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 Emergent gravity paradigm: Recent progress

2015 ◽  
Vol 30 (03n04) ◽  
pp. 1540007 ◽  
Author(s):  
T. Padmanabhan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Large Class ◽  
Gas Dynamics ◽  
Recent Progress ◽  
Field Equations ◽  
Emergent Gravity ◽  
Gravitational Field Equations ◽  
Gravitational Theories ◽  
Thermodynamic Interpretation

Research during the last one decade or so suggests that the gravitational field equations in a large class of theories (including, but not limited to, general relativity) have the same status as the equations of, say, gas dynamics or elasticity. This paradigm provides a refreshingly different way of interpreting spacetime dynamics and highlights the fact that several features of classical gravitational theories have direct thermodynamic interpretation. I review the recent progress in this approach, achieved during the last few years.

scholarly journals WHY DOES GRAVITY IGNORE THE VACUUM ENERGY?

2006 ◽  
Vol 15 (12) ◽  
pp. 2029-2058 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Gravitational Field ◽  
Cosmological Constant ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Integration Constant ◽  
Field Equations ◽  
Physical Context ◽  
Gravitational Field Equations ◽  
Higher Order Corrections

The equations of motion for matter fields are invariant under the shift of the matter Lagrangian by a constant. Such a shift changes the energy–momentum tensor of matter by [Formula: see text]. In the conventional approach, gravity breaks this symmetry and the gravitational field equations are not invariant under such a shift of the energy–momentum tensor. We argue that until this symmetry is restored, one cannot obtain a satisfactory solution to the cosmological constant problem. We describe an alternative perspective to gravity in which the gravitational field equations are [Gab - κTab]nanb = 0 for all null vectors na. This is obviously invariant under the change [Formula: see text] and restores the symmetry under shifting the matter Lagrangian by a constant. These equations are equivalent to Gab = κTab + Cgab, where C is now an integration constant so that the role of the cosmological constant is very different in this approach. The cosmological constant now arises as an integration constant, somewhat like the mass M in the Schwarzschild metric, the value of which can be chosen depending on the physical context. These equations can be obtained from a variational principle which uses the null surfaces of space–time as local Rindler horizons and can be given a thermodynamic interpretation. This approach turns out to be quite general and can encompass even the higher order corrections to Einstein's gravity and suggests a principle to determine the form of these corrections in a systematic manner.

CLIFFORD SPACE GRAVITATIONAL FIELD EQUATIONS AND DARK ENERGY

2013 ◽  
Vol 10 (09) ◽  
pp. 1350039
Author(s):  
CARLOS CASTRO
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Gravitational Field ◽  
Variational Principle ◽  
Clifford Algebra ◽  
Algebraic Structure ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Gravitational Equations

We continue with the study of Clifford-space (C-space) gravity and analyze further the C-space generalized gravitational field equations which are obtained from a variational principle based on the generalization of the Einstein–Hilbert–Cartan action. One of the main features is that the C-space connection requires torsion in order to have consistency with the Clifford algebraic structure associated with the curved C-space basis generators. Hence no spin matter is required to induce torsion since it already exists in the vacuum. The field equations in C-spaces associated to a Clifford algebra in D dimensions are not equivalent to the ordinary gravitational equations with torsion in higher 2D dimensions. The most physically relevant conclusion, besides the presence of torsion in the vacuum, is the contribution of the higher grade metric components gμ1μ2ν1ν2, gμ1μ2μ3ν1ν2ν3,… of the C-space metric to dark energy/dark matter.

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.

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