2021 ◽

Vol 103 (12) ◽

Author(s):

Shinya Tomizawa ◽

Takahisa Igata

Keyword(s):

Black Hole ◽

Circular Orbits ◽

Black Hole Spacetimes ◽

Kaluza Klein

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Correlation functions in finite temperature CFT and black hole singularities

Journal of High Energy Physics ◽

10.1007/jhep06(2021)048 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

D. Rodriguez-Gomez ◽

J.G. Russo

Keyword(s):

Black Hole ◽

Event Horizon ◽

Correlation Functions ◽

Finite Temperature ◽

Proper Time ◽

Black Brane ◽

Point Function ◽

Black Hole Singularity ◽

Point Correlation ◽

Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

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