scholarly journals Renormalization of the Einstein-Hilbert action

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Andreas Gustavsson
Keyword(s):  
Hilbert Action

Universally stable black holes

2017 ◽  
Vol 26 (12) ◽  
pp. 1743024 ◽  
Author(s):  
Pablo Bueno ◽  
Pablo A. Cano
Keyword(s):  
Black Holes ◽  
Infinite Family ◽  
High Order ◽  
Schwarzschild Solution ◽  
Unitary Evolution ◽  
Thermodynamic Behavior ◽  
Hilbert Action

We argue that, when certain higher-curvature corrections are added to the four-dimensional Einstein–Hilbert action, black holes become stable below certain mass. We show this to be the case for an infinite family of ghost-free theories involving terms of arbitrarily high order in curvature. The thermodynamic behavior of the new black holes is universal for arbitrary values of the couplings, with the only exception of the Schwarzschild solution itself, which is recovered when all the couplings are set to zero. For this class of theories, the issue of non-unitary evolution is inexistent, as black holes never evaporate completely.

SOME COMMENTS ON THE DYNAMICS OF EXTENDED OBJECTS

1998 ◽  
Vol 13 (17) ◽  
pp. 2979-2990 ◽  
Author(s):  
U. KHANAL
Keyword(s):  
Wave Equation ◽  
Energy Density ◽  
Pure Shear ◽  
Equation Of Motion ◽  
Conducting Medium ◽  
Constant Density ◽  
Metric Tensor ◽  
World Volume ◽  
The World ◽  
Hilbert Action

A variational method is used to investigate the dynamics of extended objects. The stationary world volume requires the internal coordinates to propagate as free waves. Stationarity of the action which is the integral of a variable energy density over the world volume leads to the wave equation in a medium, with conductivity given by the gradient of the logarithm of reciprocal energy density, constant density corresponding to free space. The Einstein–Hilbert action for the world curvature gives an equation of motion which, in world space with the Einstein tensor proportional to the metric tensor, reduces to the free wave equation. A similar method applied to the action consisting of the surface area enclosing an incompressible world volume undergoing pure shear again yields the wave equation in a conducting medium. Simultaneous stationarity of the volume can be imposed with a stationary area only in the case of pure shear; stationary Einstein–Hilbert action can also be included and lead to an equation of motion which has a similar interpretation of the wave in the conducting medium. Some Green functions applicable to the medium with constant conductivity are also presented.

scholarly journals COSMOLOGICAL MODELS WITH VARIABLE GRAVITATIONAL AND COSMOLOGICAL CONSTANTS IN R2GRAVITY

2006 ◽  
Vol 15 (02) ◽  
pp. 189-198 ◽  
Author(s):  
P. S. DEBNATH ◽  
B. C. PAUL
Keyword(s):  
Model Building ◽  
Cosmological Models ◽  
Higher Derivative ◽  
Gravitational And Cosmological Constants ◽  
Cosmological Solutions ◽  
Cosmological Constants ◽  
The Universe ◽  
Hilbert Action

We consider the evolution of a flat Friedmann–Roberstson–Walker Universe in a higher derivative theory, including αR2terms for the Einstein–Hilbert action in the presence of variable gravitational and cosmological constants. We study the evolution of the gravitational and cosmological constants in the radiation and matter domination era of the universe. We present new cosmological solutions which are physically interesting for model building.

scholarly journals Gödel and Gödel-type solutions in the Palatini f(R,T) gravity theory

2020 ◽  
pp. 2150014
Author(s):  
J. S. Gonçalves ◽  
A. F. Santos
Keyword(s):  
Trace Formula ◽  
Arbitrary Function ◽  
Critical Radius ◽  
Energy Momentum Tensor ◽  
Gravitational Theory ◽  
Momentum Tensor ◽  
Gravity Theory ◽  
Ricci Scalar ◽  
Independent Variables ◽  
Hilbert Action

The Palatini [Formula: see text] gravity theory is considered. The standard Einstein–Hilbert action is replaced by an arbitrary function of the Ricci scalar [Formula: see text] and of the trace [Formula: see text] of the energy-momentum tensor. In the Palatini approach, the Ricci scalar is a function of the metric and the connection. These two quantities, metric and connection, are taken as independent variables. Then, it is examined whether Palatini [Formula: see text] gravity theory allows solutions in which lead to violation of causality. The Gödel and Gödel-type spacetimes are considered. In addition, a critical radius, which permits to examine limits for violation of causality, is calculated. It is shown that, for different matter contents, noncausal solutions can be avoided in this Palatini gravitational theory.

