scholarly journals Anomalies in gravitational charge algebras of null boundaries and black hole entropy

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Venkatesa Chandrasekaran ◽  
Antony J. Speranza
Keyword(s):  
Black Hole Entropy ◽  
Abelian Extensions ◽  
Null Surface ◽  
Gravitational Theories ◽  
Virasoro Symmetry ◽  
Space Construction ◽  
Bifurcation Surface ◽  
Space Formalism ◽  
Definition Of ◽  
Systematic Derivation

Abstract We revisit the covariant phase space formalism applied to gravitational theories with null boundaries, utilizing the most general boundary conditions consistent with a fixed null normal. To fix the ambiguity inherent in the Wald-Zoupas definition of quasilocal charges, we propose a new principle, based on holographic reasoning, that the flux be of Dirichlet form. This also produces an expression for the analog of the Brown-York stress tensor on the null surface. Defining the algebra of charges using the Barnich-Troessaert bracket for open subsystems, we give a general formula for the central — or more generally, abelian — extensions that appear in terms of the anomalous transformation of the boundary term in the gravitational action. This anomaly arises from having fixed a frame for the null normal, and we draw parallels between it and the holographic Weyl anomaly that occurs in AdS/CFT. As an application of this formalism, we analyze the near-horizon Virasoro symmetry considered by Haco, Hawking, Perry, and Strominger, and perform a systematic derivation of the fluxes and central charges. Applying the Cardy formula to the result yields an entropy that is twice the Bekenstein-Hawking entropy of the horizon. Motivated by the extended Hilbert space construction, we interpret this in terms of a pair of entangled CFTs associated with edge modes on either side of the bifurcation surface.

scholarly journals Kerr–Bolt black hole entropy and soft hair

2020 ◽  
Vol 35 (25) ◽  
pp. 2050156
Author(s):  
M. R. Setare ◽  
A. Jalali
Keyword(s):  
Black Holes ◽  
Phase Space ◽  
Central Charge ◽  
Black Hole Entropy ◽  
Space Time ◽  
Limiting Behavior ◽  
Virasoro Symmetry ◽  
Kerr Space ◽  
Space Formalism ◽  
Good Agreement

Recently it has been speculated that a set of infinitesimal [Formula: see text] diffeomorphisms exist which act nontrivially on the horizon of some black holes such as Kerr and Kerr–Newman black holes.[Formula: see text] Having applied this symmetry in covariant phase space formalism, one can obtain Virasoro charges as surface integrals on the horizon. Kerr–Bolt space–time is well known for its asymptotically topology and has been studied widely in recent years. In this work, we are interested to find conserved charge associated to the Virasoro symmetry of Kerr–Bolt geometry using covariant phase space formalism. We will show right and left central charge are [Formula: see text], respectively. Our results also show good agreement with Kerr space–time in the limiting behavior.

Bekenstein‐Hawking black hole entropy, Hawking temperature, and the Unruh effect: Insight from the laws of thermodynamics

2020 ◽  
Vol 33 (2) ◽  
pp. 143-148
Author(s):  
Stephen J. Crothers ◽  
Pierre-Marie Robitaille
Keyword(s):  
Black Hole ◽  
Scientific Inquiry ◽  
Black Hole Entropy ◽  
Universal Constant ◽  
Unruh Effect ◽  
Physical Sciences ◽  
Laws Of Thermodynamics ◽  
Large Systems ◽  
Definition Of ◽  
Schwarzschild Radius

The laws of thermodynamics play a central role in scientific inquiry, guiding physics as to the validity of hypothesized claims. It is for this reason that quantities of thermodynamic relevance must retain their character wherever they appear. Temperature, for example, must always be intensive, a requirement set by the 0th law. Otherwise, the very definition of temperature is compromised. Similarly, entropy must remain extensive, in order to conform to the second law. These rules must be observed whenever a system is large enough to be characterized by macroscopic quantities, such as volume or area. This explains why ensembles comprised of just a few atoms cannot be considered thermodynamic systems. In this regard, black holes are hypothesized to be large systems, characterized by the Schwarzschild radius (rs = 2GM/c 2) and its associated “horizon” area (A = 4πrs 2), where G, M, and c represent the universal constant of gravitation, the mass of the black hole, and the speed of light in vacuum, respectively. It can be readily demonstrated that Bekenstein‐Hawking black hole entropy is nonextensive, while the Hawking and the Unruh temperatures are nonintensive. As a result, the associated equations violate the laws of thermodynamics and can hold no place in the physical sciences.

