scholarly journals Estimation of temperature of cosmological apparent horizons: a new approach

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Bhramar Chatterjee ◽  
Narayan Banerjee
Keyword(s):  
Conditional Probability ◽  
Apparent Horizon ◽  
Killing Vector ◽  
New Approach ◽  
Timelike Killing Vector ◽  
Dynamical Time ◽  
Apparent Horizons ◽  
Positive Frequency

AbstractWe consider radiation from cosmological apparent horizon in Friedmann–Lemaitre–Robertson–Walker (FLRW) model in a double-null coordinate setting. As the spacetime is dynamic, there is no timelike Killing vector, instead we have Kodama vector which acts as dynamical time. We construct the positive frequency modes of the Kodama vector across the horizon. The conditional probability that a signal reaches the central observer when it is crossing from the outside gives the temperature associated with the horizon.

scholarly journals Two physical characteristics of numerical apparent horizons

2008 ◽  
Vol 86 (4) ◽  
pp. 669-673 ◽  
Author(s):  
I Booth
Keyword(s):  
General Relativity ◽  
Apparent Horizon ◽  
Physical Characteristics ◽  
Apparent Horizons

This article translates some recent results on quasilocal horizons into the language of (3 + 1) general relativity to make them more useful to numerical relativists. In particular, quantities are described that characterize how quickly an apparent horizon is evolving and how close it is to either equilibrium or extremality.PACS Nos.: 04.20.Cv, 04.25.Dm, 04.70.Bw

ABSENCE OF APPARENT HORIZONS IN TRANSLATIONALLY-INVARIANT EINSTEIN–MAXWELL SPACETIMES

2004 ◽  
Vol 13 (03) ◽  
pp. 517-526
Author(s):  
SÉRGIO M. C. V. GONÇALVES
Keyword(s):  
Vector Field ◽  
Lie Group ◽  
Killing Vector ◽  
Cosmic Censorship ◽  
Killing Vector Field ◽  
Dimensional Spacetime ◽  
Apparent Horizons ◽  
Spacetime Metric ◽  
Group Of Isometries

We show that (3+1) Einstein–Maxwell spacetimes admitting a global, spacelike, one-parameter Lie group of isometries of translational type cannot contain apparent horizons. The only assumption made is that of the existence of a global spacelike Killing vector field with infinite open orbits; the four-dimensional spacetime metric is otherwise completely arbitrary. We discuss the implications of this result for the hoop and cosmic censorship conjectures.

scholarly journals AdS DYNAMICS FOR MASSIVE SCALAR FIELD: EXACT SOLUTIONS vs. BULK-BOUNDARY PROPAGATOR

2003 ◽  
Vol 18 (09) ◽  
pp. 1657-1670 ◽  
Author(s):  
ZHE CHANG ◽  
CHENG-BO GUAN ◽  
HAN-YING GUO
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Coordinate System ◽  
Killing Vector ◽  
Equation Of Motion ◽  
Massive Scalar ◽  
Invariant Metric ◽  
Massive Scalar Field ◽  
Timelike Killing Vector ◽  
One To One

AdS dynamics for massive scalar field is studied both by solving exactly the equation of motion and by constructing bulk-boundary propagator. A Robertson–Walker-like metric is deduced from the familiar SO (2, n) invariant metric. The metric allows us to present a timelike Killing vector, which is not only invariant under spacelike transformations but also invariant under the isometric transformations of SO (2, n) in certain sense. A horizon appears in this coordinate system. Singularities of field variables at boundary are demonstrated explicitly. It is shown that there is a one-to-one correspondence among the exact solutions and the bulk fields obtained by using the bulk-boundary propagator.

IS THERE CLASSICAL SUPER-RADIANCE ON KERR-NEWMAN-ANTI-DE SITTER BLACK HOLES?

2002 ◽  
Vol 17 (20) ◽  
pp. 2782-2782
Author(s):  
ELIZABETH WINSTANLEY
Keyword(s):  
Black Holes ◽  
Boundary Conditions ◽  
Killing Vector ◽  
De Sitter ◽  
Transparent Boundary Conditions ◽  
Asymptotically Flat ◽  
Ads Black Holes ◽  
Definition Of ◽  
Conditions At Infinity ◽  
Positive Frequency

Since the formulation of the AdS/CFT correspondence 1, there has been great interest in space-times which are asymptotically anti-de Sitter, and the properties of the Kerr-Newman-anti-de Sitter (KN-AdS) space-time in various dimensions have been extensively studied 2. However, the properties of classical or quantum fields propagating on this background have not been widely studied, and, in particular, the question of whether super-radiance occurs has not been addressed. This is an important issue since a detailed understanding of classical super-radiance is necessary before tackling quantum field theory on rotating black hole geometries 3. We considered a classical scalar field on the KN-AdS background 4, and examined the form of the separated field modes. Given the structure of infinity in asymptotically anti-de Sitter space-times, we paid particular attention to the boundary conditions at infinity. Unlike the situation for asymptotically flat Kerr-Newman black holes 5, super-radiance is not inevitable. It depends partly on our choice of boundary condition at infinity. For reflective boundary conditions at infinity, there is no super-radiance. On the other hand, if we consider transparent boundary conditions at infinity, then the presence of super-radiance depends on our choice of positive frequency. For those KN-AdS black holes possessing a globally time-like Killing vector, then the natural definition of positive frequency implies that there are no super-radiant modes. For other KN-AdS black holes, then this same definition of positive frequency again leads to no super-radiance.

