PARTICLES WITH NEGATIVE ENERGIES IN BLACK HOLES

The problem of the existence of particles with negative energies inside and outside of Schwarzschild, charged and rotating black holes is investigated. Different definitions of the energy of the particle inside the Schwarzschild black hole are analyzed and it is shown in which cases this energy can be negative. A comparison is made for the cases of rotating black holes between those described by the Kerr metric when the energy of the particle can be negative in the ergosphere and the Reissner–Nordstrøm metric.

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An introduction to black holes

Geometry of Black Holes ◽

10.1093/oso/9780198855415.003.0004 ◽

2020 ◽

pp. 117-199

Author(s):

Piotr T. Chruściel

Keyword(s):

Black Holes ◽

Black Hole ◽

Kerr Metric ◽

Schwarzschild Solution ◽

Stationary Black Hole ◽

Black Hole Spacetimes ◽

Rotating Black Holes ◽

General Vacuum

In this chapter the basics of the geometry of stationary black-hole spacetimes are presented. We start in Section 4.1 with a brief review of astrophysical black holes. We continue in Section 4.2 with the presentation of the flagship black hole, the Schwarzschild solution: we construct there its various extensions, and analyse some of its properties. The general notions arising in the context of black-hole geometries are presented in Section 4.3. A systematic discussion of extensions of spacetimes is carried out in Section 4.4. The charged counterparts of the Schwarzchild metric, namely the Reissner–Nordström metrics, are analysed in Section 4.5. The Kerr metric, expected to describe the most general vacuum, stationary, and rotating black holes, is presented in Section 4.6. The electrovacuum Majumdar–Papapetrou spacetimes, containing two or more disconnected black-hole regions, are described in Section 4.7.

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Black hole hair removal for N = 4 CHL models

Journal of High Energy Physics ◽

10.1007/jhep02(2021)125 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Subhroneel Chakrabarti ◽

Suresh Govindarajan ◽

P. Shanmugapriya ◽

Yogesh K. Srivastava ◽

Amitabh Virmani

Keyword(s):

Black Holes ◽

Black Hole ◽

Degrees Of Freedom ◽

Microscopic Analysis ◽

Flat Space ◽

Special Care ◽

Hair Removal ◽

Partition Functions ◽

Rotating Black Holes

Abstract Although BMPV black holes in flat space and in Taub-NUT space have identical near-horizon geometries, they have different indices from the microscopic analysis. For K3 compactification of type IIB theory, Sen et al. in a series of papers identified that the key to resolving this puzzle is the black hole hair modes: smooth, normalisable, bosonic and fermionic degrees of freedom living outside the horizon. In this paper, we extend their study to N = 4 CHL orbifold models. For these models, the puzzle is more challenging due to the presence of the twisted sectors. We identify hair modes in the untwisted as well as twisted sectors. We show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions agree. Special care is taken to present details on the smoothness analysis of hair modes for rotating black holes, thereby filling an essential gap in the literature.

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General Relativity

The Physical World ◽

10.1093/oso/9780198795933.003.0007 ◽

2017 ◽

Author(s):

Nicholas Manton ◽

Nicholas Mee

Keyword(s):

Black Holes ◽

General Relativity ◽

Field Equation ◽

Einstein Field Equation ◽

Kerr Metric ◽

Gravitational Lenses ◽

Field Equations ◽

Spacetime Geometry ◽

Tests Of General Relativity ◽

Rotating Black Holes

This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the equivalence principle, tidal forces in Newtonian gravity and their connection to curved spacetime geometry. This leads to a derivation of the field equation. Tests of general relativity are considered: Mercury’s perihelion advance, gravitational redshift, the deflection of starlight and gravitational lenses. The exterior and interior Schwarzschild solutions are discussed. Eddington–Finkelstein coordinates are used to describe objects falling into non-rotating black holes. The Kerr metric is used to describe rotating black holes and their astrophysical consequences. Gravitational waves are described and used to explain the orbital decay of binary neutron stars. Their recent detection by LIGO and the beginning of a new era of gravitational wave astronomy is discussed. Finally, the gravitational field equations are derived from the Einstein–Hilbert action.

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WHAT IS THE TOPOLOGY OF A SCHWARZSCHILD BLACK HOLE?

International Journal of Modern Physics Conference Series ◽

10.1142/s201019451200832x ◽

2012 ◽

Vol 18 ◽

pp. 125-129 ◽

Cited By ~ 2

Author(s):

EDMUNDO M. MONTE

Keyword(s):

Black Holes ◽

Black Hole ◽

Space Time ◽

Higher Dimension ◽

Schwarzschild Black Hole

We investigate the topology of Schwarzschild's black holes through the immersion of this space-time in space of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschilds black hole.

