We analyze an alternative theory of gravity characterized by metrics that are tensor density of rank(0,2)and weight-1/2.The metric compatibility condition is supposed to hold. The simplest expression for the action of gravitational field is used.Taking the metric and trace of connections as dynamical variables,the field equations in the absence of matter and other kinds of sources are derived.The solutions of these equations are obtained for the case of vacuum static spherical symmetric spacetime.The null geodesics and advance of perihelion of ellipes are discussed.We confirm a subclass of solutions is regular for r>0 and there is no event horizon while it is singular at r=0.
Static Spherically Symmetric Solutions in Nonconservative Unimodular Gravity
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Fesenkov Astrophysical Institute（费森柯夫天体物理研究所）；Al-Farabi Kazakh National University（阿里-法拉比哈萨克国立大学）；Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”（罗马大学“拉萨皮恩扎”大学物理系及ICRA）
It is shown that the one-loop effective action of unimodular gravity is the same as that of ordinary gravity, restricted to unimodular metrics. The only difference is in the treatment of the global scale degree of freedom and of the cosmological term. A constant vacuum energy does not gravitate, addressing one aspect of the cosmological constant problem.
We study the modified Reissner Nordstrom metric in the unimodular gravity. So far the spherical symmetric Einstein field equation in unimodular gravity has been studied in the absence of any source. We consider static electric and magnetic charge as source. We solve for Maxwell equations in unimodular gravitational background. We show that in unimodular gravity the electromagnetic field strength tensor is modified. We also show that the solution in unimodular gravity differs from the usual R-N metric in Einstein gravity with some corrections. We further study the thermodynamical properties of …
An effective theory of gravity in the infrared is proposed, which involves the determinant of the metric relative to the determinant of a prior metric taken to be that of Minkowski spacetime. This effective theory can be interpreted as a generalization of unimodular gravity. In a cosmological context with ultrarelativistic or cold matter, the resulting field equations have only one solution, empty Minkowski spacetime (selected by the prior metric of the theory). The introduction of energy exchange between vacuum and matter gives rise to nonstatic cosmic solutions. It is found that Minkowski sp…
We combine the unimodular gravity and mimetic gravity theories into a unified theoretical framework, which is proposed to provide a suggestive proposal for a framework that may assist in the discussion and solution search of the cosmological constant problem and of the dark matter issue. After providing the formulation of the unimodular mimetic gravity and investigating all the new features that the vacuum unimodular gravity implies, by using the underlying reconstruction method, we realize some well known cosmological evolutions, with some of these being exotic for the ordinary Einstein-Hilbe…
We reconstruct the geometrical $f(T)$ actions in the framework of unimodular $f(T)$ gravity. The unimodular $f(T)$ gravity yields stunning properties related to the generalized Friedmann equations. Indeed, it has been found that depending on the form of the Friedmann equations, the Lagrange multipliers may or not depend on the time parameter $τ$. Moreover we find that the reconstruction of $f(T)$ functions can be easily performed in general, not depending on a given scale factor, or can determine a particular way, depending on a given scale factor, in the vacuum. It is noted that the reconstru…
We review selected aspects of unimodular gravity and we discuss its viability as a solution of the old cosmological constant problem. In unimodular gravity the cosmological constant is promoted to a global degree of freedom. We highlight the importance of correctly setting up its initial data in order to achieve a resolution of the cosmological constant problem on a semi-classical level. We review recent path integral analysis of quantum aspects of unimodular gravity to note that the semi-classical findings carry over to the quantum level as well. We point out that a resolution of the problem …
A central aspect of the cosmological constant problem is to understand why vacuum energy does not gravitate. In order to account for this observation, while allowing for nontrivial dynamics of the quantum vacuum, we motivate a novel background independent theory of gravity. The theory is an extension of unimodular gravity that is described in geometric terms by means of a conformal (light-cone) structure and differential forms of degree one and two. We show that the subset of the classical field equations describing the dynamics of matter degrees of freedom and the conformal structure of space…
We propose a unimodular version of the Brans-Dicke theory designed with a constrained Lagrangian formulation. The resulting field equations are traceless. The vacuum solutions in the cosmological background reproduce the corresponding solutions of the usual Brans-Dicke theory but with a cosmological constant term. A perturbative analysis of the scalar modes is performed and stable and unstable configurations appear in contrast with the Brans-Dicke case for which only stable configurations occur. On the other hand, tensorial modes in this theory remains the same as in the traditional Brans-Dick…
Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the mos…
Unimodular time in JT gravity: a holographic clock
School of Mathematical Sciences and STAG Research Centre, University of Southampton（南安普顿大学数学科学学院和STAG研究中心）；School of Physics and Astronomy and Nottingham Centre of Gravity, University of Nottingham（诺丁汉大学物理与天文学院和诺丁汉引力中心）
Topological Static Spherically Symmetric vacuum Solutions in $\mathcal F(R,G)$ Gravity
给出了$\mathcal F (R,G)$ -修正引力中拓扑静态球对称度规运动方程的拉格朗日推导，并讨论了相应的解。特别地，我们找到了模型$\mathcal F (R,G)=R+\sqrt{G}$的一个新的拓扑解，并对黑洞解和热力学第一定律进行了分析。此外，还考虑了与电磁场的耦合，并推导出麦克斯韦解。
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure of space-time. Based on a canonical version of effective field theory, this paper provides a unified treatment, showing that modified space-time structures are generic in this setting. The special case of Euclidean gravity demonstrates agreement also with existing operator calculations.
