scholarly journals Dissipative fields in de Sitter and black hole spacetimes: Quantum entanglement due to pair production and dissipation

2013 ◽  
Vol 87 (12) ◽  
Author(s):  
Julian Adamek ◽  
Xavier Busch ◽  
Renaud Parentani
Keyword(s):  
Black Hole ◽  
Pair Production ◽  
Quantum Entanglement ◽  
De Sitter ◽  
Black Hole Spacetimes

scholarly journals Energy of test objects on black hole spacetimes: A brief review

2015 ◽  
Vol 24 (14) ◽  
pp. 1550103 ◽  
Author(s):  
Alejandro Corichi
Keyword(s):  
Black Hole ◽  
Asymptotic Region ◽  
Gravitational Potential Energy ◽  
De Sitter ◽  
Conservation Of Energy ◽  
Asymptotically Flat ◽  
Black Hole Spacetimes ◽  
Test Particles ◽  
Exterior Regions ◽  
Test Objects

In this paper, we review the issue of defining energy for test particles on a background stationary spacetime. We revisit different notions of energy as defined by different observers. As is well-known, the existence of a timelike isometry allows for the notion of total conserved energy to be well defined. We use this well-known quantity to show that a gravitational potential energy can be consistently defined. As examples, we study the case of the exterior regions of an asymptotically flat black hole and of the [Formula: see text] Schwarzschild–de Sitter (SdS) case, where an asymptotic region is not available. We then consider the situation in which the test particle is absorbed by the black hole and analyze the energetics in detail. In particular, we show that the notion of horizon energy as defined by the isolated horizons formalism provides a satisfactory notion of energy compatible with the particle’s total conserved energy. With these choices, there is a global conservation of energy. Finally, we comment on a recent proposal to define energy of the black hole as seen by a nearby observer at rest, for which this feature is lost.

scholarly journals Extreme gravitational lensing in vicinity of Schwarzschild-de Sitter black holes

Open Physics ◽  
2007 ◽  
Vol 5 (4) ◽  
Author(s):  
Pavel Bakala ◽  
Petr Čermák ◽  
Stanislav Hledík ◽  
Zdeněk Stuchlík ◽  
Kamila Truparová
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Gravitational Lensing ◽  
High Performance ◽  
Computer Code ◽  
De Sitter ◽  
Simulation Code ◽  
Black Hole Spacetimes ◽  
Optical Projection ◽  
Free Falling

AbstractWe have developed a realistic, fully general relativistic computer code to simulate optical projection in a strong, spherically symmetric gravitational field. The standard theoretical analysis of optical projection for an observer in the vicinity of a Schwarzschild black hole is extended to black hole spacetimes with a repulsive cosmological constant, i.e, Schwarzschild-de Sitterspacetimes. Influence of the cosmological constant is investigated for static observers and observers radially free-falling from the static radius. Simulations include effects of the gravitational lensing, multiple images, Doppler and gravitational frequency shift, as well as the intensity amplification. The code generates images of the sky for the static observer and a movie simulations of the changing sky for the radially free-falling observer. Techniques of parallel programming are applied to get a high performance and a fast run of the BHC simulation code.

Geometry of Black Holes

2020 ◽  
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Einstein Equations ◽  
De Sitter ◽  
Black Hole Spacetimes ◽  
Local Coordinates ◽  
The Subject ◽  
Basic Facts ◽  
Kaluza Klein

