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Gravitation
About: Gravitation is a research topic. Over the lifetime, 29306 publications have been published within this topic receiving 821510 citations.
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TL;DR: In this paper, a higher order generalized uncertainty principle (GUP) in the form [ X, P ] = i ℏ / ( 1 − β P 2 ) is presented, which predicts both a minimal length uncertainty and a maximal observable momentum.
184 citations
TL;DR: In this article, a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces was proposed, which largely generalizes the idea of holography such that we do not need to rely on any existence of boundaries in gravitational spacetimes.
Abstract: We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do not need to rely on any existence of boundaries in gravitational spacetimes. The present idea is motivated by the recent interpretation of AdS/CFT in terms of the tensor networks so called MERA. Moreover, we study this correspondence from the viewpoint of entanglement entropy and information metric. The Cramer-Rao bound in quantum estimation theory implies that the quantum fluctuations of radial coordinate of the AdS is highly suppressed in the large N limit.
184 citations
TL;DR: In this article, a new method of variation of the gravitational Lagrangian is proposed, which leads in a simple and straightforward way to the canonical description of the gravity field dynamics in a finite volume V with boundary.
Abstract: A new method of variation of the gravitational Lagrangian is proposed. This method leads in a simple and straightforward way to the canonical description of the gravitational field dynamics in a finite volume V with boundary. No boundary terms are neglected or subtracted ad hoc. Two different forms of gravitational quasi-local energy are derived. Each of them is equal to the field Hamiltonian, corresponding to a specific way of controlling the field boundary data. They play the role of the “internal energy” and the “free energy” respectively. A relation with the boundary formula governing the thermodynamics of black holes is discussed.
184 citations
TL;DR: In this article, the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein-Klein-Gordon (EKG) system, which results in the so called Schrodinger-Newton (SN) set of equations was studied.
Abstract: Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein-Klein-Gordon (EKG) system, which results in the so called Schrodinger-Newton (SN) set of equations. We present the numerical code developed to evolve the SN system and topics related, like equilibrium configurations and boundary conditions. Also, we analyze the evolution of different initial configurations and the physical quantities associated to them. In particular, we readdress the issue of the gravitational cooling mechanism for Newtonian systems and find that all systems settle down onto a 0-node equilibrium configuration. PACS numbers: 04.40.-b, 98.35.Jk, 98.62.Gq I. INTRODUCTION In a previous paper of ours(1), we studied the forma- tion of a gravitationally bounded object comprised of scalar particles, under the influence of Newtonian gravity. The dynamics of the system is described by the coupled Schrodinger-Newton (SN) system of equations, which is nothing but the weak field limit of its general relativistic counterpart, the Einstein-Klein-Gordon (EKG) system. As at the moment we have no hints to finding an an- alytic solution for the evolution, we found necessary to develop numerical techniques to study the formation pro- cess of the scalar objects. The study of the dynami- cal properties of the fully time-dependent SN system has been done before in the literature(2, 3, 4, 5), but more is needed in order to understand the gravitational collapse of a weakly gravitating scalar field. The main aim of this paper is to perform an exhaustive numerical study of the collapse and evolution of a spher- ically symmetric scalar object in the Newtonian regime. Here, we develop a numerical strategy to evolve the SN system, and study important issues like the stability and the formation process of gravitationally bound scalar sys- tems, a topic that has recently become attractive in Cos- mology (1, 2, 5, 6, 7, 8, 9). A summary of the paper is as follows. In Sec. II, we present the relativistic EKG and Newtonian SN equa- tions that describe the evolution of a self-gravitating scalar field in the spherically symmetric case. Corre- spondingly, it is described how the EKG and the SN
184 citations
TL;DR: In this article, the authors studied the orbits of comets near the Sun and showed that no orbit can have perihelion inside r = 3m, and in the later part of the present work a method is proposed in order to study this region, since no comet can return from it.
Abstract: This is a sequel to a paper of 3 years ago, which studied the orbits of \`comets' near a \`sun' regarded as a point source of gravitation according to general relativity. That paper expressed the forms of the orbits in terms of elliptic functions, but its method was not so well adapted to a study of the time in those orbits. In the first half of the present work these orbits and their associated times are described in a simple form, the results being expressed in terms of integrals of elementary functions, which can be easily worked out either by quadratures or by approximation. One result of the earlier paper was the proof that no orbit can have perihelion inside r = 3m, and in the later part of the present work a method is proposed in order to study this region, since no comet can return from it. It is supposed that flashes are emitted both from a distant observatory and from a comet, each signalling the ticks of his clock according to the time it is keeping. These are observed by the other and compared with the time on its own clock. The method serves to describe occurrences between r = 3m and the `barrier' at r = 2m, and it points to some unexpected results in the matter of the comet passing the barrier, which call for explanation.
183 citations