scholarly journals Coupling of quantum gravitational field with Riemann and Ricci curvature tensors

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Gravitational Field ◽  
Harmonic Oscillator ◽  
Variational Principles ◽  
Theoretical Problem ◽  
Mathematical Framework ◽  
Variational Theory ◽  
Field Equations ◽  
Covariant Quantum ◽  
Desitter Space ◽  
Curvature Tensors

AbstractThe theoretical problem of establishing the coupling properties existing between the classical and quantum gravitational field with the Ricci and Riemann curvature tensors of General Relativity is addressed. The mathematical framework is provided by synchronous Hamilton variational principles and the validity of classical and quantum canonical Hamiltonian structures for the gravitational field dynamics. It is shown that, for the classical variational theory, manifestly-covariant Hamiltonian functions expressed by either the Ricci or Riemann tensors are both admitted, which yield the correct form of Einstein field equations. On the other hand, the corresponding realization of manifestly-covariant quantum gravity theories is not equivalent. The requirement imposed is that the Hamiltonian potential should represent a positive-definite quadratic form when performing a quadratic expansion around the equilibrium solution. This condition in fact warrants the existence of positive eigenvalues of the quantum Hamiltonian in the harmonic-oscillator representation, to be related to the graviton mass. Accordingly, it is shown that in the background of the deSitter space-time, only the Ricci tensor coupling is physically admitted. In contrast, the coupling of quantum gravitational field with the Riemann tensor generally prevents the possibility of achieving a Hamiltonian potential appropriate for the implementation of the quantum harmonic-oscillator solution.

LANCZOS–LOVELOCK–CARTAN GRAVITY FROM CLIFFORD-SPACE GEOMETRY

2013 ◽  
Vol 10 (06) ◽  
pp. 1350019 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Gravitational Field ◽  
Variational Principle ◽  
Higher Dimensions ◽  
Black Brane ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Gravitational Theories ◽  
Higher Curvature Gravity ◽  
Higher Order Corrections ◽  
Curvature Tensors

A rigorous construction of Clifford-space (C-space) gravity is presented which is compatible with the Clifford algebraic structure and permits the derivation of the expressions for the connections with torsion in C-spaces. The C-space generalized gravitational field equations are derived from a variational principle based on the extension of the Einstein–Hilbert–Cartan action. We continue by arguing how Lanczos–Lovelock–Cartan (LLC) higher curvature gravity with torsion can be embedded into gravity in C-spaces and suggest how this might also occur for extended gravitational theories based on f(R), f(Rμν), … actions, for polynomial-valued functions. In essence, the LLC curvature tensors appear as Ricci-like traces of certain components of the C-space curvatures. Torsional gravity is related to higher-order corrections of the bosonic string-effective action. In the torsionless case, black-strings and black-brane metric solutions in higher dimensions D > 4 play an important role in finding specific examples of solutions to LL gravity.

scholarly journals Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 287 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Gravitational Field ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Proper Time ◽  
Theoretical Background ◽  
Space Time ◽  
Einstein Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Covariant Quantum

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

scholarly journals Classical Variational Theory of the Cosmological Constant and Its Consistency with Quantum Prescription

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 633 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Variational Principle ◽  
Cosmological Constant ◽  
Lagrange Multiplier ◽  
Proper Time ◽  
Variational Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Covariant Quantum ◽  
Hamilton Variational Principle ◽  
Extremal Metric

The manifestly-covariant Hamiltonian structure of classical General Relativity is shown to be associated with a path-integral synchronous Hamilton variational principle for the Einstein field equations. A realization of the same variational principle in both unconstrained and constrained forms is provided. As a consequence, the cosmological constant is found to be identified with a Lagrange multiplier associated with the normalization constraint for the extremal metric tensor. In particular, it is proved that the same Lagrange multiplier identifies a 4-scalar gauge function generally dependent on an invariant proper-time parameter s. Such a result is shown to be consistent with the prediction of the cosmological constant based on the theory of manifestly-covariant quantum gravity.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

Can quantum black holes be (q, p)-fermions?

2017 ◽  
Vol 32 (15) ◽  
pp. 1750080 ◽  
Author(s):  
Emre Dil
Keyword(s):  
Black Holes ◽  
Gravitational Field ◽  
Fermi Gas ◽  
Einstein Equations ◽  
Quantum Corrections ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Entropic Gravity ◽  
Two Parameter

In this study, to investigate the very nature of quantum black holes, we try to relate three independent studies: (q, p)-deformed Fermi gas model, Verlinde’s entropic gravity proposal and Strominger’s quantum black holes obeying the deformed statistics. After summarizing Strominger’s extremal quantum black holes, we represent the thermostatistics of (q, p)-fermions to reach the deformed entropy of the (q, p)-deformed Fermi gas model. Since Strominger’s proposal claims that the quantum black holes obey deformed statistics, this motivates us to describe the statistics of quantum black holes with the (q, p)-deformed fermions. We then apply the Verlinde’s entropic gravity proposal to the entropy of the (q, p)-deformed Fermi gas model which gives the two-parameter deformed Einstein equations describing the gravitational field equations of the extremal quantum black holes obeying the deformed statistics. We finally relate the obtained results with the recent study on other modification of Einstein equations obtained from entropic quantum corrections in the literature.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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