Representations and deformations of 3-Hom-ρ-Lie algebras

2021 ◽  
Author(s):  
Esmaeil Peyghan ◽  
Aydin Gezer ◽  
Zahra Bagheri ◽  
Inci Gultekin
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Abelian Extension ◽  
Abelian Extensions ◽  
Definition Of

The aim of this paper is to introduce 3-Hom-[Formula: see text]-Lie algebra structures generalizing the algebras of 3-Hom-Lie algebra. Also, we investigate the representations and deformations theory of this type of Hom-Lie algebras. Moreover, we introduce the definition of extensions and abelian extensions of 3-Hom-[Formula: see text]-Lie algebras and show that associated to any abelian extension, there is a representation and a 2-cocycle.

scholarly journals QUANTUM MECHANICS AT PLANCK'S SCALE AND DENSITY MATRIX

2003 ◽  
Vol 12 (07) ◽  
pp. 1265-1278 ◽  
Author(s):  
A. E. SHALYT-MARGOLIN ◽  
J. G. SUAREZ
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Semiclassical Approximation ◽  
Black Hole Entropy ◽  
Uncertainty Relations ◽  
Statistical Entropy ◽  
Fundamental Length ◽  
Definition Of ◽  
Liouville’S Equation ◽  
Natural Way

In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies in the fact that here the density matrix are subjected to deformation, whereas in the previous approaches only commutators are deformed. The density matrix obtained by deforming the quantum-mechanical one is named the density pro-matrix throughout this paper. Within our approach two main features of Quantum Mechanics are conserved: the probabilistic interpretation of the theory and the well-known measuring procedure corresponding to that interpretation. The proposed approach allows a description of the dynamics. In particular, the explicit form of the deformed Liouville's equation and the deformed Shrödinger's picture are given. Some implications of obtained results are discussed. In particular, the problem of singularity, the hypothesis of cosmic censorship, a possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is shown that the results obtained here allow one to deduce in a simple and natural way the Bekenstein–Hawking's formula for black hole entropy in semiclassical approximation.

scholarly journals Gravitational SL(2, ℝ) algebra on the light cone

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Wieland
Keyword(s):  
Phase Space ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Dirac Bracket ◽  
Auxiliary Variables ◽  
Null Surface ◽  
Boundary Terms ◽  
Starting Point ◽  
Definition Of ◽  
Boundary Fields

Abstract In a region with a boundary, the gravitational phase space consists of radiative modes in the interior and edge modes at the boundary. Such edge modes are necessary to explain how the region couples to its environment. In this paper, we characterise the edge modes and radiative modes on a null surface for the tetradic Palatini-Holst action. Our starting point is the definition of the action and its boundary terms. We choose the least restrictive boundary conditions possible. The fixed boundary data consists of the radiative modes alone (two degrees of freedom per point). All other boundary fields are dynamical. We introduce the covariant phase space and explain how the Holst term alters the boundary symmetries. To infer the Poisson brackets among Dirac observables, we define an auxiliary phase space, where the SL(2, ℝ) symmetries of the boundary fields are manifest. We identify the gauge generators and second-class constraints that remove the auxiliary variables. All gauge generators are at most quadratic in the fundamental SL(2, ℝ) variables on phase space. We compute the Dirac bracket and identify the Dirac observables on the light cone. Finally, we discuss various truncations to quantise the system in an effective way.

scholarly journals Privacy and Social Media: Defining Privacy in the Usage of Path

