scholarly journals Quantum gravitational optics: Effective Raychaudhuri equation

2006 ◽  
Vol 74 (4) ◽  
Author(s):  
N. Ahmadi ◽  
M. Nouri-Zonoz
Keyword(s):  
Raychaudhuri Equation

BOUNDS ON f(G) GRAVITY FROM ENERGY CONDITIONS

2010 ◽  
Vol 25 (27) ◽  
pp. 2325-2332 ◽  
Author(s):  
PUXUN WU ◽  
HONGWEI YU
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Modified Gravity ◽  
Energy Conditions ◽  
Model Parameters ◽  
Effective Energy ◽  
Raychaudhuri Equation ◽  
Accelerating Expansion

The f(G) gravity is a theory to modify the general relativity and it can explain the present cosmic accelerating expansion without the need of dark energy. In this paper the f(G) gravity is tested with the energy conditions. Using the Raychaudhuri equation along with the requirement that the gravity is attractive in the FRW background, we obtain the bounds on f(G) from the SEC and NEC. These bounds can also be found directly from the SEC and NEC within the general relativity context by the transformations: ρ → ρm + ρE and p → pm + pE, where ρE and pE are the effective energy density and pressure in the modified gravity. With these transformations, the constraints on f(G) from the WEC and DEC are obtained. Finally, we examine two concrete examples with WEC and obtain the allowed region of model parameters.

scholarly journals Kodama Time, Entropy Bounds, the Raychaudhuri  Equation, and the Quantum Interest Conjecture

2021 ◽  
Author(s):  
◽  
Gabriel Abreu
Keyword(s):  
General Relativity ◽  
Coordinate System ◽  
Negative Energy ◽  
Specific Form ◽  
Einstein Equations ◽  
Surface Gravity ◽  
Quantum Field ◽  
Raychaudhuri Equation ◽  
Dimensional Minkowski Space ◽  
Entropy Bounds

<p>General Relativity, while ultimately based on the Einstein equations, also allows one to quantitatively study some aspects of the theory without explicitly solving the Einstein equations. These geometrical notions of the theory provide an insight to the nature of more general spacetimes. In this thesis, the Raychaudhuri equation, the choice of the coordinate system, the notions of surface gravity and of entropy, and restrictions on negative energy densities on the form of the Quantum Interest Conjecture, will be discussed. First, using the Kodama vector, a geometrically preferred coordinate system is built. With this coordinate system the usual quantities, such as the Riemann and Einstein tensors, are calculated. Then, the notion of surface gravity is generalized in two different ways. The first generalization is developed considering radial ingoing and outgoing null geodesics, in situations of spherical symmetry. The other generalized surface gravity is a three-vector obtained from the spatial components of the redshifted four acceleration of a suitable set of fiducial observers. This vectorial surface gravity is then used to place a bound on the entropy of both static and rotating horizonless objects. This bound is obtain mostly by classical calculations, with a minimum use of quantum field theory in curved spacetime. Additionally, several improved versions of the Raychaudhuri equation are developed and used in different scenarios, including a two congruence generalization of the equation. Ultimately semiclassical quantum general relativity is studied in the specific form of the Quantum Inequalities, and the Quantum Interest Conjecture. A variational proof of a version of the Quantum Interest Conjecture in (3 + 1)–dimensional Minkowski space is provided.</p>

scholarly journals Kodama Time, Entropy Bounds, the Raychaudhuri  Equation, and the Quantum Interest Conjecture

2021 ◽  
Author(s):  
◽  
Gabriel Abreu
Keyword(s):  
General Relativity ◽  
Coordinate System ◽  
Negative Energy ◽  
Specific Form ◽  
Einstein Equations ◽  
Surface Gravity ◽  
Quantum Field ◽  
Raychaudhuri Equation ◽  
Dimensional Minkowski Space ◽  
Entropy Bounds

<p>General Relativity, while ultimately based on the Einstein equations, also allows one to quantitatively study some aspects of the theory without explicitly solving the Einstein equations. These geometrical notions of the theory provide an insight to the nature of more general spacetimes. In this thesis, the Raychaudhuri equation, the choice of the coordinate system, the notions of surface gravity and of entropy, and restrictions on negative energy densities on the form of the Quantum Interest Conjecture, will be discussed. First, using the Kodama vector, a geometrically preferred coordinate system is built. With this coordinate system the usual quantities, such as the Riemann and Einstein tensors, are calculated. Then, the notion of surface gravity is generalized in two different ways. The first generalization is developed considering radial ingoing and outgoing null geodesics, in situations of spherical symmetry. The other generalized surface gravity is a three-vector obtained from the spatial components of the redshifted four acceleration of a suitable set of fiducial observers. This vectorial surface gravity is then used to place a bound on the entropy of both static and rotating horizonless objects. This bound is obtain mostly by classical calculations, with a minimum use of quantum field theory in curved spacetime. Additionally, several improved versions of the Raychaudhuri equation are developed and used in different scenarios, including a two congruence generalization of the equation. Ultimately semiclassical quantum general relativity is studied in the specific form of the Quantum Inequalities, and the Quantum Interest Conjecture. A variational proof of a version of the Quantum Interest Conjecture in (3 + 1)–dimensional Minkowski space is provided.</p>

scholarly journals Light propagation and optical scalars in torsion theories of gravity

2019 ◽  
Vol 34 (04) ◽  
pp. 1950029
Author(s):  
Siamak Akhshabi
Keyword(s):  
Gravitational Lensing ◽  
Light Propagation ◽  
Raychaudhuri Equation ◽  
Angular Diameter Distance ◽  
Propagation Of Light ◽  
Light Rays ◽  
Theories Of Gravity ◽  
Torsion Theories ◽  
Basic Equations ◽  
Gauge Theory Of Gravity

We investigate the propagation of light rays and evolution of optical scalars in gauge theories of gravity where torsion is present. Recently, the modified Raychaudhuri equation in the presence of torsion has been derived. We use this result to derive the basic equations of geometric optics for several different interesting solutions of the Poincaré gauge theory of gravity. The results show that the focusing effects for neighboring light rays will be different than general relativity. This in turn has practical consequences in the study of gravitational lensing effects and also in determining the angular diameter distance for cosmological objects.

scholarly journals A NEW SINGULARITY THEOREM IN RELATIVISTIC COSMOLOGY

2000 ◽  
Vol 15 (06) ◽  
pp. 391-395 ◽  
Author(s):  
A. K. RAYCHAUDHURI
Keyword(s):  
Ricci Tensor ◽  
Energy Condition ◽  
Space Time ◽  
Relativistic Cosmology ◽  
Raychaudhuri Equation ◽  
Singularity Theorem ◽  
Strong Energy Condition ◽  
Strong Energy

It is shown that if the time-like eigenvector of the Ricci tensor is hypersurface orthogonal so that the space–time allows a foliation into space sections, then the space average of each of the scalars that appears in the Raychaudhuri equation vanishes provided that the strong energy condition holds good. This result is presented in the form of a singularity theorem.

STOCHASTIC GRAVITY AND THE LANGEVIN-RAYCHAUDHURI EQUATION

2005 ◽  
Vol 20 (11) ◽  
pp. 2364-2373 ◽  
Author(s):  
J. BORGMAN ◽  
L. H. FORD
Keyword(s):  
Stress Tensor ◽  
Langevin Equation ◽  
Raychaudhuri Equation ◽  
Operational Approach ◽  
Gravitational Effects ◽  
Quantum Stress Tensor ◽  
Physical Manifestation ◽  
Stochastic Gravity

We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources.

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