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We study the space-time geometry generated by coupling a free scalar field with a noncanonical kinetic term to general relativity in (2 + 1) dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions in static and circularly symmetric scenarios, we classify the various types of solutions and focus on a branch that yields asymptotically flat geometries. We show that the solutions within such a branch can be divided in two types, namely naked singularities and nonsingular objects without a center. In the latter, the energy density is localized around a maximum and vanishes only at infinity and at an inner boundary. This boundary has vanishing curvatures and cannot be reached by any time-like or null geodesic in finite affine time. This allows us to consistently interpret such solutions as nonsingular, lump-like, static compact scalar objects whose eventual extension to the (3 + 1) -dimensional context could provide structures of astrophysical interest. [ABSTRACT FROM AUTHOR]

The gauge formulation of Einstein gravity in AdS3 background leads to a boundary theory that breaks modular symmetry and loses the covariant form. We examine the Weyl anomaly for the cylinder and torus manifolds. The divergent term is the same as the Liouville theory when transforming from the cylinder to the sphere. The general Weyl transformation on the torus also reproduces the Liouville theory. The Weyl transformation introduces an additional boundary term for reproducing the Liouville theory, which allows the use of CFT techniques to analyze the theory. The torus partition function in this boundary theory is one-loop exact, and an analytical solution to disjoint two-interval Rényi-2 mutual information can be obtained. We also discuss a first-order phase transition for the separation length of two intervals, which occurs at the classical level but is smoothed out by non-perturbative effects captured by averaging over a modular group in the boundary theory.

We study the space-time geometry generated by coupling a free scalar field with a noncanonical kinetic term to general relativity in (2+1) dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions in static and circularly symmetric scenarios, we classify the various types of solutions and focus on a branch that yields asymptotically flat geometries. We show that the solutions within such a branch can be divided in two types, namely naked singularities and nonsingular objects without a center. In the latter, the energy density is localized around a maximum and vanishes only at infinity and at an inner boundary. This boundary has vanishing curvatures and cannot be reached by any time-like or null geodesic in finite affine time. This allows us to consistently interpret such solutions as nonsingular, lump-like, static compact scalar objects whose eventual extension to the (3+1)-dimensional context could provide structures of astrophysical interest.

In this work, we report a study on bouncing cosmology with modified generalized Chaplygin Gas (mgCG) in a bulk viscosity framework. Reconstruction schemes were demonstrated in Einstein and modified f (T) gravity framework under the purview of viscous cosmological settings. We also took non-viscous cases into account. We studied the equation of state (EoS) parameter under various circumstances and judged the stability of the models through the sign of the squared speed of sound. We observed the mgCG behaving like avoidance of Big Rip in the presence of bulk viscosity at the turnaround point and in non-viscous cases, a phantom-like behavior appears. The turnaround point equation of state parameter crosses the phantom boundary, violating NEC. The role of the mgCG's model parameters was also investigated before and after the bounce. A Hubble flow dynamics was carried out and, it was revealed that mgCG is capable of realizing an inflationary phase as well as an exit from inflation. An f (T) gravitational paradigm was also considered, where the mgCG density was reconstructed in the presence of bulk viscosity. The role of the parameters associated with the bouncing scale factor, describing how fast the bounce takes place, was also studied in this framework. Finally, the reconstructed mgCG turned out to be stable against small perturbations irrespective of the presence of bulk viscosity and modified gravity scenario. Finally, the reconstruction scheme was assessed using statistical analysis, Shannon entropy. [ABSTRACT FROM AUTHOR]

The gauge formulation of Einstein gravity in AdS 3 background leads to a boundary theory that breaks modular symmetry and loses the covariant form. We examine the Weyl anomaly for the cylinder and torus manifolds. The divergent term is the same as the Liouville theory when transforming from the cylinder to the sphere. The general Weyl transformation on the torus also reproduces the Liouville theory. The Weyl transformation introduces an additional boundary term for reproducing the Liouville theory, which allows the use of CFT techniques to analyze the theory. The torus partition function in this boundary theory is one-loop exact, and an analytical solution to disjoint two-interval Rényi-2 mutual information can be obtained. We also discuss a first-order phase transition for the separation length of two intervals, which occurs at the classical level but is smoothed out by non-perturbative effects captured by averaging over a modular group in the boundary theory. [ABSTRACT FROM AUTHOR]

We would first show that how the two fundamental constants, the velocity of light, c , and the so called, cosmological constant, Λ , arise from geometric characterization of forcefree state of spacetime. They are the two most fundamental constants as they have been synthesized in the structure of spacetime, no other constant can claim this degree of fundamentalness. Next when spacetime turns inhomogeneous, Einstein gravity arises most naturally from the spacetime geometry without any prescription from outside; i.e. the inverse square law is mandated by the geometry, and not a prescription. It would then suggest that dynamics of a fundamental force should not be prescribed but should perhaps be determined by the geometry of appropriate spacetime manifold. [ABSTRACT FROM AUTHOR]

