اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGeometrodynamics of spherically symmetric Lovelock gravity
255
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We derive the Hamiltonian for spherically symmetric Lovelock gravity using the geometrodynamics approach pioneered by Kuchav{r} in the context of four-dimensional general relativity. When written in terms of the areal radius, the generalized Misner-Sharp mass and their conjugate momenta, the generic Lovelock action and Hamiltonian take on precisely the same simple forms as in general relativity. This result supports the interpretation of Lovelock gravity as the natural higher-dimensional extension of general relativity. It also provides an important first step towards the study of the quantum mechanics, Hamiltonian thermodynamics and formation of generic Lovelock black holes.
قيم البحث
اقرأ أيضاً
Recently a {it local} true (completely gauge fixed) Hamiltonian for spherically symmetric collapse was derived in terms of Ashtekar variables. We show that such a local Hamiltonian follows directly from the geometrodynamics of gravity theories that o
bey a Birkhoff theorem and possess a mass function that is constant on the constraint surface in vacuum. In addition to clarifying the geometrical content, our approach has the advantage that it can be directly applied to a large class of spherically symmetric and 2D gravity theories, including $p$-th order Lovelock gravity in D dimensions. The resulting expression for the true local Hamiltonian is universal and remarkably simple in form.
A four-dimensional regularization of Lovelock-Lanczos gravity up to an arbitrary curvature order is considered. We show that Lovelock-Lanczos terms can provide a non-trivial contribution to the Einstein field equations in four dimensions, for spheric
ally symmetric and Friedmann-Lema^{i}tre-Robertson-Walker spacetimes, as well as at first order in perturbation theory around (anti) de Sitter vacua. We will discuss the cosmological and black hole solutions arising from these theories, focusing on the presence of attractors and their stability. Although curvature singularities persist for any finite number of Lovelock terms, it is shown that they disappear in the non-perturbative limit of a theory with a unique vacuum.
We present a detailed study of the spherically symmetric solutions in Lorentz breaking massive gravity. There is an undetermined function $mathcal{F}(X, w_1, w_2, w_3)$ in the action of St{u}ckelberg fields $S_{phi}=Lambda^4int{d^4xsqrt{-g}mathcal{F}
}$, which should be resolved through physical means. In the general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also play a crucial role in Lorentz breaking massive gravity. $mathcal{F}$ will satisfy the constraint equation $T_0^1=0$ from the spherically symmetric Einstein tensor $G_0^1=0$, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The St{u}ckelberg field $phi^i$ is taken as a hedgehog configuration $phi^i=phi(r)x^i/r$, whose stability is guaranteed by the topological one. Under this ans{a}tz, $T_0^1=0$ is reduced to $dmathcal{F}=0$. The functions $mathcal{F}$ for $dmathcal{F}=0$ form a commutative ring $R^{mathcal{F}}$. We obtain a general expression of solution to the functional differential equation with spherically symmetry if $mathcal{F}in R^{mathcal{F}}$. If $mathcal{F}in R^{mathcal{F}}$ and $partialmathcal{F}/partial X=0$, the functions $mathcal{F}$ form a subring $S^{mathcal{F}}subset R^{mathcal{F}}$. We show that the metric is Schwarzschild, AdS or dS if $mathcal{F}in S^{mathcal{F}}$. When $mathcal{F}in R^{mathcal{F}}$ but $mathcal{F} otin S^{mathcal{F}}$, we will obtain some new metric solutions. Using the general formula and the basic property of function ring $R^{mathcal{F}}$, we give some analytical examples and their phenomenological applications. Furthermore, we also discuss the stability of gravitational field by the analysis of Komar integral and the results of QNMs.
General relativity can be formulated equivalently with a non-Riemannian geometry that associates with an affine connection of nonzero nonmetricity $Q$ but vanishing curvature $R$ and torsion $T$. Modification based on this description of gravity
generates the $f(Q)$ gravity. In this work we explore the application of $f(Q)$ gravity to the spherically symmetric configurations. We discuss the gauge fixing and connections in this setting. We demonstrate the effects of $f(Q)$ by considering the external and internal solutions of compact stars. The external background solutions for any regular form of $f(Q)$ coincide with the corresponding solutions in general relativity, i.e., the Schwarzschild-de Sitter solution and the Reissner-Nordstrom-de Sitter solution with an electromagnetic field. For internal structure, with a simple model $f(Q)=Q+alpha Q^2$ and a polytropic equation of state, we find that a negative modification ($alpha<0$) provides support to more stellar masses while a positive one ($alpha>0$) reduces the amount of matter of the star.
In a thorough paper Kuchar has examined the canonical reduction of the most general action functional describing the geometrodynamics of the maximally extended Schwarzschild geometry. This reduction yields the true degrees of freedom for (vacuum) sph
erically symmetric general relativity. The essential technical ingredient in Kuchars analysis is a canonical transformation to a certain chart on the gravitational phase space which features the Schwarzschild mass parameter $M_{S}$, expressed in terms of what are essentially Arnowitt-Deser-Misner variables, as a canonical coordinate. In this paper we discuss the geometric interpretation of Kuchars canonical transformation in terms of the theory of quasilocal energy-momentum in general relativity given by Brown and York. We find Kuchars transformation to be a ``sphere-dependent boost to the rest frame, where the ``rest frame is defined by vanishing quasilocal momentum. Furthermore, our formalism is general enough to cover the case of (vacuum) two-dimensional dilaton gravity. Therefore, besides reviewing Kuchav{r}s original work for Schwarzschild black holes from the framework of hyperbolic geometry, we present new results concerning the canonical reduction of Witten-black-hole geometrodynamics.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
