Statefinder diagnostic and stability of modified gravity consistent with holographic and agegraphic dark energy

Recently one of us derived the action of modified gravity consistent with the holographic and new-agegraphic dark energy. In this paper, we investigate the stability of the Lagrangians of the modified gravity as discussed in (Setare in Int J Mod Phys D 17:2219, 2008; Setare in Astrophys Space Sci 326:27, 2010). We also calculate the statefinder parameters which classify our dark energy model.     

Canonical quantum gravity and consistent discretizations

This paper covers some developments in canonical quantum gravity that occurred since ICGC-2000, emphasizing the recently introduced consistent discretizations of general relativity.     

Black hole uniqueness from a hidden symmetry of Einstein's gravity

A theorem is proven that the only possible exterior solution for a pseudostationary, rotating, electrovacuum black hole with nondegenerate event horizon is the Kerr-Newman solution withM ²-J²/M²-Q²>0. A special role played in the proof of this theorem by the hidden symmetry groupSU(1, 2) of Einstein's equations is established.This essay received the third award from the Gravity Research Foundation for the year 1983 [Ed.].     

Is there a unique consistent theory of quantum gravity?

Superstrings have been proposed as a quantum-theoretical framework for unifying all the fundamental forces, including gravity. We consider the question of whether there might be more general supersymmetric possibilities, based on higher extended objects such as membranes, jellies, etc. We argue that all the possible extended objects in all possible spacetime dimensions are quantummechanically inconsistent except for the 10-dimensional superstring and the 11-dimensional supermembrane. These are also the only two such theories that contain massless gravitons and, thus, that can describe gravity at low energies. It is remarkable that the range of possibilities can be narrowed down to this extent. Whether these can be further narrowed down to just one consistent theory remains open to further research.This essay received the first award from the Gravity Research Foundation for the year 1988.-Ed.     

Matter stability in modified teleparallel gravity

We study the matter stability in modified teleparallel gravity or f(T)$f(T)$ theories. We show that there is no Dolgov–Kawasaki instability in these types of modified teleparallel gravity theories. This gives for the f(T)$f(T)$ theories a great advantage over their f(R)$f(R)$ counterparts because from the stability point of view there isn?t any limit on the form of functions that can be chosen.     

Self consistent description of the interplay between shape and pairing deformations: Static properties

The competition between pairing and multipole fields is studied within the framework of a two-level model, employing different theoretical approaches. The importance of a self-consistent tretment is clearly revealed. Special attention is payed to the microscopic mechanisms that take place when the system undergoes various phase transitions.     

Quantum gravity stability of isotropy in homogeneous cosmology

It has been shown that anisotropy of homogeneous spacetime described by the general Kasner metric can be damped by quantum fluctuations coming from perturbative quantum gravity in one-loop approximation. Also, a formal argument, not limited to one-loop approximation, is put forward in favor of stability of isotropy in the exactly isotropic case.     

Non-radiative solutions of Einstein's equations for dust

The quasi-spherical collapsing space-time of Szekeres is investigated. The arbitrary functions can be chosen so that it has positive density, and no Killing vectors; yet a ballr<r ₀ of it can joined to the Schwarzschild metric, and is therefore non-radiative.     

The Buchdahl stability bound in Eddington-inspired Born-Infeld gravity

We give the Buchdahl stability bound in Eddington-inspired Born-Infeld(EiBI)gravity.We show that this bound depends on an energy condition controlled by the model parameter K.From this bound,we can constrain κ≤10~8 m~2 if a neutron star with a mass around 3 M is observed in the future.In addition,to avoid the potential pathologies in EiBI,a Hagedorn-like equation of state associated with κ at the center of a compact star is inevitable,which is similar to the Hagedorn temperature in string theory.     

Exact Solutions for Einstein's Hyperbolic Geometric Flow

In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.     

Einstein's theory of quantum radiation

The stationary probability distribution of the one-step process corresponding to Einstein's theory of absorption and emission of radiation is derived. Gauss' principle is used to identify the entropy, and the second law gives the dynamical equilibrium condition or Planck's radiation law. This condition is in disagreement with Einstein's criterion of dynamical equilibrium. The physical consequences of the new condition are investigated.     

Some properties of Einstein's equations

For the matrix Q of the characteristic determinant of the field equations, left null vectors of general form are found. Some special solutions are constructed and some of their properties investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 7–9, October, 1980.I am grateful to V. L. Bonch-Bruevich, N. S. Kardashov, and I. D. Novikov for assistance.     

Characteristic manifolds of Einstein's equations

Several classes of coordinate conditions admitting the existence of different types of waves are studied. The velocity of propagation of the latter is not necessarily equal to the fundamental velocity.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 9, pp. 99–102, September, 1981.     

On stability of a neutron star system in Palatini gravity

We formulate the generalized Tolman–Oppenheimer–Volkoff equations for the \(f(\hat{R})\) Palatini gravity in the case of static and spherical symmetric geometry. We also show that a neutron star can be a stable system independently of the form of the functional \(f(\hat{R})\).     

Equilibrium and stability of relativistic stars in extended theories of gravity

We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et al. We calculate the differential equations for the stellar structure in such theories in a very generic form i.e., the Tolman–Oppenheimer–Volkoff generalization for any ETG is introduced. Stability analysis is also investigated with special focus on the particular example of scalar–tensor gravity.