Evolution of universe from Raychaudhuri equation for membranes

2019 ◽  
Vol 34 (22) ◽  
pp. 1950172
Author(s):  
Aldrin Cervantes
Keyword(s):  
General Relativity ◽  
Raychaudhuri Equation ◽  
Brane Cosmology ◽  
The One

We know that in general relativity the Raychaudhuri equation gives the congruence and evolution of the geodesics. In this work, it is proposed that in brane cosmology the Raychaudhuri equation, apart from giving the collapse of the brane, it gives the evolution of the brane. Therefore, the Raychaudhuri equation gives the same information as the one of Friedmann’s, in the context of evolution.

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 Gamma Astrometric Measurement Experiment: testing General Relativity with a small mission

2007 ◽  
Vol 3 (S248) ◽  
pp. 290-291 ◽  
Author(s):  
A. Vecchiato ◽  
M. G. Lattanzi ◽  
M. Gai ◽  
R. Morbidelli
Keyword(s):  
General Relativity ◽  
Solar Eclipse ◽  
Galactic Center ◽  
The Sun ◽  
Measurement Experiment ◽  
The One ◽  
First Time ◽  
Bending Of Light

AbstractGAME (Gamma Astrometric Measurement Experiment) is a concept for an experiment whose goal is to measure from space the γ parameter of the Parameterized Post-Newtonian formalism, by means of a satellite orbiting at 1 AU from the Sun and looking as close as possible to its limb. This technique resembles the one used during the solar eclipse of 1919, when Dyson, Eddington and collaborators measured for the first time the gravitational bending of light. Simple estimations suggest that, possibly within the budget of a small mission, one could reach the 10−6level of accuracy with ~106observations of relatively bright stars at about 2° apart from the Sun. Further simulations show that this result could be reached with only 20 days of measurements on stars ofV≤ 17 uniformly distributed. A quick look at real star densities suggests that this result could be greatly improved by observing particularly crowded regions near the galactic center.

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 Rotating Melvin-like Universes and Wormholes in General Relativity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1306
Author(s):  
Kirill Bronnikov ◽  
Vladimir Krechet ◽  
Vadim Oshurko
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Equation Of State ◽  
Symmetry Axis ◽  
Energy Condition ◽  
Flat Space ◽  
Stiff Matter ◽  
Cylindrically Symmetric ◽  
The One ◽  
The Magnetic Field

We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state p=wρ (|w|<1), carrying a circular electric current in the angular direction. This current creates a magnetic field along the z axis. Some of the solutions describe geometries resembling that of Melvin’s static magnetic universe and contain a regular symmetry axis, while some others (in the case w>0) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin’s solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, which thus forms new examples of phantom-free wormhole models in general relativity. In the limit w→1, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state p=ρ.

scholarly journals Space–time singularities and cosmic censorship conjecture: A Review with some thoughts

2020 ◽  
Vol 35 (14) ◽  
pp. 2030007 ◽  
Author(s):  
Yen Chin Ong
Keyword(s):  
General Relativity ◽  
Short Review ◽  
Big Bang ◽  
Cosmic Censorship ◽  
Space Time ◽  
Singularity Theorems ◽  
Time Singularities ◽  
The One ◽  
The Big Bang ◽  
Cosmic Censorship Conjecture

The singularity theorems of Hawking and Penrose tell us that singularities are common place in general relativity. Singularities not only occur at the beginning of the Universe at the Big Bang, but also in complete gravitational collapses that result in the formation of black holes. If singularities — except the one at the Big Bang — ever become “naked,” i.e. not shrouded by black hole horizons, then it is expected that problems would arise and render general relativity indeterministic. For this reason, Penrose proposed the cosmic censorship conjecture, which states that singularities should never be naked. Various counterexamples to the conjecture have since been discovered, but it is still not clear under which kind of physical processes one can expect violation of the conjecture. In this short review, I briefly examine some progresses in space–time singularities and cosmic censorship conjecture. In particular, I shall discuss why we should still care about the conjecture, and whether we should be worried about some of the counterexamples. This is not meant to be a comprehensive review, but rather to give an introduction to the subject, which has recently seen an increase of interest.

