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At least 37 records · Page 2Linked to original sources
arXiv2007

A unified, purely affine theory of gravitation and electromagnetism

In the purely affine formulation of gravity, the gravitational field is represented by the symmetric part of the Ricci tensor of the affine connection. The classical electromagnetic field can be represented in this formulation by the second Ricci tensor of the connection. Such a construction is dynamically equivalent to the sourceless Einstein-Maxwell equations. We generalize this construction to the case with sources, represented by the derivative of the affine Lagrangian density with respect to the connection. We show that the Maxwell equations with sources emerge for the simplest affine Lagrangian for matter, while the Einstein and Lorentz equations arise if mass has electromagnetic origin. We also show that the Maxwell equations replace the unphysical constraint imposed by the projective invariance of purely affine Lagrangians that depend explicitly on the connection.

gr-qc↗
arXiv2007

On Conformally Kaehler, Einstein Manifolds

We prove that any compact complex surface with positive first Chern class admits an Einstein metric which is conformally related to a Kaehler metric. The key new ingredient is the existence of such a metric on the blow-up of the complex projective plane at two distinct points.

math.DG↗
arXiv2009

Nonholonomic Ricci Flows: Exact Solutions and Gravity

In a number of physically important cases, the nonholonomically (nonintegrable) constrained Ricci flows can be modelled by exact solutions of Einstein equations with nonhomogeneous (anisotropic) cosmological constants. We develop two geometric methods for constructing such solutions: The first approach applies the formalism of nonholonomic frame deformations when the gravitational evolution and field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The second approach develops a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in a class of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. We also consider nonlinear superpositions of some mentioned classes of solutions in order to construct more general integral varieties of the Ricci flow and Einstein equations depending on infinite number of parameters and three/ four coordinates on four/ five dimensional (semi) Riemannian spaces.

math-ph↗
arXiv2008

The Quantum World is an AdS_5 with the Quantum Relativity Symmetry SO(2,4)

Quantum relativity as a generalized, or rather deformed, version of Einstein relativity with a linear realization on a classical six-geometry beyond the familiar setting of space-time offer a new framework to think about the quantum space-time structure. The formulation requires two deformations to be implemented through imposing two fundamental invariants. We take them to be the independent Planck mass and Planck length. Together, they gives the quantum $\hbar$. The scheme leads to {\small \boldmath\protect SO(2,4)} as the relativity symmetry. The quantum world has an AdS$_5$ `classical' geometry, which is parallel to the "conformal universe", but not scale invariant.

gr-qc↗
arXiv2007

From semiconductors to quantum gravity: to centenary of Matvei Bronstein

Investigation of the many-body condensed-matter systems allows us to connect the microscopic physics at the atomic energy scale and the macroscopic physics emerging in the low-energy corner. It gives some hints on the mechanisms of the formation of the physical laws which our Universe obeys. The paper is devoted to the centenary of Matvei Petrovich Bronstein.

gr-qc↗
arXiv2009

The Exact Solutions to the Gravitational Contraction in Comoving Coordinate System

The gravitational collapse of a star is a warmly discussed but still puzzling problem, which not only involves the dynamics of the gases, but also the subtle coordinate transformation. In this letter, we give some more detailed investigation on this problem, and reach the results: (I). The comoving coordinate system for the stellar system is only compatible with the zero-pressure free falling particles. (II). For the free falling dust, there are three kind of solutions respectively corresponding to the oscillating, the critical and the open trajectories. The solution of Oppenheimer and Snyder is the critical case. (III). All solutions are exactly derived. There is a new kind singularity in the solution, but its origin is unclear.

gr-qc↗
arXiv2008

Withrawn paper

This paper has been withdrawn by the authors due to some fatal errors in the analysis.

gr-qc↗
arXiv2009

Problem of the time and static restriction in quantum gravity

The problem of the time is one of the open issues in the quantum gravity. This problem is particular problem in the canonical quantum gravity. Even in the loop gravity the problem of the time remain. Our work is concerning to the problem of the time. The Wheeler-DeWitt itself contains time evolution part, but which part is the time evolution part is open issue. However, we can create a method that seems to solve this problem that is up-to-down method created in the previous works. We can derive equation relating to the time and static restriction in this paper. As a example we treat the problem of the time of the Friedmann universe. And we derive the static restriction in quantum gravity.

gr-qc↗
arXiv2007

Non-relativistic limit of the Einstein equation

In particular cases of stationary and stationary axially symmetric space-time passage to non-relativistic limit of Einstein equation is completed. For this end the notions of absolute space and absolute time are introduced due to stationarity of the space-time under consideration. In this construction absolute time is defined as a function $t$ on the space-time such that $\prt_t$ is exactly the Killing vector and the space at different moments is presented by the surfaces $t=\con $. The space-time metric is expressed in terms of metric of the 3-space and two potentials one of which is exactly Newtonian gravitational potential $Φ$, another is vector potential $\vec A$ which, however, differs from vector potential known in classical electrodynamics. In the first-order approximation on $Φ/c^2$, $|\vec A|/c$ Einstein equation is reduced to a system for these functions in which left-hand sides contain Laplacian of the Newtonian potential, derivatives of the vector potential and curvature of the space and the right-hand sides do 3-dimensional stress tensor and densities of mass and energy. Subj-class: Classical Physics