scholarly journals Building models of inflation in no-scale supergravity

2020 ◽  
pp. 2030011
Author(s):  
John Ellis ◽  
Marcos A. G. García ◽  
Natsumi Nagata ◽  
Dimitri V. Nanopoulos ◽  
Keith A. Olive ◽  
...  
Keyword(s):  
Cold Dark Matter ◽  
Planck Scale ◽  
Neutrino Masses ◽  
De Sitter ◽  
Building Models ◽  
Scale Models ◽  
Cosmological Inflation ◽  
Text Model ◽  
Hilbert Action ◽  
Scalar Perturbations

After reviewing the motivations for cosmological inflation formulated in the formalism of supersymmetry, we argue that the appropriate framework is that of no-scale supergravity. We then show how to construct within this framework inflationary models whose predictions for the tilt in the spectrum of scalar perturbations, [Formula: see text], and the ratio, [Formula: see text], of tensor and scalar perturbations coincide with those of the [Formula: see text] model of inflation proposed by Starobinsky. A more detailed study of no-scale supergravity reveals a structure that is closely related to that of [Formula: see text] modifications of the minimal Einstein–Hilbert action for general relativity, opening avenues for constructing no-scale de Sitter and anti-de Sitter models by combining pairs of Minkowski models, as well as generalizations of the original no-scale Starobinsky models of inflation. We then discuss the phenomenology of no-scale models of inflation, including inflaton decay and reheating, and then the construction of explicit scenarios based on SU(5), SO(10) and string-motivated flipped SU(5)×U(1) GUT models. The latter provides a possible model of almost everything below the Planck scale, including neutrino masses and oscillations, the cosmological baryon asymmetry and cold dark matter, as well as [Formula: see text] and [Formula: see text].

scholarly journals Scale-invariance, dynamically induced Planck scale and inflation in the Palatini formulation

2021 ◽  
Vol 2105 (1) ◽  
pp. 012005
Author(s):  
Ioannis D. Gialamas ◽  
Alexandros Karam ◽  
Thomas D. Pappas ◽  
Antonio Racioppi ◽  
Vassilis C. Spanos
Keyword(s):  
Scale Invariance ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Scalar Fields ◽  
Scale Invariant ◽  
Expectation Value ◽  
Hilbert Action

Abstract We present two scale invariant models of inflation in which the addition of quadratic in curvature terms in the usual Einstein-Hilbert action, in the context of Palatini formulation of gravity, manages to reduce the value of the tensor-to-scalar ratio. In both models the Planck scale is dynamically generated via the vacuum expectation value of the scalar fields.

scholarly journals QUANTUM CORRECTIONS TO GRAVITY AND THEIR IMPLICATIONS FOR COSMOLOGY AND ASTROPHYSICS

2012 ◽  
Vol 14 ◽  
pp. 73-87 ◽  
Author(s):  
JULIO C. FABRIS ◽  
PAULO L. C. DE OLIVEIRA ◽  
DAVI C. RODRIGUES ◽  
ALAN M. VELASQUEZ-TORIBIO ◽  
ILYA L. SHAPIRO
Keyword(s):  
Cosmological Constant ◽  
Free Parameter ◽  
Quantum Correction ◽  
Functional Form ◽  
Quantum Corrections ◽  
Inflationary Cosmology ◽  
Gravitational Action ◽  
Higher Derivative ◽  
Hilbert Action

The quantum contributions to the gravitational action are relatively easy to calculate in the higher derivative sector of the theory. However, the applications to the post-inflationary cosmology and astrophysics require the corrections to the Einstein-Hilbert action and to the cosmological constant, and those we can not derive yet in a consistent and safe way. At the same time, if we assume that these quantum terms are covariant and that they have relevant magnitude, their functional form can be defined up to a single free parameter, which can be defined on the phenomenological basis. It turns out that the quantum correction may lead, in principle, to surprisingly strong and interesting effects in astrophysics and cosmology .

The Einstein field equations

2019 ◽  
pp. 52-58
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Newtonian Gravity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Noether’S Theorem ◽  
Geodesic Deviation ◽  
Fundamental Equations ◽  
Hilbert Action ◽  
Qualitative Discussion

The Einstein field equations are the fundamental equations of general relativity. After a brief qualitative discussion of geodesic deviation and Newtonian gravity, this chapter derives the field equations from the Einstein-Hilbert action. The chapter contains a derivation of Noether’s theorem and the consequent conservation laws, and a brief discussion of generalizations of the Einstein-Hilbert action.

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