scholarly journals A note on the category of quasi-proximity spaces

2020 ◽  
Vol 107 (121) ◽  
pp. 75-83
Author(s):  
Muammer Kula ◽  
Samed Özkan
Keyword(s):  
Compact Objects ◽  
Topological Category ◽  
Proximity Spaces

We characterize the separation properties T0 and T1 at a point p in the category of quasi-proximity spaces. Moreover, the (strongly) closed and (strongly) open subobjects of an object, and each of the various notions of connected and compact objects are characterized in this topological category.

Pre-Hausdorff and Hausdorff proximity spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3837-3846 ◽  
Author(s):  
Muammer Kula ◽  
Samed Özkan ◽  
Tuğba Maraşlı
Keyword(s):  
Usual Sense ◽  
Topological Category ◽  
Explicit Characterization ◽  
Proximity Spaces

In this paper, an explicit characterization of the separation properties for T0, T1, PreT2 (pre-Hausdorff) and T2 (Hausdorff) is given in the topological category of proximity spaces. Moreover, specific relationships that arise among the various Ti,i = 0,1,2 and PreT2 structures are examined in this category. Finally, we investigate the relationships among generalized separation properties for Ti,i = 0,1,2 and PreT2 (in our sense), separation properties at a point p and separation properties for Ti, i = 0,1,2 in the usual sense in this category.

scholarly journals A note on closedness and connectedness in the category of proximity spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1483-1492
Author(s):  
Muammer Kula ◽  
Tuğba Maraşlı ◽  
Samed Özkan
Keyword(s):  
Topological Category ◽  
Explicit Characterization ◽  
Proximity Spaces

In this paper, an explicit characterization of the separation properties T0 and T1 at a point p is given in the topological category of proximity spaces. Furthermore, the (strongly) closed and (strongly) open subobjects of an object are characterized in the category of proximity spaces and also the characterization of each of the various notions of the connected objects in this category are given.

scholarly journals Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Zhengwen Liu ◽  
Rafael A. Porto ◽  
Zixin Yang
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Scattering Problem ◽  
Finite Size ◽  
Effective Field ◽  
Compact Objects ◽  
Scattering Data ◽  
Theory Approach ◽  
Spin Effects ◽  
Radial Action

Abstract Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to $$ \mathcal{O}\left({G}^2\right) $$ O G 2 , which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

scholarly journals Ultra-compact objects from semi-classical gravity

2021 ◽  
Vol 103 (12) ◽  
Author(s):  
I. Prasetyo ◽  
H. S. Ramadhan ◽  
A. Sulaksono
Keyword(s):  
Compact Objects ◽  
Classical Gravity

scholarly journals Exploring a New Population of Compact Objects: X-ray and IR Observations of the Galactic Centre

2008 ◽  
Author(s):  
Reba M. Bandyopadhyay ◽  
Andrew J. Gosling ◽  
Stephen E. Eikenberry ◽  
Michael P. Muno ◽  
Katherine M. Blundell ◽  
...  
Keyword(s):  
Compact Objects ◽  
Galactic Centre ◽  
X Ray

scholarly journals Holographic equations of state and astrophysical compact objects

2011 ◽  
Vol 2011 (10) ◽  
Author(s):  
Youngman Kim ◽  
Chang-Hwan Lee ◽  
Ik Jae Shin ◽  
Mew-Bing Wan
Keyword(s):  
Equations Of State ◽  
Compact Objects

scholarly journals Numerical methods for General Relativistic particles

2018 ◽  
Vol 14 (S342) ◽  
pp. 19-23
Author(s):  
Fabio Bacchini ◽  
Bart Ripperda ◽  
Alexander Y. Chen ◽  
Lorenzo Sironi
Keyword(s):  
Numerical Methods ◽  
Gravitational Lensing ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Numerical Algorithms ◽  
Relativistic Effects ◽  
Compact Objects ◽  
Light Rays ◽  
Massive Particles ◽  
External Forces

AbstractWe present recent developments on numerical algorithms for computing photon and particle trajectories in the surrounding of compact objects. Strong gravity around neutron stars or black holes causes relativistic effects on the motion of massive particles and distorts light rays due to gravitational lensing. Efficient numerical methods are required for solving the equations of motion and compute i) the black hole shadow obtained by tracing light rays from the object to a distant observer, and ii) obtain information on the dynamics of the plasma at the microscopic scale. Here, we present generalized algorithms capable of simulating ensembles of photons or massive particles in any spacetime, with the option of including external forces. The coupling of these tools with GRMHD simulations is the key point for obtaining insight on the complex dynamics of accretion disks and jets and for comparing simulations with upcoming observational results from the Event Horizon Telescope.

scholarly journals Focal Function in i-Topological Spaces via Proximity Spaces

2020 ◽  
Vol 1591 ◽  
pp. 012083
Author(s):  
Yiezi Kadham Mahdi Altalkany ◽  
Luay A. A. Al Swidi
Keyword(s):  
Topological Spaces ◽  
Proximity Spaces
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