gr-qc↗
arXiv2008

The Constant Mean Curvature Einstein flow and the Bel-Robinson energy

We give an extensive treatment of the Constant Mean Curvature (CMC) Einstein flow from the point of view of the Bel-Robinson energies. The article, in particular, stresses on estimates showing how the Bel-Robinson energies and the volume of the evolving states control intrinsically the flow along evolution. The treatment is for flows over compact three-manifolds of arbitrary topological type, although the form of the estimates may vary depending on the Yamabe invariant of the manifold. We end up showing well posedness of the CMC Einstein flow with H^{3} x H^{2} regularity, and proving a criteria for a flow to be a long-time flow on manifolds with non-positive Yamabe invariant in terms only of the first order Bel-Robinson energy.

gr-qc↗
arXiv2009

Black hole state counting in loop quantum gravity

Counting of microscopic states of black holes is discussed within the framework of loop quantum gravity. There are two different ways, one allowing for all spin states and the other involving only pure horizon states. The number of states with a definite value of the total spin is also found.

hep-th↗
arXiv2007

A Derivation of Einstein Gravity without the Axiom of Choice: Topology Hidden in GR

A derivation of the equations of motion of general relativity is presented that does not invoke the Axiom of Choice, but requires the explicit construction of a choice function q for continuous three-space regions. The motivation for this (seemingly academic) endeavour is to take the background independence intrinsic to Einstein gravity one step further, and to assure that both the equations of motion and the way in which those equations of motion are derived are as self-consistent as possible. That is, solutions to the equations of motion of general relativity endow a three-space region with a physical and distinguishing geometry in four-dimensional space-time. However, in order to derive these equations of motion one should first be able to choose a three-space region without having any prior knowledge of its physically appropriate geometry. The expression of this choice process requires a three-dimensional topological manifold Q, to which all considered three-space regions belong, and that generates an equation of motion whose solutions are q. These solutions relate the effects of curvature to the source term through the topology of Q and constitute Einstein gravity. Q is given by 2T^3+3S^1xS^2, and is embedded in four dimensions. This points toward a hidden topological content for general relativity, best phrased as: Q and q provide a structure for how to choose a three-space region irrespective of what geometric properties it has, while at the same time Q and q determine that only GR can endow a three-space with those geometric properties. In this sense, avoiding the Axiom of Choice allows one to gain physical insight into GR. Possible links with holography are pointed out.

gr-qc↗
arXiv2008

Remarks on Weyl geometry and quantum mechanics

A short survey of some material related to conformal general relativity (CGR), integrable Weyl geometry, and Dirac-Weyl (DW) theory is given which suggests that CGR is essentially equivalent to DW with quantum mass equivalent to conformal mass, and various actions can be reformulated in terms of the quantum potential.

gr-qc↗
arXiv2007

Emergent Universe in Brane World Scenario

A model of an emergent universe is obtained in brane world. Here the bulk energy is in the form of cosmological constant, while the brane consists of the Chaplygin gas with the modified equation of state such as $p=Aρ-B/ρ$. Initially the brane matter for the special choice $A=1/3$ may have negative or positive pressure depending on the relative magnitudes of the parameter $B$ and the cosmological constant of the bulk, while asymptotically in future the brane world approaches a $Λ$CDM model.

gr-qc↗
arXiv2007

Characteristic length of dynamical reduction models and decay of cosmological vacuum

Characteristic length of mass density resolution in dynamical reduction models is calculated utilizing energy conservation law and viable cosmological model with decreasing energy density of vacuum (dark energy density). The value found, $ \sim 10^{-5}$ cm, numerically coincides with phenomenological spatial short-length cutoff parameter introduced in the Ghirardi-Rimini-Weber model. It seems that our results support the gravity induced mechanism of dynamical reduction.

quant-ph↗
arXiv2007

Generating Minimally Coupled Einstein-Scalar Field Solutions from Vacuum Solutions with Arbitrary Cosmological Constant

This paper generalizes two previously known techniques for generating minimally coupled Einstein-scalar field solutions in 4 dimensions; the Buchdahl and Fonarev transformations. By applying this solution generation technique, minimally coupled Einstein-scalar field solutions can be generated from vacuum solutions with arbitrary cosmological constant in arbitrary dimension. The only requirement to a seed solution is that it posesses a hypersurface-orthogonal Killing vector field. The generalization that allows us to use seed solutions with arbitrary cosmological constant uncovers a new class of Einstein-scalar field solutions that has previously not been studied. We apply the new solution transformation to the (A)dS4 vacuum solution. Transforming the resulting Einstein-scalar field solution to the conformal frame, a two-parameter family of spatially finite, expanding and accelerating cosmological solutions are found that are conformally isometric to the Einstein static universe RxS^3. We study null geodesics and find that for any observer, the solution has a cosmological horizon at an angular distance of pi/2 away from the observer. We find that a subset of these solutions can be naturally interpreted as expanding cosmologies in which a scalar black hole is formed at late times. The conformally coupled scalar field satisfies the weak energy condition as long as the energy density is positive, while the strong energy condition is generally violated.

gr-qc↗