Narrow Results

Hawking’s singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a non-negative effective energy density (EED). The SEC ensures the timelike convergence property. However, for both classical and quantum fields, violations of the SEC can be observed even in the simplest of cases, like the Klein-Gordon field. Therefore there is a need to develop theorems with weaker restrictions, namely energy conditions averaged over an entire geodesic and weighted local averages of energy densities such as quantum energy inequalities (QEIs). We present lower bounds of the EED for both classical and quantum scalar fields allowing nonzero mass and nonminimal coupling to the scalar curvature. In the quantum case these bounds take the form of a set of state-dependent QEIs valid for the class of Hadamard states. We also discuss how these lower bounds are applied to prove Hawking-type singularity theorems asserting that, along with sufficient initial contraction, the spacetime is future timelike geodesically incomplete.

The gravitational closure of given matter field dynamics provides diffeomorphisminvariant dynamics for the very background geometry that is ultralocally employed in the matter action. Conceptual and technical key to this construction is the principal polynomial of the initially given matter field equations, which crucially depends on how exactly the background geometry makes its appearance in the matter action. In this talk, we consider two very different matter theories that employ a background geometry consisting of two Lorentzian metrics in vastly different ways. Applying the gravitational closure mechanism we derive the remarkable result that they share the same underlying gravitational dynamics.

We formulate a description of 3+1 dimensional gravitational phenomena in terms of a relativistic fluid living on the 2+1 dimensional timelike boundary of an arbitrary bulk region of spacetime, called a gravitational screen. We establish a consistent dictionary between the geometric variables describing the evolution of the screen and the thermodynamic variables describing a relativistic viscous fluid, and discuss the interpretation. We also examine the construction of gravitational screens in different spacetimes and analyze the properties of the fluids they realize.

We study the dynamical stability of self-gravitating systems in presence of anisotropy. In particular, we introduce a stability criterion, in terms of the adiabatic local index, that generalizes the stability condition < ϒ >≥ 4/3 of the isotropic regime. Also, we discuss some applications of the criterion.

Wave-function collapse following a measurement process is a longstanding controversial issue of quantum physics. It introduces an element of strong non-linearity and irreversibility in an otherwise unitary and reversible dynamics. Several proposals of modification of Quantum Mechanics have been put forward in the past few decades in order to solve such a dichotomy. Among them, some approaches and explicit models considered the possible role of gravity in the wave-function collapse as a result of the incompatibility of general relativity and unitary time evolution of Quantum Mechanics. In this contribution we present some results based on one of such models, De Filippo’s Nonunitary Newtonian Gravity, which shows several appealing features: while reproducing at a macroscopic level the ordinary Newtonian interaction, it presents a mass threshold for gravitational localization. In particular, it provides a mechanism for the evolution of macroscopic coherent superpositions of states into ensembles of pure states. On one hand, we show the results of a numerical simulation of a simple system, i.e. two particles in a harmonic trap interacting via an ‘electrical’ delta-like potential and gravitational interaction. Starting from an energy eigenstate within the ordinary setting, we find that, while energy expectation remains constant, a slow net variation of the von Neumann entropy for the system as a whole takes place, with a small modulation induced on the relative entanglement entropy of the two particles. On the other hand, we explicitly show how a one-parameter generalization of the model, reproducing the nonlinear Newton-Schrödinger equation as the parameter goes to infinity, is free from any causality-violation problem for any finite value of it.

With the technology development in the cold atomic clock etc. and the gyposcope etc., many relativistic geodetic project and the plan of Atomic Gravitational wave Interferometric Sensor (AGIS) was proposed. Here we introduce one plan of spacetime structure exploration in the earth-moon system by the above mentioned thecniques, which focus on surveying the gravitational potential and gravitational first order redshift in spacetime geometry of the earth-moon system. We also discussed that apply those satellites and instrumenmts to find Geometrodynamic field moment which include gravitomagnetic clock, the possible CPT violation (Lorentz Invariance Violation) from Gravitional second order Redshift.

A covariant canonical gauge theory of gravity free from torsion is studied. Using a metric conjugate momentum and a connection conjugate momentum, which takes the form of the Riemann tensor, a gauge theory of gravity is formulated, with form-invariant Hamiltonian. By the metric conjugate momenta, a correspondence between the Affine-Palatini formalism and the metric formalism is established. For, when the dynamical gravitational Hamiltonian ${\tilde{H}}_{Dyn}$ does not depend on the metric conjugate momenta, a metric compatibility is obtained from the equation of motions, and the equations of motion correspond to the solution is the metric formalism.

The classical singularity theorems of General Relativity rely on energy conditions that are easily violated by quantum fields. Here, we provide motivation for an energy condition obeyed in semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. Using SNEC as an assumption we proceed to prove a singularity theorem. This theorem extends the Penrose singularity theorem to semiclassical gravity and has interesting applications to evaporating black holes.

We summarize the talks presented at the BH3 session (Black Holes in Alternative Theories of Gravity) of the 16th Marcel Grossmann Meeting held online on July 5-10 2021.