There exists a large scientific literature on black holes, including many excellent textbooks of various levels of difficulty. However, most of these prefer physical intuition to mathematical rigour. The object of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject. The first part of the book starts with a presentation, in Chapter 1, of some basic facts about Lorentzian manifolds. Chapter 2 develops those elements of Lorentzian causality theory which are key to the understanding of black-hole spacetimes. We present some applications of the causality theory in Chapter 3, as relevant for the study of black holes. Chapter 4, which opens the second part of the book, constitutes an introduction to the theory of black holes, including a review of experimental evidence, a presentation of the basic notions, and a study of the flagship black holes: the Schwarzschild, Reissner–Nordström, Kerr, and Majumdar–Papapetrou solutions of the Einstein, or Einstein–Maxwell, equations. Chapter 5 presents some further important solutions: the Kerr–Newman–(anti-)de Sitter black holes, the Emperan–Reall black rings, the Kaluza–Klein solutions of Rasheed, and the Birmingham family of metrics. Chapters 6 and 7 present the construction of conformal and projective diagrams, which play a key role in understanding the global structure of spacetimes obtained by piecing together metrics which, initially, are expressed in local coordinates. Chapter 8 presents an overview of known dynamical black-hole solutions of the vacuum Einstein equations.

Further selected solutions

2020 ◽  
pp. 200-258
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
De Sitter ◽  
Stationary Black Hole ◽  
Static Vacuum ◽  
Black Hole Spacetimes ◽  
Wide Range ◽  
Dimensional Black Hole ◽  
Horizon Topology ◽  
Basic Features

In previous chapters we presented the key notions associated with stationary black-hole spacetimes, as well as the minimal set of metrics needed to illustrate the basic features of the world of black holes. In this chapter we present some further black holes, selected because of their physical and mathematical interest. We start, in Section 5.1, with the Kerr–de Sitter/anti-de Sitter metrics, the cosmological counterparts of the Kerr metrics. Section 5.2 contains a description of the Kerr–Newman–de Sitter/anti-de Sitter metrics, which are the charged relatives of the metrics presented in Section 5.1. In Section 5.3 we analyse in detail the global structure of the Emparan–Reall ‘black rings’: these are five-dimensional black-hole spacetimes with R × S 1 × S 2-horizon topology. The Rasheed metrics of Section 5.4 provide an example of black holes arising in Kaluza–Klein theories. The Birmingham family of metrics, presented in Section 5.5, forms the most general class known of explicit static vacuum metrics with cosmological constant in all dimensions, with a wide range of horizon topologies.

scholarly journals THERMODYNAMICS OF HORIZONS: A COMPARISON OF SCHWARZSCHILD, RINDLER AND de SITTER SPACETIMES

2002 ◽  
Vol 17 (15n17) ◽  
pp. 923-942 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Black Hole ◽  
Vacuum State ◽  
Quantum States ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Black Hole Spacetimes ◽  
Conformal Field ◽  
Symmetric Spacetimes ◽  
Transverse Area

The notions of temperature, entropy and 'evaporation', usually associated with spacetimes with horizons, are analyzed using general approach and the following results, applicable to different spacetimes, are obtained at one go. (i) The concept of temperature associated with the horizon is derived in a unified manner and is shown to arise from purely kinematic considerations. (ii) QFT near any horizon is mapped to a conformal field theory without introducing concepts from string theory. (iii) For spherically symmetric spacetimes (in D = 1 + 3) with a horizon at r = l, the partition function has the generic form Z ∝ exp [S - βE], where S = (1/4)4πl2 and |E| = (l/2). This analysis reproduces the conventional result for the black hole spacetimes and provides a simple and consistent interpretation of entropy and energy E = - (1/2)H-1 for deSitter spacetime. The classical Einstein's equations for this spacetime can be expressed as a thermodynamic identity, TdS - dE = PdV with the same variables. (iv) For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. (v) In the case of a Schwarzschild black hole there exist quantum states (like Unruh vacuum) which are not invariant under time reversal and can describe black hole evaporation. There also exist quantum states (like Hartle-Hawking vacuum) in which temperature is well-defined but there is no flow of radiation to infinity. In the case of deSitter universe or Rindler patch in flat spacetime, one usually uses quantum states analogous to Hartle-Hawking vacuum and obtains a temperature without the corresponding notion of evaporation. It is, however, possible to construct the analogues of Unruh vacuum state in the other cases as well. The implications are briefly discussed.

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