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

2021 ◽  
Author(s):  
◽  
Gabriel Abreu

<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>

2021 ◽  
Author(s):  
◽  
Gabriel Abreu

<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>


2014 ◽  
Vol 12 (2) ◽  
pp. 77-83
Author(s):  
Neven Bilic ◽  
Dijana Tolic

Analog gravity models of general relativity seem promising routes to providing laboratory tests of the foundation of quantum field theory in curved space-time. In contrast to general relativity, where geometry of a spacetime is determined by the Einstein equations, in analog models geometry and evolution of analog spacetime are determined by the equations of fluid mechanics. In this paper we study the analogue gravity model based on massless pions propagating in a expanding hadronic fluid. The analog expanding spacetime takes the form of an FRW universe, with the apparent and trapping horizons defined in the standard way.


2010 ◽  
Vol 25 (27) ◽  
pp. 2325-2332 ◽  
Author(s):  
PUXUN WU ◽  
HONGWEI YU

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.


Author(s):  
JE-AN GU

We discuss the stability of the general-relativity (GR) limit in modified theories of gravity, particularly the f(R) theory. The problem of approximating the higher-order differential equations in modified gravity with the Einstein equations (2nd-order differential equations) in GR is elaborated. We demonstrate this problem with a heuristic example involving a simple ordinary differential equation. With this example we further present the iteration method that may serve as a better approximation for solving the equation, meanwhile providing a criterion for assessing the validity of the approximation. We then discuss our previous numerical analyses of the early-time evolution of the cosmological perturbations in f(R) gravity, following the similar ideas demonstrated by the heuristic example. The results of the analyses indicated the possible instability of the GR limit that might make the GR approximation inaccurate in describing the evolution of the cosmological perturbations in the long run.


Author(s):  
H.S. Vieira ◽  
V.B. Bezerra

In this paper, we use the Lagrangian formalism of classical mechanics and some assumptions to obtain cosmological differential equations analogous to Friedmann and Einstein equations, obtained from the theory of general relativity. This method can be used to a universe constituted of incoherent matter, that is, the cosmologic substratum is comprised of dust.


In this contribution, my purpose is to study a new mathematical instrument introduced by me in 1958-9: the tensor and spinor propagators. These propagators are extensions of the scalar propagator of Jordan-Pauli which plays an important part in quantum-field theory. It is possible to construct, with these propagators, commutators and anticommutators for the various free fields, in the framework of general relativity theory (see Lichnerowicz 1959 a, b, c , 1960, 1961 a, b, c ; and for an independent introduction of propagators DeWitt & Brehme 1960).


2021 ◽  
Vol 81 (6) ◽  
Author(s):  
G. G. L. Nashed ◽  
S. D. Odintsov ◽  
V. K. Oikonomou

AbstractIn this paper we shall consider spherically symmetric spacetime solutions describing the interior of stellar compact objects, in the context of higher-order curvature theory of the $${{\mathrm {f(R)}}}$$ f ( R ) type. We shall derive the non-vacuum field equations of the higher-order curvature theory, without assuming any specific form of the $${{\mathrm {f(R)}}}$$ f ( R ) theory, specifying the analysis for a spherically symmetric spacetime with two unknown functions. We obtain a system of highly non-linear differential equations, which consists of four differential equations with six unknown functions. To solve such a system, we assume a specific form of metric potentials, using the Krori–Barua ansatz. We successfully solve the system of differential equations, and we derive all the components of the energy–momentum tensor. Moreover, we derive the non-trivial general form of $${{\mathrm {f(R)}}}$$ f ( R ) that may generate such solutions and calculate the dynamic Ricci scalar of the anisotropic star. Accordingly, we calculate the asymptotic form of the function $${\mathrm {f(R)}}$$ f ( R ) , which is a polynomial function. We match the derived interior solution with the exterior one, which was derived in [1], with the latter also resulting to a non-trivial form of the Ricci scalar. Notably but rather expected, the exterior solution differs from the Schwarzschild one in the context of general relativity. The matching procedure will eventually relate two constants with the mass and radius of the compact stellar object. We list the necessary conditions that any compact anisotropic star must satisfy and explain in detail that our model bypasses all of these conditions for a special compact star $$\textit{Her X--1}$$ Her X - - 1 , which has an estimated mass and radius $$(mass = 0.85 \pm 0.15M_{\circledcirc }\ and\ radius = 8.1 \pm 0.41~\text {km}$$ ( m a s s = 0.85 ± 0.15 M ⊚ a n d r a d i u s = 8.1 ± 0.41 km ). Moreover, we study the stability of this model by using the Tolman–Oppenheimer–Volkoff equation and adiabatic index, and we show that the considered model is different and more stable compared to the corresponding models in the context of general relativity.


2021 ◽  
Author(s):  
Satish Ramakrishna

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.


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