2019 ◽  
Author(s):  
Mashita Phitaloka Fandia Purwaningtyas
Keyword(s):  
Social Media ◽  
Personal Information ◽  
Personal Space ◽  
Social Recognition ◽  
Reciprocal Relationship ◽  
The Self ◽  
Self Presentation ◽  
Space Construction ◽  
Media Platform ◽  
Definition Of

The existence of social media has changed the landscape of human’s relationship. Through social media, people are able to present many versions of themselves in many platforms. In this era of polymediation of the self, the discussion regarding to privacy becomes arguable, moreover, with the presence of Path; a social media platform which presents itself as a private social media. Hence, in the sociocultural context of Indonesian society, it is important to see how the definition of privacy is constructed by the existence of Path. Therefore, this research is conducted in order to analyze and explore how privacy is perceived by the social media users nowadays, particularly the users of Path, and why they perceive it in that certain way. This research is conducted with ethnography as the main method and virtual ethnography as the supporting method. From the research, it is found that users’ way of defining privacy is embodied in two levels: online self-presentation and personal space construction. In the first level, the stages of privacy offered by Path have created the fragmented-self among users. This fragmentation has resulted in “the ambivalent self”, “self that desires recognition”, and “self that searches for freedom”. In the second level, the mediality of Path has served the users of the ability to construct their own personal space in social media space. This construction of the personal space has resulted in “space of comfort in similarity”, “space of pseudo-liberation”, and “space that demolishes the panoptic”. Henceforth, these findings lead to a conclusion that usage practices of social media has killed the authentic self and created a personal space that gives the sense of the absence of control, hierarchy, and social surveillance. Eventually, privacy for Path is defined by the process of exchange of “the self and personal information” with “social recognition, sense of equality, and reciprocal relationship”.

THE FREEDMAN-TOWNSEND MODEL IN TWO AND THREE DIMENSIONS

1992 ◽  
Vol 07 (09) ◽  
pp. 2005-2020 ◽  
Author(s):  
D.G.C. MCKEON
Keyword(s):  
Configuration Space ◽  
Three Dimensional ◽  
Transverse Component ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Sigma Model ◽  
Four Dimensions ◽  
Space Formalism ◽  
Vector Theory ◽  
Definition Of

Using a mechanism similar to that employed by Freedman and Townsend in four dimensions, we discuss a variety of two- and three-dimensional gauge theories. The simplest of these models is equivalent to the nonlinear sigma model; another corresponds to a massive vector theory. In three dimensions, there exists a gauge invariance associated with the auxiliary vector ϕμa; when we quantize, this is accommodated using both the Batalin-Vilkovisky configuration space formalism and the Batalin-Fradkin-Vilkovisky configuration space formalism. Explicit one-loop calculations in the simplest two-dimensional model are carried out. The regularization used is a variant of operator regularization, allowing one to remain in two dimensions, hence circumventing problems associated with definition of the antisymmetric tensor εμν. This model is renormalizable, with renormalization mixing the scalar field ϕa and the transverse component of the vector field Vμa.

scholarly journals Scattering of quantum fields by a MOG black hole

2020 ◽  
Vol 35 (15) ◽  
pp. 2050121
Author(s):  
Ciprian A. Sporea
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cross Section ◽  
Free Parameter ◽  
Spherically Symmetric ◽  
Gravitational Theories ◽  
Partial Wave Method ◽  
Hole Geometry ◽  
Definition Of ◽  
Analytical Expressions

This paper aims to investigate the scattering of fermions by spherically symmetric MOG black holes, which are a type of black holes encountered in scalar–tensor–vector modified gravitational theories. After determining the scattering modes in this black hole geometry, we apply the partial wave method to compute analytical expressions for the phase shifts that enter into the definition of scattering amplitudes. An analysis of the influence of the MOG parameter [Formula: see text] on the differential scattering cross-section and the induced polarization is conducted. Also, a comparison with Schwarzschild scattering (for which [Formula: see text]) is performed. Furthermore, it is also shown that glory and spiral/orbiting scattering are more significant for higher values of the free parameter [Formula: see text].

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Sign in / Sign up

Export Citation Format

Share Document