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

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.

scholarly journals Black Hole Interior from Loop Quantum Gravity

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Leonardo Modesto
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Event Horizon ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Semiclassical Analysis ◽  
Schwarzschild Solution ◽  
Quantum Black Hole ◽  
Minimum Value ◽  
Black Hole Interior

We calculate modifications to the Schwarzschild solution by using a semiclassical analysis of loop quantum black hole. We obtain a metric inside the event horizon that coincides with the Schwarzschild solution near the horizon but that is substantially different at the Planck scale. In particular, we obtain a bounce of theS2sphere for a minimum value of the radius and that it is possible to have another event horizon close to ther=0point.

scholarly journals THE MILNE SPACETIME AND THE HADRONIC RINDLER HORIZON

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1379-1384 ◽  
Author(s):  
H. CULETU
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Time Dependent ◽  
Anisotropic Fluid ◽  
Direct Relation ◽  
Schwarzschild Black Hole ◽  
Black Hole Interior ◽  
Flat Metric ◽  
Shear Tensor ◽  
Hadronic Rindler Horizon

A direct relation between the time-dependent Milne geometry and the Rindler spacetime is shown. Milne's metric corresponds to the region beyond Rindler's event horizon (in the wedge t ≻ |x|). We point out that inside a Schwarzschild black hole and near its horizon, the metric may be Milne's flat metric. It was found that the shear tensor associated to a congruence of fluid particles of the RHIC expanding fireball has the same structure as that corresponding to the anisotropic fluid from the black hole interior, even though the latter geometry is curved.

Kantowski-Sachs Cosmology, Weyl Geometry and Asymptotic Safety in Quantum Gravity

2020 ◽  
Author(s):  
Carlos Castro Perelman
Keyword(s):  
Black Hole ◽  
Planck Scale ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Exterior Region ◽  
Asymptotic Safety ◽  
Sign Change ◽  
Average Action ◽  
Black Hole Interior

A brief review of the essentials of Asymptotic Safety and the Renormalization Group (RG) improvement of the Schwarzschild Black Hole that removes the r = 0 singularity is presented. It is followed with a RG-improvement of the Kantowski-Sachs metric associated with a Schwarzschild black hole interior and such that there is no singularity at t = 0 due to the running Newtonian coupling G(t) (vanishing at t = 0). Two temporal horizons at t _- \simeq t_P and t_+ \simeq t_H are found. For times below the Planck scale t < t_P, and above the Hubble time t > t_H, the components of the Kantowski-Sachs metric exhibit a key sign change, so the roles of the spatial z and temporal t coordinates are exchanged, and one recovers a repulsive inflationary de Sitter-like core around z = 0, and a Schwarzschild-like metric in the exterior region z > R_H = 2G_o M. The inclusion of a running cosmological constant \Lambda (t) follows. We proceed with the study of a dilaton-gravity (scalar-tensor theory) system within the context of Weyl's geometry that permits to single out the expression for the classical potential V (\phi ) = \kappa\phi^4, instead of being introduced by hand, and find a family of metric solutions which are conformally equivalent to the (Anti) de Sitter metric. To conclude, an ansatz for the truncated effective average action of ordinary dilaton-gravity in Riemannian geometry is introduced, and a RG-improved Cosmology based on the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is explored.

scholarly journals On the Trapped Surface Characterization of Black Hole Region in Vaidya Spacetime

2018 ◽  
Vol 10 (1) ◽  
pp. 59
Author(s):  
Mohammed Kumah ◽  
Francis T. Oduro
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Surface Characterization ◽  
Local Approach ◽  
Null Infinity ◽  
Trapped Surfaces ◽  
Marginally Trapped Surfaces ◽  
Trapped Surface

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.

scholarly journals THE SCALAR WAVE EQUATION IN A NON-COMMUTATIVE SPHERICALLY SYMMETRIC SPACE-TIME

2008 ◽  
Vol 05 (01) ◽  
pp. 33-47 ◽  
Author(s):  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO ◽  
GENNARO MIELE
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Rest Mass ◽  
Physical Space ◽  
Scalar Fields ◽  
Space Time ◽  
Asymptotic Behavior Of Solutions ◽  
Scalar Wave ◽  
Null Infinity ◽  
Scalar Wave Equation

Recent work in the literature has studied a version of non-commutative Schwarzschild black holes where the effects of non-commutativity are described by a mass function depending on both the radial variable r and a non-commutativity parameter θ. The present paper studies the asymptotic behavior of solutions of the zero-rest-mass scalar wave equation in such a modified Schwarzschild space-time in a neighborhood of spatial infinity. The analysis is eventually reduced to finding solutions of an inhomogeneous Euler–Poisson–Darboux equation, where the parameter θ affects explicitly the functional form of the source term. Interestingly, for finite values of θ, there is full qualitative agreement with general relativity: the conformal singularity at spacelike infinity reduces in a considerable way the differentiability class of scalar fields at future null infinity. In the physical space-time, this means that the scalar field has an asymptotic behavior with a fall-off going on rather more slowly than in flat space-time.

scholarly journals NONSINGULAR BLACK HOLES FROM GRAVITY–MATTER-BRANE LAGRANGIANS

2010 ◽  
Vol 25 (08) ◽  
pp. 1571-1596 ◽  
Author(s):  
EDUARDO GUENDELMAN ◽  
ALEXANDER KAGANOVICH ◽  
EMIL NISSIMOV ◽  
SVETLANA PACHEVA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Constant ◽  
Radial Coordinate ◽  
De Sitter ◽  
Wormhole Solution ◽  
Interior Region ◽  
Exterior Region ◽  
Inner Horizon ◽  
Self Consistent

We consider self-consistent coupling of bulk Einstein–Maxwell–Kalb–Ramond system to codimension-one charged lightlikep-brane with dynamical (variable) tension (LL-brane). The latter is described by a manifestly reparametrization-invariant worldvolume action significantly different from the ordinary Nambu–Goto one. We show that the LL-brane is the appropriate gravitational and charge source in the Einstein–Maxwell–Kalb–Ramond equations of motion needed to generate a self-consistent solution describing nonsingular black hole. The latter consists of de Sitter interior region and exterior Reissner–Nordström region glued together along their common horizon (it is the inner horizon from the Reissner–Nordström side). The matching horizon is automatically occupied by the LL-brane as a result of its worldvolume Lagrangian dynamics, which dynamically generates the cosmological constant in the interior region and uniquely determines the mass and charge parameters of the exterior region. Using similar techniques we construct a self-consistent wormhole solution of Einstein–Maxwell system coupled to electrically neutral LL-brane, which describes two identical copies of a nonsingular black hole region being the exterior Reissner–Nordström region above the inner horizon, glued together along their common horizon (the inner Reissner–Nordström one) occupied by the LL-brane. The corresponding mass and charge parameters of the two black hole "universes" are explicitly determined by the dynamical LL-brane tension. This also provides an explicit example of Misner–Wheeler "charge without charge" phenomenon. Finally, this wormhole solution connecting two nonsingular black holes can be transformed into a special case of Kantowski–Sachs bouncing cosmology solution if instead of Reissner–Nordström we glue together two copies of the exterior Reissner–Nordström–de Sitter region with big enough bare cosmological constant, such that the radial coordinate becomes a timelike variable everywhere in the two "universes," except at the matching hypersurface occupied by the LL-brane.

STRINGS FROM BLACK HOLES

1992 ◽  
Vol 01 (02) ◽  
pp. 355-361 ◽  
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.

scholarly journals Quasinormal Modes in Extremal Reissner–Nordström Spacetimes

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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