In this work, we report a study on bouncing cosmology with modified generalized Chaplygin Gas (mgCG) in a bulk viscosity framework. Reconstruction schemes were demonstrated in Einstein and modified f(T) gravity framework under the purview of viscous cosmological settings. We also took non-viscous cases into account. We studied the equation of state (EoS) parameter under various circumstances and judged the stability of the models through the sign of the squared speed of sound. We observed the mgCG behaving like avoidance of Big Rip in the presence of bulk viscosity at the turnaround point and in non-viscous cases, a phantom-like behavior appears. The turnaround point equation of state parameter crosses the phantom boundary, violating NEC. The role of the mgCG’s model parameters was also investigated before and after the bounce. A Hubble flow dynamics was carried out and, it was revealed that mgCG is capable of realizing an inflationary phase as well as an exit from inflation. An f(T) gravitational paradigm was also considered, where the mgCG density was reconstructed in the presence of bulk viscosity. The role of the parameters associated with the bouncing scale factor, describing how fast the bounce takes place, was also studied in this framework. Finally, the reconstructed mgCG turned out to be stable against small perturbations irrespective of the presence of bulk viscosity and modified gravity scenario. Finally, the reconstruction scheme was assessed using statistical analysis, Shannon entropy.

Abstract In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang–Han’s proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painlevé) of coordinates as well as in different gravity frames, the adiabatic invariant $$I_\mathrm{adia} = \oint p_i dq_i$$ I adia = ∮ p i d q i introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang–Han’s proposal reasonably in more general gravity frames (including Einstein’s gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area.

The following paper makes an endeavor to derive from scratch, the Einstein gravity from purely novel and subtle set of statistical ansatz. The theory developed is that of statistical geometrodynamics in close conjunction with the standard statistical thermodynamics, thereby extending the Einstein theory to three laws involving the Holographic Principle in a totally different way.A Boltzmann-like formula is derived right after the second law of geometrodynamics. The author hopes that the following work will shed some light on the fundamental understanding of the underpinnings of gravity and information in a nonconventional way. The rest of the latter part of the paper consists of discussions and possible conclusions that could be drawn by the author at the time of writing the paper. [ABSTRACT FROM AUTHOR]

We study properties of resonant solutions to the scalar wave equation in several axially symmetric spacetimes. We prove that nonaxial resonant modes do not exist neither in the Lanczos dust cylinder, the extreme (2 + 1) dimensional Bañados-Taitelboim-Zanelli (BTZ) spacetime nor in a class of simple rotating wormhole solutions. Moreover, we find unstable solutions to the wave equation in the Lanczos dust cylinder and in the r2 < 0 region of the extreme (2 + 1) dimensional BTZ spacetime, two solutions that possess closed timelike curves. Similarities with previous results obtained for the Kerr spacetime are explored. [ABSTRACT FROM AUTHOR]

General solution for braneworld dynamics coupled with the bulk Einstein equation is considered under the Schwarzschild ansatz. They relate the brane metric to the exterior configurations, and establish conditions for the braneworlds to reproduce successful results of the Einstein gravity. [ABSTRACT FROM AUTHOR]

After criticizing the various existing attempts at extending the concept of the Minkowski space, the following problem is considered: If there is the ultimate theory at all, how should the space-time in it be formulated? The principle of "quantum priority" is proposed, and under this principle, it is argued that the ultimate theory should have the affine symmetry in the framework of quantum gravity. It is shown that the Poincaré symmetry of particle physics is realized as a result of spontaneous breakdown of the affine symmetry. [ABSTRACT FROM AUTHOR]

A new framework for perturbative quantum gravity is proposed following the geometry of non-holonomic distributions on (pseudo)Riemannian manifolds. There are considered such distributions and adap-ted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce to two-loop renormalizable effective actions. We use a key result from our partner work arXiv: 0902.0911 that the classical Einstein gravity theory can be reformulated equivalently as a non-holonomic gauge model in the bundle of affine/de Sitter frames on pseudo-Riemannian space–time. It is proven that (for a class of non-holonomic constraints and splitting of the Levi–Civita connection into a "renormalizable" distinguished connection, on a base background manifold, and a gauge-like distortion tensor, in total space) a non-holonomic differential renormalization procedure for quantum gravitational fields can be elaborated. Calculation labor is reduced to one- and two-loop levels and renormalization group equations for non-holonomic configurations. [ABSTRACT FROM AUTHOR]