scholarly journals Bartnik mass via vacuum extensions

2019 ◽  
Vol 30 (13) ◽  
pp. 1940006
Author(s):  
Pengzi Miao ◽  
Naqing Xie
Keyword(s):  
Initial Data ◽  
Scalar Curvature ◽  
Apparent Horizon ◽  
Gauss Curvature ◽  
Positive Mass Theorem ◽  
Data Sets ◽  
Penrose Inequality ◽  
Asymptotically Flat ◽  
Apparent Horizons ◽  
Positive Gauss Curvature

We construct asymptotically flat, scalar flat extensions of Bartnik data [Formula: see text], where [Formula: see text] is a metric of positive Gauss curvature on a two-sphere [Formula: see text], and [Formula: see text] is a function that is either positive or identically zero on [Formula: see text], such that the mass of the extension can be made arbitrarily close to the half area radius of [Formula: see text]. In the case of [Formula: see text], the result gives an analog of a theorem of Mantoulidis and Schoen [On the Bartnik mass of apparent horizons, Class. Quantum Grav. 32(20) (2015) 205002, 16 pp.], but with extensions that have vanishing scalar curvature. In the context of initial data sets in general relativity, the result produces asymptotically flat, time-symmetric, vacuum initial data with an apparent horizon [Formula: see text], for any metric [Formula: see text] with positive Gauss curvature, such that the mass of the initial data is arbitrarily close to the optimal value in the Riemannian Penrose inequality. The method we use is the Shi–Tam type metric construction from [Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature, J. Differential Geom. 62(1) (2002) 79–125] and a refined Shi–Tam monotonicity, found by the first named author in [On a localized Riemannian Penrose inequality, Commun. Math. Phys. 292(1) (2009) 271–284].

Charged perfect fluid gravitational collapse in f(R, T) gravity

2019 ◽  
Vol 34 (20) ◽  
pp. 1950153 ◽  
Author(s):  
G. Abbas ◽  
Riaz Ahmed
Keyword(s):  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Coupling Parameter ◽  
Apparent Horizon ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Apparent Horizons ◽  
Spherically Symmetric Metric

We explore the problem of charged perfect fluid spherically symmetric gravitational collapse in f(R, T) gravity (R is Ricci scalar and T is the trace of energy–momentum tensor). We have taken the interior boundary of a star as spherically symmetric metric filled with the charged perfect fluid. In order to study charged perfect fluid collapse, we have investigated the exact solutions of the Maxwell–Einstein field equations solutions using the most simplified form for f(R, T) model f(R, T) = R + 2[Formula: see text]T, where [Formula: see text] is model parameter. This study involves the effects of charge as well as coupling parameter on collapse of a star. We studied the nature of trapped surfaces, apparent horizon and singularity structure in detail. It has been found that singularity is formed earlier than the apparent horizons, so the end state of gravitational collapse in this case is black hole.

Fundamental Notions in Relativistic Geodesy - physics of a timelike Killing vector field

2020 ◽  
Author(s):  
Dennis Philipp ◽  
Claus Laemmerzahl ◽  
Eva Hackmann ◽  
Volker Perlick ◽  
Dirk Puetzfeld ◽  
...  
Keyword(s):  
Gravity Field ◽  
Vector Fields ◽  
Dimensional Space ◽  
Killing Vector ◽  
Three Dimensional ◽  
Scalar Function ◽  
Gravity Potential ◽  
Static Case ◽  
The Earth ◽  
Timelike Killing Vector

<p>The Earth’s geoid is one of the most important fundamental concepts to provide a gravity field- related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions within Einstein’s theory of General Relativity is inevitable.<span> </span></p><p>Building on the theoretical construction of isochronometric surfaces we define a relativistic gravity potential as a generalization of known (post-)Newtonian notions. It exists for any stationary configuration and rigidly co-rotating observers; it is the same as realized by local plumb lines and determined by the norm of a timelike Killing vector. In a second step, we define the relativistic geoid in terms of this gravity potential in direct analogy to the Newtonian understanding. In the respective limits, it allows to recover well-known results. Comparing the Earth’s Newtonian geoid to its relativistic generalization is a very subtle problem. However, an isometric embedding into Euclidean three-dimensional space can solve it and allows an intrinsic comparison. We show that the leading-order differences are at the mm-level.<span> </span>In the next step, the framework is extended to generalize the normal gravity field as well. We argue that an exact spacetime can be constructed, which allows to recover the Newtonian result in the weak-field limit. Moreover, we comment on the relativistic definition of chronometric height and related concepts.</p><p>In a stationary spacetime related to the rotating Earth, the aforementioned gravity potential is of course not enough to cover all information on the gravitational field. To obtain more insight, a second scalar function can be constructed, which is genuinely related to gravitomagnetic contributions and vanishes in the static case. Using the kinematic decomposition of an isometric observer congruence, we suggest a potential related to the twist of the worldlines therein. Whilst the first potential is related to clock comparison and the acceleration of freely falling corner cubes, the twist potential is related to the outcome of Sagnac interferometric measurements. The combination of both potentials allows to determine the Earth’s geoid and equip this surface with coordinates in an operational way. Therefore, relativistic geodesy is intimately related to the physics of timelike Killing vector fields.</p>

scholarly journals On Finsler spacetimes with a timelike Killing vector field

2018 ◽  
Vol 35 (8) ◽  
pp. 085007 ◽  
Author(s):  
Erasmo Caponio ◽  
Giuseppe Stancarone
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Timelike Killing Vector
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