This is a summary of my talk at the 16th Marcel Grossmann conference, given on-line in July 2021. Various aspects of the averaging problem – the problem of finding an effective large-scale cosmological solution of the Einstein field equations, when small-scale perturbations are present — are discussed, and treated with the multiple-scales technique of singular perturbation theory. This allows one to show that a split between a background metric that varies only on large scales, and perturbations to it, is consistent, provided certain conditions are met. I finish by giving an explicit example of the backreaction of a perturbation consisting of a single small-scale mode, and point at possible future directions.

We construct conserved charges in curved backgrounds, specifically in the asymptotically AdS spacetime. As is well-known, the definition of energy in gravitating theories is a rather delicate issue. In this paper, which is a brief summary of our recent work, using the background Killing vectors, we define energy ( and angular momenta) in asymptotically AdS spacetimes that are solutions to generic higher curvature gravity models as well as Einstein's gravity.

The equations of a string inspired noncommutative gravity model on a brane are shown to admit a first integral, generalizing the five dimensional Friedman equation for the FRW Hubble parameter.

Simple one-dimensional models of blood flow are widely used in simulating the transport of blood around the human vasculature. However, the effects of gravity have only been previously examined briefly and the effects of changes in wall properties and their interaction with gravitational forces have not been investigated. Here the effects of both gravitational forces and local changes in wall stiffness on the one-dimensional flow through axisymmetric vessels are studied. The governing fluid dynamic equations are derived from the Navier-Stokes equations for an incompressible fluid and linked to a simple model of the vessel wall, derived here from an exponential stress-strain relationship. A closed form of the hyperbolic partial differential equations is found. The flow behavior is examined in both the steady state and for wave reflection at a junction between two sections of different wall stiffness. A significant change in wave reflection coefficient is found under the influence of gravity, particularly at low values of baseline non-dimensional wall stiffness.

It is shown that classical gravity coupled with quantum fields can be renormalized with a finite number of independent couplings, plus field redefinitions, without introducing higher-derivative kinetic terms in the gravitational sector, but adding vertices that couple the matter stress-tensor with the Ricci tensor. The theory predicts the violation of causality at high energies.

It is known from the modern accurate observations, surprising us greatly, that the current universe is mainly about 90 percents fulfilled with the unknown dark components: dark energy and dark matter. The most recent WMAP observations are consistent with the universe made up of 74% dark energy, 22% dark matter, and 4% ordinary matter such as baryon. The modern universe not only needs the dark components but also inflaton leading to early accelerating expansion. These unknown components of the universe may be not independent of the unified theory of all forces existing in nature. For the recent studies of the unified theory, one of most promising approaches is a superstring theory, or M-theory, considered as a quantization of fields including gravitational interaction. The cosmological implications of string theory are currently receiving considerable attention, the so-called string cosmology. This interest has been inspired in part by the recent advances that have been made towards a non– perturbative formulation of the theory. The goal of superstring cosmology is to examine the dynamical evolution in these theories and re-examine cosmological questions in the light of our new understanding of string theory such as dark energy and dark matter. String theory has a much richer set of fundamental degree of freedom, consisting of D-branes. This fundamental objects, D-branes denote non–perturbative effects of string theory as “soliton” of strings, while string theory has been only described in perturbative form. Inspired by such speculation, recently a new paradigm on the early universe has been proposed, the so-called brane-world. The existence of models with more than one brane suggests that branes may collide. Colliding branes would be a fundamental phenomena in the string cosmology. We have studied several applications of colliding branes to string cosmology.

Curvature and torsion are the two tensors characterizing a general Riemannian space–time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space–time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space–time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.

Local events are characterized by “where”, “when” and “what”. Just as (bosonic) spacetime forms the backdrop for location and time, (fermionic) property space can serve as the backdrop for the attributes of a system. With such a scenario I shall describe a scheme that is capable of unifying gravitation and the other forces of nature. The generalized metric contains the curvature of spacetime and property separately, with the gauge fields linking the bosonic and fermionic arenas. The super-Ricci scalar can then automatically yield the spacetime Lagrangian of gravitation and the Standard Model (plus a cosmological constant) upon integration over property coordinates.

We report on the latest determination of the Newtonian gravitational constant G using our atom interferometry gravity gradiometer. After a short introduction on the G measurement issue we will provide a description of the experimental method employed, followed by a discussion of the experimental results in terms of sensitivity and systematic effects. Finally, prospects for future cold atom-based experiments devoted to the measurement of this fundamental constant are reported.

Pulsar timing provides two avenues for testing the predictions and implications of the theory of general relativity. High precision timing experiments of individual systems — particularly of pulsars in binaries, but also of isolated pulsars — allow stringent tests of equivalence principles and the dynamical predictions of general relativity. They provide the strongest constraints on the majority of the parameters in the parameterized post-Newtonian formalism. Pulsar timing arrays — experiments measuring the arrival times of pulses from an ensemble of millisecond pulsars with high precision — are kiloparsecscale gravitational wave detectors sensitive to the low-frequency (nHz) emission expected from the mergers of supermassive black holes. In this paper, I will give a brief overview of both techniques and of recent results.

We discuss how the ghost free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization and obtain the effective four-dimensional action by solving the bulk configuration for given boundary metrics and substituting back the solution into the action. In the obtained effective theory, two gravitons interact through the Fierz-Pauli mass term and the radion remains as a scalar field, but its coupling to the metrics is non-trivial.