scholarly journals GENERAL RELATIVITY AS A THEORY OF TWO CONNECTIONS

1994 ◽  
Vol 03 (02) ◽  
pp. 379-392 ◽  
Author(s):  
J. FERNANDO BARBERO G.
Keyword(s):  
General Relativity ◽  
Phase Space ◽  
Hamiltonian Formulation ◽  
The One

We show in this paper that it is possible to formulate general relativity in a phase space coordinatized by two SO(3) connections. We analyze first the Husain-Kuchař model and find a two connection description for it. Introducing a suitable scalar constraint in this phase space we get a Hamiltonian formulation of gravity that is close to the one given by Ashtekar, from which it is derived, but has some interesting features of its own. Among them are a possible mechanism for dealing with the degenerate metrics and a neat way of writing the constraints of general relativity.

scholarly journals Einstein’s quadrupole formula from the kinetic-conformal Hořava theory

2017 ◽  
Vol 27 (01) ◽  
pp. 1750174 ◽  
Author(s):  
Jorge Bellorín ◽  
Alvaro Restuccia
Keyword(s):  
General Relativity ◽  
Degrees Of Freedom ◽  
Coupling Constants ◽  
Asymptotically Flat ◽  
Weak Source ◽  
The Family ◽  
Linearized Theory ◽  
Leading Mode ◽  
The One ◽  
Generally Covariant

We analyze the radiative and nonradiative linearized variables in a gravity theory within the family of the nonprojectable Hořava theories, the Hořava theory at the kinetic-conformal point. There is no extra mode in this formulation, the theory shares the same number of degrees of freedom with general relativity. The large-distance effective action, which is the one we consider, can be given in a generally-covariant form under asymptotically flat boundary conditions, the Einstein-aether theory under the condition of hypersurface orthogonality on the aether vector. In the linearized theory, we find that only the transverse-traceless tensorial modes obey a sourced wave equation, as in general relativity. The rest of variables are nonradiative. The result is gauge-independent at the level of the linearized theory. For the case of a weak source, we find that the leading mode in the far zone is exactly Einstein’s quadrupole formula of general relativity, if some coupling constants are properly identified. There are no monopoles nor dipoles in this formulation, in distinction to the nonprojectable Horava theory outside the kinetic-conformal point. We also discuss some constraints on the theory arising from the observational bounds on Lorentz-violating theories.

scholarly journals EINSTEIN GRAVITY AS AN EMERGENT PHENOMENON?

2001 ◽  
Vol 10 (06) ◽  
pp. 799-806 ◽  
Author(s):  
CARLOS BARCELÓ ◽  
MATT VISSER ◽  
STEFANO LIBERATI
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
High Energy ◽  
Einstein Gravity ◽  
Low Energy ◽  
Lorentzian Geometry ◽  
Long Distance ◽  
Emergent Phenomenon ◽  
Effective Dynamics ◽  
The One

In this essay we marshal evidence suggesting that Einstein gravity may be an emergent phenomenon, one that is not "fundamental" but rather is an almost automatic low-energy long-distance consequence of a wide class of theories. Specifically, the emergence of a curved spacetime "effective Lorentzian geometry" is a common generic result of linearizing a classical scalar field theory around some nontrivial background. This explains why so many different "analog models" of general relativity have recently been developed based on condensed matter physics; there is something more fundamental going on. Upon quantizing the linearized fluctuations around this background geometry, the one-loop effective action is guaranteed to contain a term proportional to the Einstein–Hilbert action of general relativity, suggesting that while classical physics is responsible for generating an "effective geometry," quantum physics can be argued to induce an "effective dynamics." This physical picture suggests that Einstein gravity is an emergent low-energy long-distance phenomenon that is insensitive to the details of the high-energy short-distance physics.

scholarly journals Towards the Raychaudhuri equation beyond general relativity

2018 ◽  
Vol 98 (2) ◽  
Author(s):  
Daniel J. Burger ◽  
Nathan Moynihan ◽  
Saurya Das ◽  
S. Shajidul Haque ◽  
Bret Underwood
Keyword(s):  
General Relativity ◽  
Raychaudhuri Equation
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