Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneral properties and some solutions of generalized Einstein - Eddington affine gravity I
101
0
0.0
(
0
)
Authors
A. T. Filippov
Ask ChatGPT about the research
No Arabic abstract
After a brief exposition of the simplest class of affine theories of gravity in multidimensional space-times with symmetric connections, we consider the spherical and cylindrical reductions of these theories to two-dimensional dilaton-vecton gravity (DVG) field theories. The distinctive feature of these theories is the presence of a massive/tachyonic vector field (vecton) with essentially nonlinear coupling to the dilaton gravity. In the massless limit, the classical DVG theory can be exactly solved for a rather general coupling depending only on the field tensor and the dilaton. We show that the vecton field can be consistently replaced by a new effectively massive scalar field (scalaron) with an unusual coupling to dilaton gravity (DSG). Then we concentrate on considering the DVG models derived by reductions of D=3 and D=4 affine theories. In particular, we introduce the most general cylindrical reductions that are often ignored. The main subject of our study is the static solutions with horizons. We formulate the general conditions for the existence of the regular horizons and find the solutions of the static DVG/DSG near the horizons in the form of locally convergent power - series expansion. For an arbitrary regular horizon, we find a local generalization of the Szekeres - Kruskal coordinates. Finally, we consider one-dimensional integrable and nonintegrable DSG theories with one scalar. We analyze simplest models having three or two integrals of motion, respectively, and introduce the idea of a `topological portrait giving a unified qualitative description of static and cosmological solutions of some simple DSG models.
rate research
Read More
We discuss generic properties of classical and quantum theories of gravity with a scalar field which are revealed at the vicinity of the cosmological singularity. When the potential of the scalar field is exponential and unbounded from below, the general solution of the Einstein equations has quasi-isotropic asymptotics near the singularity instead of the usual anisotropic Belinskii - Khalatnikov - Lifshitz (BKL) asymptotics. Depending on the strength of scalar field potential, there exist two phases of quantum gravity with scalar field: one with essentially anisotropic behavior of field correlation functions near the cosmological singularity, and another with quasi-isotropic behavior. The ``phase transition between the two phases is interpreted as the condensation of gravitons.
We investigate the effect of massive graviton on the holographic thermalization process. Before doing this, we first find out the generalized Vaidya-AdS solutions in the de Rham-Gabadadze-Tolley (dRGT) massive gravity by directly solving the gravitational equations. Then, we study the thermodynamics of these Vaidya-AdS solutions by using the Minsner-Sharp energy and unified first law, which also shows that the massive gravity is in a thermodynamic equilibrium state. Moreover, we adopt the two-point correlation function at equal time to explore the thermalization process in the dual field theory, and to see how the graviton mass parameter affects this process from the viewpoint of AdS/CFT correspondence. Our results show that the graviton mass parameter will increase the holographic thermalization process.
We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $Pto X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/Hto X$ are treated as classical Higgs fields. Its most comprehensive example is metric-affine gauge theory on the category of natural bundles where gauge fields are general linear connections on a manifold $X$, classical Higgs fields are arbitrary pseudo-Riemannian metrics on $X$, and matter fields are spinor fields. In particular, this is the case of gauge gravitation theory.
In this work we show that Einstein gravity in four dimensions can be consistently obtained from the compactification of a generic higher curvature Lovelock theory in dimension $D=4+p$, being $pgeq1$. The compactification is performed on a direct product space $mathcal{M}_D=mathcal{M}_4timesmathcal{K}^p$, where $mathcal{K}^p$ is a Euclidean internal manifold of constant curvature. The process is carried out in such a way that no fine tuning between the coupling constants is needed. The compactification requires to dress the internal manifold with the flux of suitable $p$-forms whose field strengths are proportional to the volume form of the internal space. We explicitly compactify Einstein-Gauss-Bonnet theory from dimension six to Einstein theory in dimension four and sketch out a similar procedure for this compactification to take place starting from dimension five. Several black string/p-branes solutions are constructed, among which, a five dimensional asymptotically flat black string composed of a Schwarzschild black hole on the brane is particularly interesting. Finally, the thermodynamic of the solutions is described and we find that the consistent compactification modifies the entropy by including a constant term, which may induce a departure from the usual behavior of the Hawking-Page phase transition. New scenarios are possible in which large black holes dominate the canonical ensamble for all temperatures above the minimal value.
A new variational principle for General Relativity, based on an action functional $I/(Phi, abla)/$ involving both the metric $Phi/$ and the connection $ abla/$ as independent, emph{unconstrained/} degrees of freedom is presented. The extremals of $I/$ are seen to be pairs $/(Phi, abla)/$ in which $Phi/$ is a Ricci flat metric, and $ abla/$ is the associated Riemannian connection. An application to Kaluzas theory of interacting gravitational and electromagnetic fields is discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