Spherical vacuum and scalar collapse for the Starobinsky R^2 model is simulated. Obtained by considering the quantum-gravitational effects, this model would admit some cases of singularity-free cosmological spacetimes. It is found, however, that in vacuum and scalar collapse, when f' or the physical scalar field is strong enough, a black hole including a central singularity can be formed. In addition, near the central singularity, gravity dominates the repulsion from the potential, so that in some circumstances the Ricci scalar is pushed to infinity by gravity. Therefore, the semiclassical eff…
We consider the excitation of a finite-length inertial Unruh detector in the Minkowski vacuum with an adiabatic switch on of the interaction in the infinite past and a sudden switch off at finite times, and obtain the excitation probability via a numerical calculation using the expansion of the quantum field in spherical modes. We evaluate first the excitation probabilities for the final states of the field with one particle per mode, and then we sum over the modes. An interesting feature is that, despite of the inertial trajectory and of the vacuum state of the field, the multipole components…
We suggest a Lorentz non-invariant generalization of the unimodular gravity theory, which is classically equivalent to general relativity with a locally inert (devoid of local degrees of freedom) perfect fluid having an equation of state with a constant parameter $w$. For the range of $w$ near $-1$ this dark fluid can play the role of dark energy, while for $w=0$ this dark dust admits spatial inhomogeneities and can be interpreted as dark matter. We discuss possible implications of this model in the cosmological initial conditions problem. In particular, this is the extension of known microcan…
A new spherically-symmetric solution for a gravitational field is found in the conformally-unimodular metric. It is shown, that the surface of the black hole horizon in the standard Schwarzschild metric can be squeezed to a point by converting coordinates to the conformally-unimodular metric. In this new metric, there is no black hole horizon, while the naked singularity corresponds to a point massive particle. The reason for the study of this particular gauge (i.e., conformally-unimodular metric) is its relation to the vacuum energy problem. That aims to relate it to other physical phenomena …
We demonstrate how plane fronted waves with colliding wave fronts are the asymptotic limit of spherical electromagnetic and gravitational waves. In the case of the electromagnetic waves we utilize Bateman's representation of radiative solutions of Maxwell's vacuum field equations. The gravitational case involves a novel form of the radiative Robinson--Trautman solutions of Einstein's vacuum field equations.
In this paper we study properties that the vacuum must possess in the minimal extension to the teleparallel equivalent of general relativity (TEGR) where the action is supplemented with a quadratic torsion term. No assumption is made about the weakness of the quadratic term although in the weak-field regime the validity of our previously derived perturbative solution is confirmed. Regarding the exact nature of the vacuum, it is found that if the center of symmetry is to be regular, the mathematical conditions on the tetrad at the isotropy point mimic those of general relativity. With respect t…
We study the finite time singularity correspondence between the Jordan and Einstein frames for various $F(R)$ gravity theories. Particularly we investigate the ordinary pure $F(R)$ gravity case and the unimodular $F(R)$ gravity cases, in the absence of any matter fluids. In the ordinary $F(R)$ gravity cases, by using specific illustrative examples, we show that it is possible to have various correspondences of finite time singularities, and in some cases it is possible a singular cosmology in one frame might be non-singular in the other frame. In the unimodular $F(R)$ gravity case, the unimodu…
Static spherically symmetric Kundt vacuum solutions of higher-derivative gravities
Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院理论物理研究所）；Institute of Mathematics of the Czech Academy of Sciences（捷克科学院数学研究所）