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Shadow cast of noncommutative black holes in Rastall gravity

Modern Physics Letters A ◽

10.1142/s0217732320501631 ◽

2020 ◽

Vol 35 (20) ◽

pp. 2050163 ◽

Cited By ~ 2

Author(s):

Ali Övgün ◽

İzzet Sakallı ◽

Joel Saavedra ◽

Carlos Leiva

Keyword(s):

Black Holes ◽

Black Hole ◽

Emission Rate ◽

Model Parameters ◽

Spherically Symmetric ◽

Image Model ◽

Schwarzschild Black Hole ◽

Physical Validity ◽

Shadow Cast ◽

Noncommutative Parameter

We study the shadow and energy emission rate of a spherically symmetric noncommutative black hole in Rastall gravity. Depending on the model parameters, the noncommutative black hole can reduce to the Schwarzschild black hole. Since the nonvanishing noncommutative parameter affects the formation of event horizon, the visibility of the resulting shadow depends on the noncommutative parameter in Rastall gravity. The obtained sectional shadows respect the unstable circular orbit condition, which is crucial for physical validity of the black hole image model.

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Hawking radiation of charged fermions from accelerating and rotating black holes with generalized uncertainty principle

International Journal of Modern Physics D ◽

10.1142/s0218271819501025 ◽

2019 ◽

Vol 28 (08) ◽

pp. 1950102

Author(s):

Muhammad Rizwan ◽

Khalil Ur Rehman

Keyword(s):

Black Holes ◽

Black Hole ◽

Uncertainty Principle ◽

Hawking Radiation ◽

Generalized Uncertainty Principle ◽

Hawking Temperature ◽

Black Hole Evaporation ◽

Rotating Black Holes ◽

Gravity Effects ◽

Made In

By considering the quantum gravity effects based on generalized uncertainty principle, we give a correction to Hawking radiation of charged fermions from accelerating and rotating black holes. Using Hamilton–Jacobi approach, we calculate the corrected tunneling probability and the Hawking temperature. The quantum corrected Hawking temperature depends on the black hole parameters as well as quantum number of emitted particles. It is also seen that a remnant is formed during the black hole evaporation. In addition, the corrected temperature is independent of an angle [Formula: see text] which contradicts the claim made in the literature.

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HAMILTONIAN FORMALISM FOR BLACK HOLES AND QUANTIZATION II

International Journal of Modern Physics D ◽

10.1142/s0218271896000163 ◽

1996 ◽

Vol 05 (03) ◽

pp. 227-250 ◽

Cited By ~ 34

Author(s):

MARCO CAVAGLIÀ ◽

VITTORIO DE ALFARO ◽

ALEXANDRE T. FILIPPOV

Keyword(s):

Hilbert Space ◽

Black Holes ◽

Black Hole ◽

Invariant Measure ◽

Hamiltonian Formalism ◽

Quantization Method ◽

Schwarzschild Black Hole ◽

Canonical Formulation ◽

Gauge Fixing ◽

Rigid Transformations

We quantize by the Dirac-Wheeler-DeWitt method the canonical formulation of the Schwarzschild black hole developed in a previous paper. We investigate the properties of the operators that generate rigid symmetries of the Hamiltonian, establish the form of the invariant measure under the rigid transformations, and determine the gauge fixed Hilbert space of states. We also prove that the reduced quantization method leads to the same Hilbert space for a suitable gauge fixing.

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VOROS PRODUCT AND NONCOMMUTATIVE INSPIRED BLACK HOLES

Modern Physics Letters A ◽

10.1142/s0217732313500302 ◽

2013 ◽

Vol 28 (09) ◽

pp. 1350030

Author(s):

SUNANDAN GANGOPADHYAY

Keyword(s):

Black Holes ◽

Black Hole ◽

Extremal Point ◽

De Sitter ◽

Schwarzschild Black Hole ◽

Standard Identity ◽

Schwarzschild Geometry ◽

Area Law

We emphasize the importance of the Voros product in defining the noncommutative (NC) inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner–Nordström (RN) black holes show that the area law holds up to order [Formula: see text]. The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy E for these black holes is then obtained and a deviation from the standard identity E = 2STH is found at the order [Formula: see text]. This deviation leads to a nonvanishing Komar energy at the extremal point TH = 0 of these black holes. The Smarr formula is finally worked out for the NC Schwarzschild black hole. Similar features also exist for a de Sitter–Schwarzschild geometry.

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CHARGED ROTATING BLACK HOLES IN DILATON GRAVITY

International Journal of Modern Physics A ◽

10.1142/s0217751x07037032 ◽

2007 ◽

Vol 22 (26) ◽

pp. 4849-4858 ◽

Cited By ~ 13

Author(s):

A. SHEYKHI ◽

N. RIAZI

Keyword(s):

Black Holes ◽

Black Hole ◽

Angular Momentum ◽

Dilaton Field ◽

Dilaton Gravity ◽

Charged Black Holes ◽

Static Solutions ◽

Rotating Black Holes ◽

Small Rotation ◽

Type Potential

We consider charged black holes with curved horizons, in five-dimensional dilaton gravity in the presence of Liouville-type potential for the dilaton field. We show how, by solving a pair of coupled differential equations, infinitesimally small angular momentum can be added to these static solutions to obtain charged rotating dilaton black hole solutions. In the absence of dilaton field, the nonrotating version of the solution reduces to the five-dimensional Reissner–Nordström black hole, and the rotating version reproduces the five-dimensional Kerr–Newman modification thereof for small rotation parameter. We also compute the angular momentum and the angular velocity of these rotating black holes which appear at the first order.

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