For (2 + 2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as nonholonomic deformations of the Levi–Civita connection. Such deformations and induced geometric/physical objects are completely determined by a prescribed metric tensor. Reformulation of the Einstein equations in nonholonomic variables (tetrads and new connections, for instance, with constant coefficient curvatures and/or Yang–Mills like potentials) reveals hidden geometric and rich quantum structures. It is shown how the Einstein gravity theory can be redefined equivalently as certain gauge models on nonholonomic affine and/or de Sitter frame bundles. We speculate on possible applications of the geometry of nonholonomic distributions with associated nonlinear connections in classical and quantum gravity. [ABSTRACT FROM AUTHOR]

The general relativity theory is redefined equivalently in almost Kähler variables: symplectic form, θ[g], and canonical symplectic connection, $\widehat{{\bf D}}[{\bf g}]$ (distorted from the Levi–Civita connection by a tensor constructed only from metric coefficients and their derivatives). The fundamental geometric and physical objects are uniquely determined in metric compatible form by a (pseudo) Riemannian metric g on a manifold V enabled with a necessary type nonholonomic 2 + 2 distribution. Such nonholonomic symplectic variables allow us to formulate the problem of quantizing Einstein gravity in terms of the A-model complexification of almost complex structures on V, generalizing the Gukov–Witten method [1]. Quantizing $({\bf V},\theta [{\bf g}],\,\widehat{{\bf D}}[{\bf g}])$, we derive a Hilbert space as a space of strings with two A-branes which for the Einstein gravity theory are nonholonomic because of induced nonlinear connection structures. Finally, we speculate on relation of such a method of quantization to curve flows and solitonic hierarchies defined by Einstein metrics on (pseudo) Riemannian spacetimes. [ABSTRACT FROM AUTHOR]

In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define a fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction. We simulate the spacetime manifold by a very specific congruence of curves and use the Landau–Raychadhuri equation to study the behavior of such a congruence. The lattice appears because we are forced to associate to each curve of the congruence a sort of fundamental "particle". The world-lines of these particles should be identified with the congruence fulfilling the spacetime manifold. The conclusion is that when describing the deformations of the spacetime the Einstein equations emerge and the spacetime metric should be treated as a secondary (not fundamental) object of the theory. [ABSTRACT FROM AUTHOR]

Metrics representing black holes in General Relativity may exhibit naked singularities for certain values of their parameters. This is the case for super-extremal (J2 > M > 0) Kerr and super-extremal (|Q| > M > 0) Reissner-Nördstrom spacetimes, and also for the negative mass Schwarzschild spacetime. We review our recent work where we show that these nakedly singular spacetimes are unstable under linear gravitational perturbations, a result that supports the cosmic censorship conjecture, and also that the inner stationary region beyond the inner horizon of a Kerr black hole (J2 < M) is linearly unstable. [ABSTRACT FROM AUTHOR]

Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics. However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and the laboratory can be considered Newtonian, since all the velocities involved are much smaller than the velocity of light) which provides a privileged coordinate system and therefore seems to destroy the possibility of having a perfectly defined relativistic emergent world. In this essay we ask ourselves the following question: In a homogeneous condensed matter medium, is there a way for internal observers, dealing exclusively with the low-energy collective phenomena, to detect their state of uniform motion with respect to the medium? By proposing a thought experiment based on the construction of a Michelson-Morley interferometer made of quasi-particles, we show that a real Lorentz-FitzGerald contraction takes place, so that internal observers are unable to find out anything about their ‘absolute’ state of motion. Therefore, we also show that an effective but perfectly defined relativistic world can emerge in a fishbowl world situated inside a Newtonian (laboratory) system. This leads us to reflect on the various levels of description in physics, in particular regarding the quest towards a theory of quantum gravity. [ABSTRACT FROM AUTHOR]

We summarize a series of observational tests of the law of gravity on large astrophysical scales. These tests account for testing both the Poisson equation (inverse square law) using weak lensing and the Einstein equivalence principle through the test of the constancy of the constants of Nature. We emphasize the need to test general relativity on cosmological scales in light of the cosmological constant problem and of recent observational claims concerning the variation of fine structure constant. [ABSTRACT FROM AUTHOR]

We investigate the stability of polytropic spheres in classical general relativity influenced by a departure from homogeneous spherical symmetry. We utilize the Vaidya–Tikekar ansatz to generate models of superdense stars obeying a polytropic equation of state of the form p r = κ ρ 1 + 1 n − β. Models with polytropic index n = 1 (quadratic equation of state) and n = 2 are generated for the general spheroidal parameter. We investigate the physical viability of these models and show that they describe strange star candidates such as SAX J1808.4-3658 to a good approximation. An interesting finding of this work shows that these models become unstable as the spheroidal parameter is decreased which leads us to conclude that stability is compromised with departure from homogeneous spherical symmetry. • This paper produces a new model of a dense relativistic star with a spatial spheroidal geometry. • The physical requirements for a physically reasonable stellar object are satisfied. • For the first time it is shown that the stability of the structure is related to the spheroidal parameter. • The deviation away from 3-dimensional spherical symmetry affects the stability. [ABSTRACT FROM AUTHOR]